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MICROCOPY RESOLUTION TEST CHART
MICROCOPY RESOLUTION TEST CHART
NATIONAL BUREAU OF STANOAROS-1963·A
NATIONAL BUReAU Of STANDARDS-1963-A
..
.
1'eclmical Bulle/in No. 929 . October 1946
•
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."i'~~'."'."i\,siAT~.~J
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DEPA.BTMEN.'l';'~OF AGOICUL'JURE .'
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Passage of Liquids, Vapors, and Dissolved
Materials Through Softwoods 1
By
ALFRED
.
.r. S'I'AMM,2 prindpal chemist, Forest Proilucis [,aboraiory,3 Forest Service
CONTENTS
!'ngl'
Introduetion ___ .. ~~_._._ ._-.
2 Appendix-Continued
Fiber length __ ... __ • _____ _
58
2
Capillnry structure of softwoods_
59
Effective fiber-cavity length_
2
Woodfibers. ___
---{)
Average number of fiber
llesin c1ucts___ ­
Wood rays ____ _
cavities and walls in series
7
per unit distance in long­
7
Bordered pits_
59
itudinal rlirectiolL. .
'l'rnnSil'llt; cell-wall capil­
Average
number of fibers per
lari!,), __
7
unit distance in the radial
Structure through which passage
59
and tan~cntial directiolls_
occurs ________ - -' _ _. - .. - -.
8
Frnctional voiel cross scction
9
Diffusion calculations
.. ,
60
of the fiber cavities
Diffusion of a solute into Average cross-sectional area
water-satumted he a t­
61
of fibers and fiber cavities_
wood ___ •
. -- ... - ..
14
Average mdius of fiber cav­
Diffusion of solutes into
ities and thickness of
heartwood saturated with
doublc cell walls and pit
19
a nonswellin~ solvent
61
mcmbranes..
19
Drying of heartwood
Fractional nrea of walls of
Pressure permeability ealculn­
62
fibers covered with pits.
41
tions.__
....
Averago mdius of perman­
Systems free from gas-liquid
63
41
ent pit-membmne pores_
menisci. __ _
Systems contllining gas-liq­
Effective fractional cross see­
43
'\lid menisci. .
. ..
tion of permanent pit­
membmnc pores_____ ..
48
66
Treating processl's.__ ... - . -.
51
SUlluunry _____ .
. .. -. - . -Uadius of transient cell-wall
52
Litcmturc citccL.
.. -"" -- .-­
capillaries effective for
Appendix: Compilation of phy­
68
flow _ __
_.. - ..... -- -- ...
sical and struct.urnl data used
Effective fractional crO::lS sec­
56
in ealculations_._ .
tion of transient cell-wall
56
Fiber-satumtion point. _ - -­
71
cn pillaries __ .. _" _.. _-- .... Specific gravity of wood and
Symbols and cquations ____ _
75
57
of wood substnncc __ ....
Symbols__________ ., ___ • __
75
Comprellsion of adsorbed
Equations ... __ ... ______ .. - ..
78
58
water .... _... - - - .. - - - .. " -.
I Submitted for publication March 5, 1946.
Prepared in 1940; publication
deferred because of war activities.
2 Acknowledgment is made to L. F. Hawley, formerly Principe,1 Chemist,
Forest, Products Laboratory. whose interest in the fundamentals of the movement
of liquids, vapors, and dissolved materials through wood has served as a stimulus
for collecting the material givt'll in this publication and WhOSl! assist,ance in the
critical analysis of the subject has materially aided in the correlation of the
•
•
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fin.ding~.
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.
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mversl't yo f "'.
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7145.16°-47-1
1
2
'l'ECl:L.N"ICAL BULLE'l'IN 929, U, S, DEPT, OF AGlUCUL'l'URE
INTRODUCTION
An understanding of the nature of the various capillary components
of wood and the C-'ctent to which each is effective in controlling the
passage of liquids, vapors, and dissolved matet'ials through wood
under different treating conditions should be of major importance in
tlle fur,ther dovolopmt·nt of the procl'SS(,S for the seasoning of wood,
tho p(1l1otro,tion of chips with cheynicals in pUlping, and the penetration
of wood with pl'eServlltives, fh'e retardants, and antishrink chemicals,
Wood is made Up of (Ufl'crent t'\1)CS of capillaries varying in size
from structUl'es visiblt' to the 2Ulhd eye down to cnpillaries thnt
approach moll'culnt, dim(,llsions, These are intrieatdy combined in
sel'ips in (,och individual pnth through the wood and mnny such single
sel'i!'s pntils arc combinNI in pat'allel throughout the toinl structure,
'1'he way in which eltch of tll('se capillary structures I'('sponds to the
passage of mott'rioJs varies not only with tho structul'e but also with
tho IllttUl'e of the driving force, It is thus essentinl to consider
separnt('ly eneh kind of dl'iving fot'ce and its relationship to structw'e
in l')rder to calculate th<} extent of passage of matcrinls thl'Ough wood,
nnd to detel'nline the s;,tucllll'(, chidly r('sponsible for controlling this
pnssng(',
'I'll(' PUl'pos(' of this publication is. to nssemblo the necessary cnpil­
Inry-stJ'uctmal datn and to pres('nt approximate calculntions covering
the differl'l\c('s in the structuJ'(' efl'ective fOl' thO' passnge of liquids"
vnpors, nnd solutes t1u'ough wood und('I' the motivating forces of
diffusion nnd PI'('S3me pel'lneability, The annlysis is confined to the
softwoods (conif('l'Ous, 01' llN'dIe-lenn·d species) because sufficient
cnpillnl'Y dnt.a nn' not nvnilabl(, for the more complex hnrdwoods
(deciduous or broadl('nYcd species),
•
•
CAPILLARY STRUCTURE OF SOFTWOODS
WOOD FIBERS
'rhe fibers, or longitudinal trncheids, which form the bulk oithe wood
strudUl'P of softwoods, are hollow tubes closed at both ends that
('xt('nd i.n the verticni dU'('ction in the tree, They are shown in a
thn'l'-din1l'llsional sketch (fig, 1) nnd 0:.1'1,' d('signated by the lettel's tr,
'I'll('), urc nlso shown in the photomicrogruphs (figs, 2, 3, and 4) of
shortll'nf pine secJions cut in each of the thl'ce major structul'lll
dil'(~ctions, which al'c at right angles to each other, Figure 2, a trnns­
verse section of the tree, shows the fib('rs, tr, in cross section. Figure
3, n rndinl section cut in a pInne through the center of the tree, nnd
figUl'e 4, n tangeotiul section cut in a planc tangent to the growth rings
of the tn'e, show 1111e fibers, tr, in the longitudinal direction, The
fib('rs al'e laid down in quite ('egular rows in the radial direction (fig, I,
rr), This regultu'ity is iIlustrnted more elenrly in the transverse
section (fig, 2),
Fib(·J'S vary considernbly in width in the rndial direction, depending
on th(' part of the gro"'ing senson in which they were formed, The
springwood fib('J'S (fig, l, 81) have relativ('ly thin wnlIs and lnrge cavi­
ties, ",he'I'Nls the sunm1l'l'wood fib('rs, 8m, which are laid' down Inter
in the growing senson, have thicker walls and smaller fibcr caviti('s,
•
PASSAGE OF LIQUIDS, VAPORS, ETC" TH.HOUGH SOFTWOODS
•
3
Springwood and sutnmerwood of a single growing season make up the
annual ring (fig, I, ar), The fiber width ics uniform in the tang('lltial
din'ctiol1, tt, for etl('h radial row of fibl'l"S but app('lu"s to ValY npp:'eci­
ably from row to row, This is lnrgdy a<"collllted for by th(J filet that
•
MI7010F
I.-Magnified three-dimensional sketch of a softwood: U. End surface;
til. tangential. surface; rr, rndial SI/,rfacc; IT, trnchcids, or fibl'fS; 1I1T, wood ray;
/1I1r. fusiform wood my; vTd, yerUeal resin duct; Imi, horizontal resin duct; 8P,
spring wood ; Sill, Slllllm('rWlIod; (iT, 1\I111ua1 ring,
FIOURE
•
the fiben1 nre taperl'd tnng('Iltially nenr their ('neis and the ends o~cur
at about tht' same it'yel in ('n('h rndinl row of trnchei<is.
Fiber arrnngenll.'nt is shown mOl'e clelldy in the rndial section of
figure 3 wh(>1'<,' pl"lleticnlly nIl tht' fibl~l"s end tWIt\" the wood my Inter
d.escribC'd, The rndinl rows of nppnn1ntly nnlTOW fibC'l"s shown in
cross section in figures 1 and 2 nppeur narrow becllusc the cross­
4
TECHNICAL Bt:I.LETIN 020, 1!. S. DEPT. OF AGRICULTURE
sedionni pinno cuts tl1<'se pllI-ticuhu' fibers neor their C'nds. In the
tlln~('ntilll (\ireetion (fig. 4) tlwl'C' is no suell l'('gularity of til(' position
of the fib('l' ends, In working with onlil1nry-sized pieces of wood, a
PC'l·f('('{.ly mndom distribution of the position of fibe!' ('nds enn bi~
•
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TIINCEHT{IIL DIRECt/ON
M3B689F
PIGt'RE 2.-Trnns\'l'rsc Sl'ction of shortlenf pine: tr, Trnclll'iC\s, or fibers; lOr,
wood mys; IIp, bordl'rl'.r} pits: vrel, YNticllL rl'.siJr duct. Magnification about 154 X.
assumed. The number of fibN'S terminnting in It d('finite-sized trn.'lS­
st'l'tion of wood of fixed thiekuess is very uniform fOl' different
pllrts of til(' \\~ood (87, 88).4
yel'S~'
IltULic llulI1bers in parentheses refer to Literature Cited, i). 52,
•
PASSAGE} Ob~ LIQUIDS, VAPORS, E'l'C., THHOUGH SOF'l'WOOD:;'
5
•
•
RA[)IAL OIRECTlON
•
M_ Fwt!!n: 3.- Hmlial lO('cHolI of shortlcnf pint:': tr, Trtlcll(~ids, or fibers; wr, wood
r!\y; bp, bordered pit.
l\lngnificntioll about 221 X.
6
'l'E('HNIC'AL BliLU~TIN 020., U. S. DEP't'. OF AGmCUVl'UHE
RESIN DUCTS
Some softwoods ('ontain V('rti('al resin du('ts (figs. 1 flI1d 2, t'rd)
thut haYQ It largl'l' diallwt('l' thun tho fibpI'S, or longitudinnl trucheids.
Tht'st' I11UY in sonw ('usps be visible to tht' lIulu'd lTC', but tlll'ir (·fI'(,c­
•
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TI1NGENTIIIL DIRECTION
M38688F
4,-'rungentiul seelioll of shortlenf pine: lr, Tmcheids, or fibers; wr, wood
my;;,: lip, bord('l'ed pits; Iml, horizullt.nl resin dueL; fwr, fusiform wood my
l\lngnificntion ubout 154 X.
FIOl"ltE
tiY('Ilt'SS ill OlP pns~ugp of liquids and gases is often smull b(lcuuse they
uri' doggl'd with I'('sin 01' stl'll('tlll'lllly tl'I'minatpd, In gl'nl'I'ul, the
pnssugt' 'of Iiq uids undl'r pressllrc tlirollgh softwoods contuining longi­
•
PASSAGE QIt' LIQUIDS, VAPOHS, ETC" THHOUGH SOF'rWOODS
•
7
tudinal resin ducts and. thosc lacking th('m docs not difTer appI'l~ciably
(11,32,37,38), Fo!' this reason thl' pl'l'IlH'ability efT('ds of resin ducts
will not be considered in the cl),I('ulntions des{'l'ibl'd in this pUblication,
'VOOI) RAYS
Although tho dlid fibcl' strUellll'(' of wood ('xtpnc\s in the longitu­
dinnl dil'o('tion, 0101'(\ ar(> somp gl'onps of {'ells t'xtl'IHling in n mdinl
dh'('('tion ill tlw tr<'t' tl'lmk, IH'I'I)(,lIdklllal' to tlH' fibpI's nnd nl'l'OSS tho
annllnl rings, hnving n void VOillll1l' of ouly 1 to 2 I><'I'eput of t\tt' total
void yoluu\(' of the wood (37, 38), Thl'sP ('('II gl'OUI)"; RI'l' known ns
wood l'I\ys nnd,al'l' dl'signllt(,d by thl' I(,t(prs '1('1' ill figlll'(,s 1 to 4, Tlu,'y
al'{' fltirly ('out1I11101lS in l'xtPlIt, but hllV(\ ('I'oss-wIIII ml'lllbl'nnl.'S whieh
I'pdll('(\ their cnpillary It,n'pe{,iv('IH'sS, Some woods contllin mOl'r eom­
plt'x I'ny-epll systl'lns in whid, hOl'iwntnl l'<'sin duets (fig, 4, hrcl) 111'('
bord(,I'l'd by a Il('terogl'lH'OIlS SyMl'1ll of I'ay ('('lis, knowu eolll'etivl'ly
as fllsifOl'rn wood mys (figs, 1 and 4, .f101') , Hlllf-bol'lIPI,t'd pits com­
munieat(' lwtW('('1l tit(' I'ny N'lls alld tlH' tmclu'ids,
.
Tn gl'I1('I'al, thl' rays, in otht'r thnn thl' thil1llt'st taugl'ntial scctions,
have b{'('n shown by pl'essun' lWl'lllenbility lind cnpillnrity n\('n~IlI'e­
men\;.<; (11, 37, 38) to contl'ibul(' only slightly to till' pnssng(' of mnt('­
rinls into 01' thl'Ollgh wooel, l~xt('nsiYl' studi{'s of thr PI'CSSlll'C tl'ent­
l1I('nt of wood wit,1t PI'('sPI'vl\.tivl's huyl' shown thnt tlH' L'n:ys nn',
npPI'l'l'inbly ('fl'('din' only in t.lH' tl'l'ntnH'nt or SOil I(' sPP(,lI'S of pine
(2m, n ('lI(,l' the l'ny'S will nlso be ignolwl in the caleulu tions here
dis('ussl'd,
•
BOlIl>~:HEI) PITS
Alt hough wood fibl'I'S,
01' tl'nehl'ids. nr(' dORt'l1 n,t both ('nds, com
(\o('s O('('llI' fl'Om fibr(' ellvity to fibcl' <lltvity through the
bOl'dpI'('d pits, '1'II('S(' nl'(' unlhiek('IlNI points of the a<ijnc(,lIt. ('dl
wnlls spnnnpd by n thin nH'mbl'UIH" n continuntion of the midrll('­
lanwllll bptw(,l'n th(' fibrl's, TIll'sl' bol'(\(,I'(,c\ pit.s npP(,flI' ns cone{'lltric
disks with 11 dfll'kpnpd (,pnh'I'in figut'l, 3 nnd ns ('hnins of bends ulong
tht' £ibN' \\'nlls in figul'l' 4, Thl' pit ('hnIlli)l'r, bl'tw('ell tIll' pit orifice
and thl' pit IllNnbl;lIn(', in(,l'ensl's in dinIllctt'r from the orifiee to the
Ill('mbl'alll' nbout thn,(,fold to fourfold,
Thl.'l'l' nl'(' npPl'oximntrly 50 to 300 pits pl'r fibcr, These pits are
('Olle('11t I'ntl'd dtil'fly on tlw ..nllinl fn('{'s nnd in the ov('rlnp part of the
('nels of thl' fiI)('I'S, Thl' pit nll'IIlI.H'lIneS hnye n. Cl'ntt'al thi('kl'ned por­
tion, eull('{l thl' torus, wbkh is oft('11 puslH'd against the cdl-wall
opt'ning nnd possibly s('alcd ill this position with rcsillollS material so
thnt tlH'il' eO'petivl'nl'SS to till' pnssuge of mll,tl'rinls is con~iderably
r('du('{'d (2,3, 18, 19), Sueh pits IlI'C known ns nspimt('d pits, Per­
IllfllH'nt pl'rfol'lltions 01' POI'{'S oel'ur in tlH' pnl't of the pit m('mb1'l1nes
surrounding tllt' tOl'US, Th('sl' nl'l' gcn(,1'Illly su bmiel'oscopic in size,
but ImelPI' (,(,I'lnin ('onditions dll'('ks ueross the membranes (2, 3),
whkh Illlltl'1'illlly il1('r('llSe their efT('div{\ness, are. microscopically
visible,
111 unkntion
•
TUANSIENT CELL-WALL CAPILLAUITY
There is also a trnnsi('nt enpilhu'y structul'l' c,dsting in the cell
walls wll('n tll(\Y IH(, in th(\ swollell ('ondition, The ('l,ll wnlls are
made up of bundles ofthrcndlik~ units known as fibrils that incline
8
~L'ECHNICAL BULLE'l'IN 020, U, S, DEPT, OF AGRICUL'l'URE
more or l('ss to the fib(\!' dir(wtion with an outN'laym' at l'ight nnglos to
the fiblW nxis (33,34-), 'rho fibl'ils aro mndo up of still smnllN' spindlo­
shnped pltl,tidos known ns fusifol'm bodies (33, 34-), These, ill. turn,
8.re made up of bundles of thl'endlike molecules known ns micelles or
crystnUilcs (4-6),
X-my meltsurements hnvo shown that ndsorption of water by
cellulose fibers tnkcs pln,cc bl\tw('(~n th<.' mirdll's bu t. not within the
mieelles (22, 23, 24), 1'he capillltl'Y struduI'e of tlH'. cell witH wiI!
thus consist of tlw intermiedlnl' volume thnt is oC(~\lpi('d by tho swelling
m('diulll, "~hen. this int.l'l'llliel'llnr yolume is It lllltxitnulll, tho wood
is said to be nt the fiber-snlumtioll point with respect to t.he swelling
medium,
'l'}u. fine ('(,ll-wltll cnpillal'y stl'lletUl'I.' exists ollly ItS n result of sw{.lling
nnd ('I\n only be efl\'divc, to tlH' passage of liquids 01' solutions whieh
enllSt' swplling, '1'0 l'1llphnsi~(' this fuet tI\{' ('{,U-wll.ll ('npillndt's will
be dl'siglllttl'd ItS tl'lIllsit'nt l'lIpillnl'i('s, 'I'I\(' ('dl walls nl'n illllwl'moltble
to hydl'oclu'bons, whidl ('IlUSt' no s\n'lling, bu t nn' IWI'lIlen.ble to wnter­
solublt' tt'l'u.lin~ llUtL(:I:inls lind pulpin~~<!,'Ill'll~i(,lIl~ which e!\.\ISO swelling,
EVI.'n though till.' mdll of th(~Sl' edl-wllll ('ltpllln.nes n.ppI'ondt moleeulnr
siz(', thl'y m'e lllHlu('stionubly l'fi'pdh'l' in Lhe dill'usion of nqueous
solut('s Imvin(? l'l'httiydy small molc('ales, '1'he nuthol' hns shown
thnt wnh'I'-s01uhll' inol'gltnic snIt solutions n,tt.nin a ('oncen.tl'lttiou
within til(' ('pll Willi yit,tunlly ('qull,l to lli(' extel'lllll eoneentmtion (43),
Pl't'lll(~Hbility of th(' int('I'lIli('dlal~ ,'olullle to solutes is fll1'thcr illus­
trllt('d by til(' t'('SI.'Itl'e!ws of FI'py-W'yssling (13,14-,15) who procipitlttod
sih'N' erystllls from solu tion within the intel'mieclllll' volume Itnd
studil'd (Ill' Ilt'I'n.ngl'llwnt of lhe erystnls by llH'lI,nS of X-my technique,
Bnil('y (4) has 11150 suecccded in fonning iodine cl'ystltls within the
int(\l'mie('llnl' volume,
•
•
STRUCTURE THROUGH WHICH PASSAGE OCCURS
Spl'eWe infol'lllntion on the diull'llsions of thn diffel'('ut cn:pillnry
cQmpoll('nts is pss('ntinl fOl' l he d('sired (l!tleuJn.tions on the pn.ssngc of
mntl'I'ill.ls tlll'ough softwoods, Although some of these wood proper­
tit's \'nl'Y bu t sligh tly fl'om spt'l'jes to sp(l('ies, others Vll.l'y apprecinbly,
~lethods thtlt rive statist il'nl n\'{'t'ngl~ vnlta's din'etly have been used
itS fnl'. ItS possiL>ll\ in milking the vnl'ious structural mCltsurements of
vltrinbll' Pl'OIWI'til'S in Ol'dl' I' to minimize Cl't'OI'S dllo to stl'llCtural
vat'inlions, In ellscs where the dlltn al'e· nVllilabll', the !wernge valuo
fOl' the propl'l'ties obtnilU'd from mensnrements mnde on the hClll't­
wood of snYl'l'Ill diff('I'('nt softwood spceies will be used, Effect of
possible YlIl'in,tions in tIlt' stru('tul1l1 PI'OIwI,ties on diffusion nlld
Pl'l'SSl\t'I.' perlllNlbili ty will n,lso be considered,
'
I~noring the l)l'l'IlH~nbili t,r eli'pets of resin duet n.nd wood-ray
cnpilltu'ity, whieh is essl'l1till1 in order to make the following cnlcula­
tions, thl' pn,ssnO'l~ of a mntl.'rinl thl'Ough wood in nny of the three
major stJ'ueturll'f dil,('etions consists of It pnssnge through fiber cnvities
in seril's with pit eluunbN'S and pit IllCmimtlll'S, with mnny of the
chamb('I'S Ilnd membl'lIlH'S in pnrnllcl with t,he transient ccll-wltll
cnpillj~ri('s, In plll'll11p\ with this ('ombiuNl path thl'I'c mny a.lso be n
continuous path tl\l:ou~h tilt' t1'ltllsil'nt ('dl-wllll en.pilln.l'ies, This eOffi­
binntion of series aml pnmllcl cnpillnry pnths in softwoods is shown
•
PASSAGE OF LIQUIDS, VAPORS, ETC" THHOUGH SOF'l'WOODS
•
•
9
dingmmmf.tLienUy in tho sketch of n tnl1gentiltl seetion of softwood
(fig, 5), Itud in tho sketch of n trltnsv(,l"Se section of softwood (fig, 6),
in whieh n1i white nr('tl, l'(\prescnts citpilltuies, :Fibel' length itS shown
in fi~ll1'e 5, hns been foreshortened for convenienee, Tho micelles
mnklllg up tho cdl WI1US M'O not ill reality sepnmte units' completely
envdoped by wtttm' itS tho dingmms suggest, but Itl'l} connected n'r,
vndous points nlol1" their length with the ndjueent micelles (1),
Tho swollen cell wnirs thus consist of continuous thrcndliko networks
with swdling mcdit(IIl bctWl)on them (1),
FouL' speclfic llleltSlll"l'lllcn ts of the Cl1pillnrv propt'i"ties of elteh type
of cnpillnl'y Sll'lIl'LUI".' lU"e needed for the ci~lcllh~tions, nnmcly, the
nVl'I'ngo (1Il'eeti\'o cnpillnl'Y length, the Iltllnbl'I' of sueh c!\pillal'Y lengths
trll.Vel'st.d pl'!' unit distullce, the tWl'!'nge l'O'eeti\To cnpillnry m(lius, !l,nd
tIl(' drectiyo cltpillal'Y el'OSS section of tht' Hbl'I' cavities, pit chambers,
M32498F
5.-Dil\grnrnmatic sketch of a swollen tangential section of 1\ soft,wood,
illust.rating Ow cornpiex sNies and parallel COlli bination of fiber clwities, pit
chambers, pit-membrane pores, I\nd trullsient. cell-wall capillaries,
FlOUltB
pit-llll'mlmuw po I'('S, ttnd tmnsi(~nt {'\·ll-wnll cnpillltries in both the
101l~itlldil1al und trn.nsYel'se din~ctions, These dntn, togl'tlll'r with
oUWt' infol'lllntiol1 1'l'qllirNI in the ('n.k-ulntions, nn' nssembled in tn.ble 1.
TIlt' tnlUlIIl'I' in whidl sonw oJ tlH's!' ('n.pillnry dinwnsions were obtuinecl
is mUu.'I' inyolyed. li'OI' lhis I'(·n.son the diseussion of the metlsurell1('nts
nnd enieulntions mild" in obtniliing Yfl,hll~s given in tubIe 1. urI.' ~h'en
in the App(·lHlix,. AILholl"h th(·y Ilrt' of impol'tnnce to nnyonc desIrous
of gnining n. complete uncll·rstnnding of the subject, tllt'Y nrc of minor
impOt'tnnt'l' to those who l\I'l' ml'l'(·ly inll'I'('stNI in gnining n. genernl
COlWl'pt of lho wny in which mnterials pnss through wood or in using
the conclusions,
DIFFUSION CALCULATIONS
•
The ph('nomenol1 of difrusion, the spontaneous equalization of con­
centl'ntion, is I\nnlogous to the conduction of I\n elecLric current, The
rn.tc of difrusion COI'l'('sponcls to the rIlte of flow of electric cUlT('nt,
nnd tllt' ('ol1cl'ntrnlion grndient corresponds to the potential drop,
The. elN'tri<: ('urn'nt flowing through n. conductor in unit tilTie und('r
n dl'Hnil!' (·ketI'iClll potcntilLl yn.ries directly ns th(~ cross section of the
conductor nnd inYcl'scly nsiLs length, 'Vhell a number of conductors
7l4550°-47-2
10
'l'ECHNICAL BULLE'!:IN 029, U. S. DEP'l'. OF AGlUCUUl'URE
•
+
~
I'J
f
1:
t..
C'\.J
*E t
~
+
•
M38S71F
FIGURE 5.-Diagrammatic sketch of a swollen transverse section of a softwood,
illll>!trating the complex series and parallel combinatioll of fiber cavities, pit
chambers, pit-membralle poret', and transient cell-wall capillaries. (For
significance of symbols, see table 1.)
•
PASSAGE OF LIQUIDS) VAPORS, ETC,) THROUGH SOF'l'WOODS
•
11
arc cOlllwded in pltl'Il11('I, the clUT('n. t flowing t1Il'ough the combined
SYSt(llll is t1w slim of the ('IIITl'nt (lowing tlll'ough cach of the separntc
condudol'S, Wlwn It 1111Illb('r of conductol's Ilol'{\ connected hi scries,
the l'l'cipI'O('al of tho totul ('urn'nt flowing through the systcm is equal
to tlw SUIll of tho reciprocals of the current flow throu~h cach indi­
vidual eOllcluctol' WhNl tested I\lone. DiHusion througll a complex
enpill,!tI'Y SyStl'lll Cfin thus be culculuted, using these basic electrical
prllH'lples,
Pnssngc of u Illltt<.'riul thl'ough wood under difi'usion conditions is
cnlculntcd by combining tho l'l.ltttive mtes of difl'usion through the
vnl'ious ('npillltl,y compo nell ts of the wood in their sm'ies nnd pn.rnllel
I
FlUIl C'.:;A~Y.:..:n~~/.:.ES=-- _ _ __
A/7/ OR I
P£RMAN!NT PIT­
M!M8RAN! PORES i:- Of?.f..
p
p
PITCHAMlJUS
~
•
I
-
m
TI?M.sIENT PIT­
M!MlJI?IINE POKE:}
'lm
7p
REPEAT l,5 x PER etn, FOR LONGIT(JP/NAL PASSAGE
JOO x PER etn, FOR TlMNSVE/?SE PASSAGE
CELL-WALL CAPILLARITY
CONTlN(JO(JS CELL - WAL"t. CAPILLIIRITY
~---------------------~~~~~~~~~~~~~~-----------------.+.
(I-II",) ~ OR ./'" nt S,
.Floolu~
7.-Diagrnll\ of the series and parallel combined passages through soft­
woods per unit dilltllllce, The ratios are for the effective cross-sectional area
divided 1)\' the length. Whell two values are given, the first is for longitudinal
pnssnge nild the second for trnllsver::;e passage, Whell one value is given, the
pnSsnge is the sallle in both directions,
•
combinntions, using the analogy between electrical conductivity and
diffusion, 'I'hl.' diffusion of n. solute through n block of swollen wood
(fig, 7), will depend upon the diffusion through thefibcl' cavities in
sel'il.'s with til(' dW'usioll through the pit cbnmbers and the pit-mem­
bmne ('npillurics, with mnnyof the two luttel' kinds of cnpilln.ries in
pl1. 1'n.11 <.'1 with the tmnsient cell-wall capillal'ies, The pit-membrane
cnpillnril's Il.l'l' mnde up of pel'mnneut pit-membmne pores and tmn­
si('nt ('npilllu'ics, Cllus('d by swelling, thnt are conncctl'd in pnrnllel.
This ('Olllph'x combinll.tion of series Il.nd pll.t:nllel pnssngcs will be in
pn.rnllcl with n continuous diffusion through tho cell walls,
12
'rECHNICAL BULLETIN 929, U, S, DEP1'. OF AGRICULTURE
In cait'ulntillg thl' longitudinal difl'usion through a swollen block. of
wood of ',mit It'ngth and cross SCCtiO!l, the following fOl'muht is used:
(1)
•
llnd in cnleuhtting tl'tHlS\'(I!'se difl'usloll, the formuln:
(2)
In
thNle ('qulltions Do r('pl't's(,I1ts the nOt'mal diffusion constant of tho
$o\ut(' PN' unit, din1t'llsions of til(' bulk difl'usion mediulll; D, the
difl'usioll constant l'fl'('dive in the compll,tely wator-filled wood in the
longitudinn.l <Iil'pction pm' unit diuwllsions of wood; and D, the COl'­
l'l'spondillg vn.1ue for the tl'n.nSyel'Se difl'usioi.l; the other symbols have
thl' SigIlifi('I\l1('l~ shown in table 1. The first term inside the paren­
tlH'ses'in each of tho eqlllttions l'epl'est'nts the serit's and pa1'!1llcl
difl'usioll tlu'ough the system of .fiber cHvities, pit membl'ttlles, and
communicnting' ('('ll-wall ('!tpillnries; tIll' second term represents
continuous din'usion through the cell walls.
I.-.Average
l'XBLE
t'apillary·dillle1/~'ioll
•
dolo and Ihrir Bource, for Ihe hcartwood of
a soflwood with a swollen·vo/lll11t' specific gravUy of 0.365
l'ro\lerty or dllllension
SYlllbol
FnlCtional \'old vol\lIne and cross·sce·
tionaillrea:
],'Ibcr cllvltics 01 dry wood I.........
Ad
0.722
A ..
.65
~'Ib~r
m\·\tics 01 swollen wood to••••
A\'~rngo cross·S\.'CUonalllrclI:
Dr)' wood Jlbcrs ....................
ad
1,000.",:
wood •••••••••••••••••••••••••••••
a,
72'2.1" Swollcn·wood fibers •••••••••••••••••
SpecifiC groyity:
Apparent, swollcn·wood sUbstancc ••
a.
Wood (dry·volume basis) •••••••••••
gd
\,{ood (swollcn·volumo basis) •••••••
Wood substllnc,,- •••••••••••••••••••
A verngc thickness, double reU wnUs of
dry wood I ............................
AvcroKII ctrcctivo fibcr'CIwlty length ••••
Avcroge fiber length ••••••••••••••••••••
g.
g.
1.46
Id
I.
5.2/1
.285 em.
.38 cm.
Fiber cavitics
ot
swollon and dry
g.
1/
Source of vlllue
Valno
1,111.1"
1.53
1-~
g.
l-(!l!!!+~)
u. p
I-S
11,:'"
..t~
Ad(l-S)
nl' or "-'11'T­
1
n,''''
Water displllccmcnt.
g..
.406
1=8
.365
Assumcd valuo.
Ilc\ium dlsplaccment.
2(rd-rr)
From 1/ and fiber o\·crlap.
Statistical /low methods (table 4,
p.59).
•
PASSAGE OF LIQUIDS, VAPORS, E'l'C., 'I'1mO'UGH SOE'TWOODS
13
~l'ADL~l I.-Average ('llpillllry-dimc1Ision clata (/nd lhr'ir sour('c, for the hcar/wood of
tI softwood with It HwollCII-l'ollll/l/J ~J!edJi{' gravity of O.365-Continued
•
S~'lIlblJl
or dlmonslon
,I, \'Crn~l\ thickness:
•
A\·l'l·n~l\
/.
m
II/
. OO:~~
I'I'OIII ."I. 11I1t1
structllrul cousl!lortl·
t101lS,
~~lcctro·OSIll(1S0IllCIlSl1rOmollts .
'1.
•014
M ICl'OscoplclI1 cstimntc •
mcctro·osmoso nwn~uremcnts.
q.
17.S,.
l~rom
1'l1\,itlcs o( 5woll1'n lind dry
r/
15.2,.
Prolll III, l1.<sumlng fiber cl1\'\ly
of swollen. "'0011 I
r ..
IS,NI'
1'.
28.2111,.
I'('rlllllll('nt plt.membmnu Ilores
5\\'olll'n wood.
or
Hn!lhis 01 th" llilnsll'll( t'l'lI·wnll ellplI· Illl'les ctfccUI'O (or tho flow of wntl'~. .2111'"
s
~'rllcliol\lIl ~.tterl\n\
volumetrlo ~hrlllk·
wood to ovell·dry COlldltloll.
FmrllOllnl cross Sl'CtlQU:
'1'1'1UISICllt cell,wlIlI 01l1'1II11rll'5 01
wllt~r·swollcII wood elT,'ctlvc lor
thv !]IlSSlIgO 01 moll'cules the SilO
(,I t 10 wllter mOlecule h. IIber
dln'cUolI.'
'I'l'IIll~lont cell,wlIlI clIPlUnrll'S 01
wall'r·swollcn wood CITI'Ct\VC lor
the IlIlSSlIgC 01 lIIo1~eu II's the size
or t Ie wilt~r molecull' lit right I
nucks to tho fiber lllrcct{on.'
:
FrnctlOlllllllquld \'olnllu) 01 5\\ ollcn cellI'
willi,
Avcril~o sl~ciflc
•
1/1.-1
.00011
w(llHl.
ng(l o(
2.5
.()(J(l3
rmltus:
1~IlJllrs
111.
1\I1cI'!lscnpic couul nud mOllsum·
llllln~ (tubloS. p. ("l).
.101
'\o'lhl'rs or (Iry wood I.................
~'Ilwr
3. :;
:100.
llw
----~----
2(r.,-r,)
M IOrOSl~)\1iCIII estllulI!I',
Sorption 1IIC1lsurl~lIIullts (flg. 24, p.
58).
I ..
Douhll"Cl'll Willis 01 swollen wood I.
Pit mllmllI'llIlCs,." """ ,. "" ..
Frnctlllllill IIllllstllro content or wood nt
tho Jlber,slILlIl'lltlml point lit 25° ('.
(",cllthL blls\s).
NnlJlbl'r o( IIbcr clIvltll's trn\'cl'liI,!1 IWr
Uti it Icngt,h In lonllitllllhmi direction.
A \'erllg\lnllntbcr 01 flbl'rs trnvcrsctl per
cClltlmNl'r In tho [1\(11111 nnd tl1Il'll'n·
tll1\ dlt'Cl'UtlllS (ot' 8woll\'11 wood. I •
Nllmbcrol pit membrullcs or doubl" cell
Willis tmVl'rsl't1 III 5cl'108 wht'll tho
length In tllU fiber direction Is 1 cm.
\"flWtfOllll\ ('I'USS sl'ctlnn:
'I'ruusll'nt l'\lIl'WIlII ('lIpllIlIl'les 01
wlIl!'r·swolh\1I wllod ~tT"cth'I' lor th"
11I1SSIl~1l o( mnll'I'\llcs thll slzo of thl'
\\'lIlt'l'moll'Culc In tim IQngltudhml
dhwtlon (rQIII ono fiber clI\'lty to
IUlothor,1
'['rllllsk'n! cl'lI·wnll cllplllllrle~ 01
wlller·swoll,'11 wood I' lTect! \'ll tor tho
IIIIS.'!II~O 01 mo\ccuit!S tho slzo o( tho
wlltl'r nlOll'cult) ill tho tmIlSI'!!I1'U
llh'c('tions (rOUl OliO IIber Cllvlt)' 10
ill\f)Ull'r. 1
'1~IT,,(·tI\'l' Imctionlll cl'oss~~I'ctlollnl Ml'n
01 thl' pcrnlllllont I1lt-mclllbnlllu porus
for IQnltllU(\lnllll1ns~lIg(,.3
J"rlle! 10llnl crus~ SI!(!tiIlU of tho tl'llllsiollt
p1t·mCl1lhmn~\ cnpllhtrics o( Willer·
swulll'll wood lor th(, pIIS';lIgU 01 mole·
CUI,'S tho slzo 01 the wllter molecule,
('.~clllsivu , 1'l1l11'l1Il1l1l'UI !lOn's.'
~·rllctlol!,.l 111'('1\ o( tho tnllglnltJnl wnlls
of tho IIhurs co\well h~' lilts.
g'lc('tlvc lructlollill cross·sectionlll IIrCII
or till' Iwrnlllllon( p\l'l1Icmbrnnu pores
lor trllUSVO'I'llC !lllSSngo.3
Sourco o( vnhlO
VuluQ
_._----------- --­ ------
I'rO(lI'I't~·
..,--,-.."...
grll\,ity 01 ndsorhed
I
.10
aJ, Ilssnmlllg Obor cross sec·
tlou clrculnr.
cross ScCtioll cireuillr.
li'1'01l1 tim, ns~uIllil1g flbcr cross scc~
tion cireuillr.
l'c1'IIICuhllity mClIsurumcnts to IIlr
01 dltTcrcut rclntlvo humldltlcs
(llg. 26. p. 6.~).
J~stlnllltull Irom distribution of
cnplllllry size curve (fig. 30, p. 70),
nnd Immohlllzntlou 01 sllrlllcc'
IIdsorhcd 11I0lecules.
Awmge cxpcrimcntnl vIIIIIO lor
sonwoods with 11 SWOIlOll-\'oIIlI1lC
specific grll\'lty 01 O.3UIi.
.0154
l~rol1l
s.
.0078
l~rolll 81
","
.287
p
1.113
I' corrected IQr IrlctioulIl cl·
leets nlld structurIll eonsidcrIl'
Uous.
tions.
nud structllral couslclcrIl'
-=~~.I)::~~~:~:I PO_h_lt_._-'-____...:..____,
I '1'Ill~SI' (tlllllltltlCS wllllncrclIso with inCrl',\sin~ moi~turc COil tent In II lIn1ctlclIlly IInel1r mnnner,
'·I'hl'.~c qlll1rltltl~s wlll \'I\ry with tim moisture coutt'liL II.' shown on P. 74 01 the Apllelullx.
3 't'hose quantitieS wllIllccrcllllo with Incrcuslng moisture content 111 n prnctlclIlly IInclIr I1I1U1IIer.
14
TECHNICAL BULLRTIN 929, U. S. DEP1'. OF AGmCULTURE
Tho terms .,,-~!'
...
~V+qm
und
_.31'
_ ropresent
q,+q",
the recipl'oCttls of the com­
bined cfl'ccth;eness of tho permanent and transient pit-membrane
pores that nre connected in paruHel. lm/q1l is the reciprocal of the
efl'e(ltiveuess of tbe pit chambl\rs. As this structure is in series with
the combined pit-membmne system, the. reciprocals are n,e1ded, The
totul pit systems are in purllilcl with pn,rt of the cell-wnH cl1.pillat,y
sYAtems with efl'ectivenesse1 Q,fl", find Qt/l", so thn,t these t'fl'ectivenesses
hilve to he ndded. Thl. combined fiber-cavity communicating efl'ec­
tivenesst's,
in equation] nnel the corresponding vn.lue in eqlllttion 2 nrc in series
with the fibt,1l' cavities. The l'eeiproeals of the combined fiber-cavity
eonummicltting eil'ectivClll'ss multiplied by the number of commu­
nicating structures trnversed per unit distnnce in series (n. o for longi­
tudinltl pnssnge nnc! '1/., for trnnsverse pnssnge) nnd the reciproenls of
1
the fi1..>er-cnvity efl'ectiveness
for longitudinnl pnssage and
for
.l m
lrn.llSVl'1'SO pnssnge) fil·!.' ndded.
In equation 2 the fibel'-eltvity eil'edin'ness reduces to unity as tho
cross s('ction is eqUId to 1 X21'",'/l.r, nnd tho combined length is equal
to 2r".'Il,. 'rhe continuous ditrusion through cell walls in the longi­
tudinnl direction is through nil the wood substance, the cross section
of which is 1 minus the cross section of the fiber cavities, 1- Am, nnc~
the length of paths is unity per cube of wood 1 centimeter in each
dimension. In the trallsverse directions the continuous passage is
through only part of the cell wnll, fiS shown in figure 6. The cross
sl'etion of anyone pnth per centimeter cubed of wood is lm X 1. As
there are n/ paths pel' centimeter of breadth, lrn X 1/" is the totnl cross
sedion efi'l'ctivc for continuous passage through cell walls, and the
length of pnth is unity.
(-1
•
1
•
DIFFUSION OJ.' SOLUTES IN'fO \YATEU-SATUHATED HEARTWOOD
When the vnlues given in table 1 for the cn,pillary dimensions of a
water-swollen softwood with a swollen volume specific gravity of
0.365 nre substituted in rquations 1 and 2, the following values are
ohtailll'd:
J)(~:.DG(_l_ ~_~ +0.005)
0.650+ 13+140
=D.(1.53S!0.016 +0.005)=0.649 Do
and
Dr=Do(
1300
1
+4.76+-S.75
+0.0017)
•
PASSAmJ OF LIQtlIDS, VAI'ons, I'JTC., THHOUGH SOF'fWOODS
•
15
-Jij 9+0.0017)=0.0448 D•
=Dv(l·+·
D,/D,=14.5
....oJ ....
The stt)PS in lhe solution t\l'e given to show the {'fft'cts of ench struc­
tuntl elNHont.. In the lon~itlldinnl dil'eetion the I'esistnnce to diffu­
sion of the combined pit-system nnd t.rnnsient cell-wnH cnpillnries is
negligible in compltl'ison with the resistnnce through the fiber cavities.
The longitudinnl ditrusion is limited almost entirdy by the cross
seetion of Lhe fiber clwities, the contribution to the difl'l1sion by the
eontinuous transient (Jell-wall cn.pillarity being PI·lIcticlI.lly negligible.
In the cnse of the trn.nsverse difrusion, the resistance due to the pit
system is about twofold greater than that due to trnnsient cell-wall
('n.pill n.des. 'fhch' combined resistance is considerably grentel' than
Ihnt nttributnble to the fiber clwities,
It is of inh'I'cst, to detel'Iniuc how the valucs of D, nnd D t and their
mtio, which hnve been cnlculn.ted for specific capillm'X dimensions, will
Vttl'y ovet' the normnl mnge of varintioll of the capIllary dimensions,
Vlwintions in the !ibm' ll'n~th and fiber overlnp have a ne~ligible effect
on D I since Ute n.nd Q, nre pnwtien.lly incfl'ecti ve in eq uatlOll 1. Vari­
alions in the dinmeter of the fibers hn.ve fl. minor effect on D t since
an increase in nt is necompnnicd b:y a corresponding decrease in l"" I'm,
nnd 1'/. An ineronse of li, from 300 to 400 causes a decrease in D t of
0.5 percent, nnd a deerellSl\ of n, f!'Om 300 to 200 causes an increase
in D, of 9.4 percent. A change in the specific g1'll.vity of the wood
chnngcs both D, and D I appreciably as a result of the chnnges in Am
nnd in r" wllieh n.fl'pets Qt, and changes in l",. 'fhe varintions in D'I
D I, und D,fD I with ehnnges in the. specific grnvity of the wood are
given in figurl1 8. ]) I dccI'l1aSOS in fl. practicallv linear manner with
an inel'ellSe in the spocific gravity of the wood, vwhereas D I decreases
more mpidly in the low speeific-grnvity range thl111 in the high specific­
gnwity l'ltnge, with inerensing specific gmvity. The mtio D,fD , is
fairly constn.nt over t.he normal speeific grnvity range of wood.
D,fDo is pmetienlly equnl to Am, whereas D,fDo shows no simple
relationship with Am.
Vnl'iationsin the effective pit.-membrane pore m:oss seetion n.nd
lhidoH'sS ClI and lp will not be eff('etive in determininf? D, and will be
only mod('l'Ittely {'ffective in deLel'luining D" Doublmg the value of
ClI will elt\lse a 16.7 percent illcrense in D I, and halving q, will cause au
11.4 pereent decl'cnse in D I' Doubling t.he values of q", and ql' will
cause a 9.S percent incrense in D" and halving both qm and qp will
l'ause a 7.8 pereent decrense in D t , Doubling the value of tl' will
('I\\Ise a 14.1 pel'e('nt decrellse in D t and halving lp will cause a 19.4
IH'rcent ineretlSe in D I' . Normal variations in the effective capil­
Inry cross section of the cell wnll will have a negligible effect on
D,. Variations of Q/ and S, whieh also affect qm, hl1ve an appreciable
effect upon D t • Doubling the vnJues of Qt, S/, and qm will cause a
65.6 percent incrense in D" whereas halvhlg Qt, St, Ilnd qm will cause
1134.4 percent d('crease in D t. Variations in S, and St between species
should hot be great, as is indicated by the relative constancy of the
fiber-snturlltion point of different :lpecies of wood (40). The un­
c('rtninty of tht' exiwt yalu(' of St rn.ther thnn vnriations in S, between
species will nifect the value of D t,
•
•
16
TECHNICAL Bl'LLET:i'N 021), U. S. DEPT. Ol~ AGIUCULTURE
It is thus evident lhnl only v!U'illtions in the specific gl'Uvity of a
softwood causo n,PP1'eeinblo ynl'intions in D /. D I is also affected by
chunges in the specific gl'lwity of the wood, and to a considemblo
extent by the othQl' vllriabll's. As the Ylllues of D / and D I are simi­
larly nlfe<:ted by the spueific gl'avily of the wood within bhe normal
1'1U10'e, the 1'I1tio is only slightly nfl'ectcd. In /tny cnse the yarint.ions
in DI nnd D I cllused by yarinlions in the cu:pilhu'y structul'C, al'e very
small ('ompnred with the variations in pl'essure permeability with
vnl'inUons in structlU'e thnt will be considered latm·.
zo
I
_h __ .""".
10 ,.."'.....-.-
--,
:.-"
"" f·...· ...
S 09 ... ...
,- -r
,.,
~
;:; O.d
~
~ 0.7
c:.
c:.
~ 0.6
~
~ 0.5
.....
~04
0.3
O.Z
0, I
k::::::::
'"~.~-
~Fi=
---- .-~~-I
i
.... " C "
I
....
- e-·--I--lI
---r---
i
~
"-~"-'-
+- ; ­ -- f
'
i
~~-~,,-",~
~I
'II
I
I
t
t
i'! ;;.,. . ," ,
···· . ·_·t..-r-
I
I
i
I
!
,
t
L;
'I r t ·
r--t-.,
­
.--.~-,
,
.... "" t,,··· . .-.+.,.-,.
'" 1,0
~
~,
-~
1=
l l t.---1
PF
5 1'--'" ",,,~
~ 0
h:
IO'hl
-
15
j
!
~-'-, -TT--r-+- . "k I
.... T , I i . -- '+---j -+ K r-....... ." '~.--" -1-'t 1 I ''--'
-- "~!t--L
.;.. -~- '----m
rio"
\
t
o
o
. _~...
I
".
_
......... , . . .
't .....
.............
~2
~3
•
{::!oo .......... c"...... _ ._ _ I
~I
•
.
~4
~5
a6
a7
0.8
SPECIFIC GRAVITY OF WOOD (SWOLLEN-VOLUME BASIS)
S.-Cnlculnted diffusion functions rdnt.ivc to bulk diffusion for the
pnssl\!-(c of $ol.ull~s with lIlolecu\!'s U1(' size of till! wnter molcculc through watcr­
snturI\\·ed wood of differcnt specific grnvities.
FIOITRt:
In thl'calcu\ntion of tIl(' vahws for D, the fibl'r cavities have been
consid('fod uniform capillary tubes with a uniform radius over their
entire length. As mentioned elulier (p. 3), fibers are tapered nenr
U1eir ends. The differences in fiber-cnvity diameters that occur in
cnch tangentinll'ow of .fibers, shown in trnnsv('rSl' section in figlU'e 2,
pngl' 4, are largely due to this tnper, The diffl'rcnces occurring in
the rndinl rows; however, are IHrgcly seasonal yuriations and exist
oY('r n1t' ",ho](' fiber length. In the tHngl'lltinl di1't'ction the nnrrower
third of the fiber cHvities in nny trnnSVl'rse plnlle s('ction aVl'rnge
from ubout one-third to onc-hulf of the dinlllcter of the broader third
•
l'ASSA(l~J OF LIQLllDS, \'I\POHS,E'l'C" ,!'lLHOUOrr SOF'l'WOODS
•
•
17
of the filwr cl1\'iti<'s, 'l'lu'rl' is thus til(' possibility of It S('vl'I'alfold
vnl"ifL1ioll ill tIl(' m'l'll of cross s('ctioll of It singl('c tilll'I' cuvity along its
h\lIgth,
('ollsidrt" fOI" (·xnmpl(' ('ns(' 1), two cupillnl"il's of IInilll'ngth--ono
wi lh u. IIniform C1'OSS s('dion of 2 II IIi ts Iwd tIl(' olhl'I' with It CI"OSS S('ctiOIl
of 1 unit. '('ht' difl'lIsioll thJ"()lIgh Uwse lwo cnpillul"i('sin pl1l"1llll'1
will be 3D.. Thl'n eonsicll'l' (ellsl' 2) two ellpilllll"i('S rnlldo up of u
hnlf-llnit length of eneh of the two cnpillnry silws, Tho difi'llsion
throllgh two of Ul('s!.' cnpillnl"il's in pnmlld lhnt htlVl' till' snm(\. IWl'l"Ilg(\.
(:1"08S s('clion ns in (~nst' 1 will be 2,67 Do, TIl(' nOlllllliformity of hOI'('
of ('1I('h ellpilinl"~r in this insttill('r- 1~l'<lucPS the· vl1lm' of D, by 11 P(·I'(·(·nL.
If 1iH'I'(' \\"('1'(, It thl'ppfold Ylll"illlion ill the ('ross S('CtiOIl of t'nell eupilllll'Y
1Il(' (lifl"usion vnltl(' would he I'(,!lu('l'd by 25 Pl'I'N'IIt.
Cndy IIml "~.il\jIlIllS (7) (\('t.(,I'minl'd ('xlll'l"inwll1nlly LIte (lifrusion of
UI'('n, gIY('t'I:ol, nnd Indosl' into Sl'\'('I'1I1 Sl)l'('i('s of wat(\l'-sntUl"utN\
softwoods I"l'lntiVl' to Ull.·il~ difl"lIsion ill wlth'I", 'I'ho 10ngillldinui.
difl"lIsioll in to til(' woods whieh t1lPY l)('li('vl' gun' CI"t'(' unstirr('(l diffu­
SiOH IU'(' gin'n in tnu!l' 2, logl'tiwl' with till' ditrusion yulues ('ulelllll.t('(1
from ('(pllllion 1 for Mil' difl"usion of It 11101('("ul(' til(' sizlI of the wut('I'
moIN,tllt.., 'I'll(' I'xp(·rinwlI tnl \'nltll's jtJ'l' in nU ('us('s lower UUUl till'
('uleuln.tNI \'nhws bv n.n nllloullt ('ollsistellt with lhl' l'fl"l·(~tS due to
nOllunifol'mity of tiH' bon' of till' fibet' (,lIyities, lind the faet thllt
tlH' l'xpl'rinH'ntnl difl"usillg' Illoh-eutes m'(' Inl'gcr thltn the wntl.'l'
l1lo1('('ult', 'l'lw pnl"t of tlu'il" clntn whieh tlwy .indicntc ns showing
"hind('I"t'(1 difl"usion l l mnv b(, the I"l'sult of a vllrilllioll in the fib,,!,
ellvity eross sl'('[ion nlong .its l(mgth of more thlln thI"t1(~fold, Their
"81il"l'('<1 difl"usion." whidl OC('UITNl only in sllpwood. is uppnl"(\J\Uy due
to stining dI"N'\S lll'ing tl'llnsmittNI from Olle (11)('1" ellvity to nnoO\('r
through th(' pil-Ilwmbl"nn(' ol)('nings, whirh IIl"e sufIieilmUy ltu"gl~ to
1)(,1"Ini t ('OltY('('t iOlt,
'I'AUU) 2,-J)iffll.~i()II, III Ih/J /oll!/r"llldtlHll dtrec!.ior1, of s()llllc.~ in.lo 11.'l1Ier-sal.llrntetl
sjlCCi/llCII,~ of lIt'verui s(lflll'oods rrill/.ivt! /.0 the bulk t!iffllsh",
R\Xll~'dllr W('SH'rt!...
00
'.
Flr,whit,\
.,
D o . . .. '
1>0
...
lIctllloek, w~sh~nL ..........
~.~o
." ,.
0.·125
. ·125
.:150
• al~1
CllYl"l>rol
1,'lct(~<t·
........ [
.
.
I
., ••"....
t,t1cto~o
.,.......... '.,3.'>0 ,l'n'lI
...... ......
OIY('t!rol
.~II ! (Jln'~rot
. ..• ......
0.0(;,
54 I
0.69
,5U
6,1
8.5
18.2
18,2
:5.11
•M
,till
• (~I
.M
,55.
,(iti
18~2
.58
5.2
~.4, 1 L"~tu~...._._.'_"_'_'.!.-_ _•4_S..!I_ _ _,_[>!!-!._ _ _17~'2
..<0<0: ___",. 1.,.•
1 DlItll ()t ('lIdy IIlId Wlllilllll. (7),
•
III. nn l'Itl'li('r study (,42), the eiceb'i('1l.1 conduetiyity of wood filled
"'ith dilutt, snIt solutions wus dt'tt'I'min('d, A suflidl'nt. ('oncentmtion
of t'lN.'t.rolyti.' WI1S uSNl so us to nullify SlIrfuel.'-l'onciut'tivity ctfl.'cts,
The dutn for t\wse I1ll'llsun'nwn1s, ('Xpl'l'sSNI ns the ('ondut'tiyity
l"('lntiw t.o thnt of til(' bulk solution for the pnssngn of CUlTl'llt in tho
tibl'J: dil'c<'tioll of the wood, arc giwil in tll.blo 3 1 together with the
iH:iii\l'· -4i--3
18
'l'EC:aNlCAL DULLE'l'lN 929, U. S. DEP'l'. O~, AGlUCUUJ~UHE
CGI"I'C'sponding theoretical condudiviti('s cakulute(i from equation l.
In this cUSC', ns wdlns in the case of diffusion just giv('n, the expcl'i­
mentnl vnlul's are low{'l' thnll the cniculllted by thl' nmount pl'cdictcd
from til(' nonuniformity of tho bore of tlwfib('l' cnvities, 'l'hc sntis­
fnctory ngreement betwel'l1 both diffusion nnd elcctl'knl-conductivity
dutu witli the th(,ory of tlwir equivtllence serves to cslnblish the
vnlidity of equution 1.
•
TAR[;tl 3.-Elerlri('(1/ ('llIldl/eliot/y of wood sn{ur(ltetl with ciihl/e ,mit solulio7ls rel(l­
ti!!(' to Iht! bulk cOII(/ll('tivil!l of the sollllioll
..- - "
~"""""."
. -."".""".-..",,,
,"~""
"
-<
SIl('dOc
gnl\'ltr
wood
or
(ftl1.'(,11l!
"ohml,,)
~:;'~\'''~~kn ~:~::-dl--~--i---~;;:;:
nCcll..~dllr. \\'\~~ll'ru (hl'urlwuod, _,
Dou~h~.·t1r (hCtlrtw(mdL
Do,
DOl/gllls·Ur (SIII,woo\ll.
,
I'hw. ~hL'h (hcllrtwoodl
I'hw. shish (SIII,\\'oo,)I
Sprul'\" Sltkll hl'llrtwuod) .
110
I)u
1.1>111110(::>111111111
_..
j
l
.'..'1X)
,3211
.6~~j
i , 4(~1
:
,-laO,
. ·15\1 ~
. ~'Il7 ;
,:H'
.3.0
!!
Pl'rlOCntnJ,!e
~'XI>~rllllclltnJ: ('lIlcuillt"t\ . <Iol'llitton or
r~~IIU\'e 1'1,,1" ,
n~llIth'c
~XI,crhllentlll
trieul
COil"
~
l'lt!ctr.il'nl
f
r~olH
cHleu·
<Iueth'ity t I' ~OIltluctl\'ily llntl,,1 rcilltl\'~
COtultlc!lI'H.y
O,4i6.
,tHS
..'iSI!
.~:lS
'\:---0-,r-'iS-'
,5:1:3 I'
• -liS
,4i8 !
• fl07 ,
,5tH:
.(iH
I
,72'2
,tlS7
.4\18
,tIl·1
,/)S$
.51H
, ii" I
.lltl7 i
,IHll'
17, tI
10,2
H, i
12.0
13,2
10,2
15, ~
Hi. I
15.-1
15,s
w!',
(1lldv 5 dd('I'llllned ('xIWl'iml'nlal Yulu('s fol' the tl'ltnsvcl'SC difrusion
of un'a; gIYN'I'ol, tllld Illdos(' inlo wntl'I'-sntllI'nt('d wood, Becltllsc
duplienlp nthit's ('oult! llol b(, obUlilll'd wit.h uny UPPl'c('il1blc dcgree of
IWCUl'lley, tlwSt' lll('i1SUI'('Il1l'lltS \\'('1'(, 0111iltNI fl'om the f01'111111 pllbliC'll­
lion (7) sumllliu'izing his studies, The I1Yl'I'ugc vnlues and the IllnxiIII 11 111. deyintioll f!'Om th(' IW('mge of D dD u oblained with white fil'
huving n swoll('lI-yoluIllP sppeific gmvity of 0.:350 un'as follo"'s:
Thl'(,(' ll1ellSUI'ellll'n ts wi tit Ul'PH, 0,069 ± 25 Pl'l'(,l'llt; S('Y('II 1l1('11Slll'(,­
n1(ln ts wi tit gly('('rol, O,O;j\) ± 20 PN(,(,II t; nnd two ll1('USUI'l'nH'lIts with
luctosl" O.l06± 1:3 Pl'I'('('IIt.
Tltl'Pt' of tlte Illl'llSlIl'ellll'llts ,,-ith glycl'rol W('I'(, mnde in tht\ tn.ngl'lI­
tinl dil'l'(,tion of till' \\'ood, All othN' 1lH'IlSIII'('ml'lIts W('I'(, ll1ndl' in the
rndiul din'ction, No dilfN'N1C(', in vip", of the limits of nc('ul'I!l'Y of
Illl'IISUI'l'IlH'l1t, wns obtllinNl.i11 tI)(' two difl'l'I'l'nl dil'('ctions. Values fOl'
D,fDv outninl,d with IIl'l'tL lind glycl'1'01 Itgl'el' fnidy well with the
t1ll'ol'etl('nl vuhl<' O,04i3 fol' wood of thl' Slun(' sp('(~ific gl'lwity, The
expl'riml'lltnl Yllhl(' obtninNI with Inctose nppelll'S to be somewhat
hi ..lH'I', 'l'ht, gl'IH'1'Il1 ngn'('IlH'lIt, how('v('l', S<'l.'IUS sutisfndol'Y.
1\[l'llslIl'l'd in th(' tnngl'lItiul dil,(,(,tioll of wood (42) l the elcetricnl
condu('tivit.y of sOlltll('l'll. pin(' (5\\'01lel1-,-011lIlW sp('cifie gl'lwity 0.430)
r('lntin' to tilt' bllik l'Olldudhrity wns 0.046 ns compnrcd to the
theon'ticnl VHhH' fol' ]),'/)0 of o,oas, 'I'll(' ('xlWl'illwlltnl cle('tl'icnl
('OlldIlCti\'ity ,-nlla' for Douglns-fil' (swollell-volulllc speeific gl'llyity
O,~{2G) WIIS O,O:~7 ('ompul'NI to the tht'Ol'(,tieul ynlue of O.04\). Aguill
the l'lgn'('lll('nt Iwlwl'Nl tlw ('xpl'l'illlt'nbll dill'lISioll Ilnd ell'ctl'ical COI1­
dudiyity vlllues with those pl'('dictt'd from the theory is suflkil'lIt to
indiellte thnt (,«lIntion 2 will ut l(':lst St'I'\,(' ns It ll1('llllS of obtllining
good npproximllLiOlis of lhe ll'HlIsnl'sc di/rusion through wood.
~ ('AO\\
thesis.
L. C . .\\OJ.g('I'\",\H ()In-t'IHOX 1:-;"1'0 WOOD, 1934, [Unpublished doctor's
Copy on file Librnry, l:1Ii\', Wis" Madison.]
•
•
F~SSAGE1 OF LIQUIDS, VAPOnS, ETC., THHOUGH SOH'WOODS
19
Dln'0510N 0." SOI.UTES INTO n"~,\IITWOOn S,\,(,UltATED WITH A NON­
SWELLlNG SOLn;NT
•
It is of illi:l'rl'st h) ("tleulttt(~ lhl' expeetl\<t diffuf;ion of soluh~s into
wood (·onlnining nonswl'lling solvents. ende!' lIH'S(1 eOJulilionf; 8"
8" (~" and () I will nil he (,(phil to Zl'ro itS. th(1 edl-wltH l~npillnli ly bn­
('Olllt'S n('~li~~iblo,
.1\,,, (A.l lIl,tnbl() 1),. Jl" 11.:111 1, will illl bO,inm'l:lIs(\d,
IUld '17& Will be dN:I'ensl't! (ld III tnble 1). rhl' nUlllb('I' of hbnl's tmv­
l'I'set\ pet' el'utimot('I', ~~OOJ will be in('1'l'l1s('(1 to 316 by tho multiple
1
fnelot' f.:-S bel'lIus(' of lIll' ll'lInS\'('I'8(' shrillkng(1 of the wood.
The
ilH'I'{'IlS(' in q,lllld 9., d\ln to the (It'ying of the wood amounts lo 37 percent
(p. US),
•
•
Substituting thl'SI' vuhlos in l'qulllions 1 nnd 2 !!in's D,=O,<i55 Do,
D,=O,OI73 Df/ lind J),/lJ,=:37,O, 'I'll(' rl'lnliw difl'usion of II solute
lhl'ou!!h wood ill tlll' IOllgit.udiuill dil'l'{'(ioll, DdD,), ehllll!!('d but, slightly
by sh ift ing frolll II n nq Ul'OUS to n Ilonswl'lling d ifl'usion IIIl'd hUll, wlwl'NIS
till' 1'('lllli,"(' II'IIIHW('I'SI' difl'lIsion, V,;D", i5 IIPPJ'('dlll)ly dl~l'I'('lIsod !,p­
('n.uS!' of 1111' fnd lhnt difl'usion t!tl'oll!!h thl' (,(,II Willis is oliminlltod,
Figul'(' !) shows t IH~ dl'N't of til(' sp{'('ifie gl'llYily of till' wood UpOJl
U,jD", {),I!),,, nnd [),;f),. D,'!)" <11'('1'('05('5 ulmost linl'lll'ly with IUt
inn!'lls(' in spt'cHi(' !!I'nYity, D,rD" dt'('I'(':lsPs n'I'y slightly "'ilh IIIl
ilH'n'lIsl' in t h!' sp<,('ili(' !!I'llyi ty of thl' wood lhl'oughou t tlH' nOl'l\1l\.lly
l)('('UI'I'jugl'llngl' of SI)('('ifk !!I'llyily yuhit's. [),)), hilS I\, Il1I\.XimUIll ilt It
SPN,j(jt gl'llyity ,'ulll(' twlo,," Ihllt of 1\lly known wood iUld dl'l'I'1'I1SI'S
slightly with in('l't'nsing sp('dfie grn"ily of tlw wood above this point.
Dnn~G 0.' Ih';AIITWOO()
1'h(\ drying of wood is 11 1lIt1('h mOl'e ('omplient('(l pl'Oeess than the
diffusion of II 50luil' into wood Ihnt is ('omplt,tely sntlll'lIted wit.h l'itlw\'
1\ poilu- 01' II nonpollll'liquid,
~t05t of Ih!' l'vid('n(,l' indientes thlll the
j.?I'O('('SS is ul \(.'IISt in {)Ilt'!; n difl'w:\ioll plH'nOllwnon. Tuttle (55),
5ht'I'woot\ (a5), nnd Kollllnnn (25, :26) hlln shown thnt tho moist.ul'o
rrnt\il'ntR nnd <!l'yil.lg 1'.lltt'S ohlnilH'di,n drying wood undel' <to!in!te
lJo,ln(\n.ry conditIOns ('llII b!' Hworl'tll'nlly 1'l'pl'Odu('!'(\ by ]IO\ll'WI'
nnnl.n;is llll'thods (21) with n fnil' dl'grN' of n('l'UI'I\{'Y by IIsslIming thttL
tilt' plWllollwnon is OIW of simpl(1 difl'tISioll o"el' the ('omplet.e moisture­
('onll'nl l'nn'~I'. If (\t'ying Wl'l'l' 1'(Hllt'olll'd b:r simplc diffusion, how1'V(,I', tll(\ diffusion eonslnnt lind III(' difl'usi"ity in the 1"ollliel f01'1ll of
the ('qllution shQuld Iw indl'\wlld<'nt of llIoistUl'o eontent, This is not
the ('use for eithN' lhl' longitudinnl OJ' 1I'!H\SVt'I'SC drying of wood
t1ccol'(\ing to till' 1ll('IISUI'l'lll('nts of Stillwell Ui..O Itlld of Mnrtlcy {SO)
in whi('h th!' l'(juilibl'iullI III0 ist\ll'('· gl't1dients sot lip under stcildy
stllte (\I'yilw ('onditions WeI'(' detel'mined,
Tht'se' ('o~lplicntions ulldoublNlly nl'ise from tho complex nnture of
UtI' ('llPillllr:r stl'udUl'e of wood. In the drying of wood tho dimensions
9f the s.tl'u~,tul'nl units "1111' from llllllinn to lliminn ill the diredion of
the dryhlggl'ildie.l\t /IS. 111'l'SlIlt of thl' 1I('eomplinying shrinking, The
mov('Il1('nL of liquid or VIl POI' in responS(1 to this gl'lldil'nt .is further
compliclIll·d by the fnet thilt three different driving forces clln be
20
'l'.ECHNICAL BULLETIN 020, U, S, DEP1'. OF _-\GRlCUL'l'URE
effl'cliv(', un1Uf'ly, (1) the flow of tiq uid through the conrse:. cnpilJm'y
strudul'l' du~' to enpilllu'y foJ'c('s, (2) the flow of YUpOl' through the
com'St' ('npillltry structlU'('· due to It rdatiye vnpol'-prcssure gl'lltiiOllt,
itnd (3) th(' movement of bound wtltel~ through the ccll wluls due to
it moisluro-<:ontent g1'lldicnt,
A sli~hL deprl'ssiOIl of Ow vn.pOI' pr('ssul'6 mlty ocelli.' Itbove the fiber­
sn.tumtlon point (p, 56), wi I(' II this point is ddined ns the moisture
<.~on!(\nt Itt whi('h lit(' (,('II wnlls UJ'C snt.u1'Ilted but no frcw wlltel' exists
in Llw cell l'ltvilics, This will fUl'llish It motiYlLting fOl'ce for the
•
50
D,r/ot
....
40
-
I
I---
30
I
zo II
~ 10
c:::.
i:::
..... 0
~
'" 0,9
~
.~. 0,8
~
~
c:::.
...
"
..,
I'-- f'-....
0,7
f"-... r---...,
~J/oo
r---- P-­
~ 0.6
10.;
~
~-
r-­
~ 0.5
.........
~ 0.4
--
r­
•
-...;;;;.:::,
r-- t-......
0,3
Ot/oox /0
02
I
0, I
o
o
al
az
a3
a4
as
a6
SPECIFIC GRAVITY OF WOOO (ORY- VOLUME BMU)
a7
0,8
FWl!IIE !l,-Calculatcd diITllsion functions in relation to bulk diffusion for tho
pa."SIl~l' of I'ohlk:; with molt'cull's I he size of the \\'Ill<"r lIlolecule through wood
of diIT<,'rclltspccific grnvii icslmturulcd with Ililollswclling solvent,
moYcm('nt of cnpillary wuter nnd wutel' vnpor above the fiber-satura­
tion point. TIl('. moycmcnt of this virtually free water is considered
luter (p. 43),
The moycnwnt of both bound wuter und wuter vapor below the
fibl,,'-slttumtiotl point should be contl'Olled by diffusion, The diffusion
will, of course, bt, complicuted by the fnet thnt two different cit'iving
for('('$ !ll'(' invQlvl'd, Th(, proportion of cnd, thn tis efl'cctive will vary
with ('hnng<'s which O(,CUl' in thc cnpillnl'y structure IlS it result of
moisture-content chunges, In spite of these complexities, the drying
•
PASSA(l~1 OF LIQt'lDS, ,'.\1'On8,
PI'OC('S:; elln ht' IInnlyz('d in
•
It WilY
m'e"
'rIlIWPOH SOIi'1'WOOD8
:;imillll' to Ihll11151'd
diltllsi 0 II. of Ow sol tl ((·s thl'OlIgh 'wood Sil t 1I1'1l1l'd wi I II
ill
nnillyzing till'
Ii. s\\,(·lling
pi till'!'
01' It IUlI\SWt'U i ng
tiq uid,
li\)l' silllplieily,t1H.\ wood will lin (·onsiti(II·(,(lus IIIl1dl' lip of iailllinlls of
dl'Y wood MId luminlls ('onillinillg OIH'-folll'th, olH'-hnlf, thl·P('··folll·ths,
nnd nil of lilt' moislul'(\ N{uiYIlINlt. t.o tl\(' fibl'I·-slItlll'ltt.ion point {'ondi­
lion OIL II \'olullw of Wllh'I' JWI' unit. volllllle of s\\'ol1('n \\,ood slIhstunel\
bllSis, '1'11(1 ('II\)illlll'Y dinwnsi(lns il".. f".. i"" q" und 'Il, (tnblt' 1, p, 12)
will Vill'Y linN\I' y b(\lwN'n lilt· dl'Y Ilnd fihN'-sntlll'lIlion poiJlt ('ondition,
'I'll!' chllngl's ill 8, nnd 8, wit.h moistlll'(' ('onll'IlL 111'(' gh·(·n on pllgl' 74
of thl' ApP(,IHlix,
TIlt' dill'usion of wllll,'I' \'I\POI' in nit' ellll \)(', ('xPI'('ss('d by th(, following
eqlHilion (Int('l'Illlliollltl (1r'itielll '1'1\1>\(.:;);
..
'/' )1'7(, 7HO
d," 0.220(;,....,
.... 1 t.l
•
'-J> u
It--_..30
-,,..,.,---,,>
f
I
,
i--_·~_·
10
FlOt'Utl
•
21
/I
10.-, Elf('d of h'mpt'rllllln~ 01\ til{' diffusion COlIslnnls of wat.er vapor and
hound WIl(('r,
in whieh tip, ill ~qUj\l'(' ('(·.nlinwU'I·s IWI' 8('('ol)d, IS L1w diffusioll (,Ollstant.
of wntl'l' nipOI' in iii I' fOl' lhe IIbsoilli('. h'IIIJ)(,I'nllll'(' 'I' Ilnd lIil' pl'('SSIII'I~
P u (ill l.nillin\('I('I's of ml'ITUI'Y). At 40° C, nlHllI.lmosplll'l·ic 1)l'(~SSIII'l',
(1,=0,280, Tht' dilrllSIOIl YllitWS, in whi('h Ow gl'lIdi(·IIt. is ill t('I'ms of
('h!lnge-in gl'iuns of Wllh'I' VllpOI' IWI' ('uhi(' (,l'ntillwtl'l', ('I\n bl' tmns­
posl'Cllo 1\ l'('illtiyl' vnp0l'-pl'('ssul'e chl\ngl' gl'l1dit-nt. bilsis by multiply­
ing lh(, YIIIII(' by till' Illuubel' of gl'lUlIS of wntN' in n ('ubk ('l'ntiru(,tt,1' of
snl\ll'nl('d Wllll'I' \'npOl', At. 4()0~, this is O.2S0X5,lXlO~5 01' 1.43X
lO~3. Th(> ynl'intiOlls of tht:' difl'uslon ('OIlSi.HlIt of wult'l' vapOI' pel' unit
I'l'lntivl' YllPOI' PI'('SSUl'(' with ehilllges in tempel'ntlil'C nl'o giYI.m in
figuJ'(\ 10,
22
'l'E('lINI('AI. BULLE'l'lN 929, U. S. DEPT. Ol~ AGHlCUL'I'URE
Tlw diffusion ('Onstllllt foJ' till' llIQVl'll1('llt. of bound wnlPI' within the
cell-wall struclul'(1 ('lUI b(' ('slimnl('(1 from l~insl('in's difrusion t'quntioll:
(4)
in whkh dll! is thl' diffusion (.'OllstlUlt fOl' til(' difrusillg substtUlCl' in
S((11l1l'(\ ('('lItimetl'I'S P('I' sl'('on<i, R is thl' gns ('Ollstunt (8,alGXL07), Tis
tlw nbsolut(, tPII1I)('l'lltUI'(" N is AYogndl'O's ('ollstant «(i,O()Xl0!!3), 7] is
tilt' yis('osity of t \(' difl'usion m(ltliull1, nnd 1'0 is tilt' t'f1'{'diY(' I'IldillS of
till' difl'llsing partie\(, or 11101('('u\(', il1I in ('('ntillll'tl'l'-rl'llln-s{'('ond units.
'L'his eqlllltion WIIS <I(,I'iy('<I fOl' thl' dHl'usioll of dilut(, solutions of It
solute with sphl'I'jelll mol{'(,llles in it liquid SOIV(,lIt, Thl'. vis('osity
h'I'1l1 is thnt fOl' tht' soln'lIL In thl' ('n5(, ('onsid('I'NI h('I'(" a· 1110110­
Illolt'('ulal' Iny('l' of wate'r (nholl t G Iwr('(\n t (50)) will bt' imlllohiliz('li
by thl' wood so thllt down to this poillt till' diH'liSioll ('fill btl ('onsitit'I'ed
Its the difl'usion of polymolf.'l'lllnr Inyr!'s of wnt('!' thl'ollgh n sysl;('lIl of
m()1I01ll01t,(,ttllll'ly hdd Wilt ('I'. It thus SN'IllS justifinbl(, to uSt' t.hl'
vis('osily of tIlt' Wllll'l' liS n first ilpproximntion fot, thllt of the solvent.
'rlH' ('((lintion on this bugis giYl'g II YHlu(' fOl' <It< of l.i4 X 10-5 ilt 40° O.
'.I'll(' YlIl'inLioll of dll! with tpmpC'I'lltlll'(' i:; nlso giY<'n ill fi~ul'l' 10.
)'Ioistul'(' gl'lldi('nts in wood Ill'(' normull.,· ('xpl'l'ss('{1 in tpl'lllS of the
w(,ight of With'l' P('I' unit wl'ight of dl'Y wootl ChlllW(' 1)('1' uilit distllll(,('.
In til(' (,US(' of difl'usion thl' gl'lIdil'lIt is nOl'llllllly ('~PI'l'S:;N\ ill lC'I'ms of
tilt' w('ight 1)('1' IInit yolun1C' ('h!lllge.' P('I' ullit disillll('('. TIl(' difl'usion
of both WII Lpl' Yn pOI' und bound wntl'l' wns hl'II('l' t1'lInspos('d to this
InUl'I' ('0111111011 hnsis. TIll' difl'usion ('ollglnnL of "'HtPI' \'npol' through
wood, D., will Ill' ('qunl to th(, di(l'usioll eOl1stnnl of Wl1t!.'I' Vllpot' ppr~
uuit r('lntin' YnllO!' pn'ssun', d., obtllillN\ from figlll'l' 10 for thl' t('m­
Pl'l'lltUI'P und('1' eonsid('l'Iltion, multiplied by the I'll tt, of. chnngp of
. mOIS
, t urI.' COil t cnt, tlH
I t ·I\'l' Y pOI' pn'sslII'p WI. tl Ie Iinngl's 111
1'('11
tim' 0 bt'
IlIlle d
•
•
from th(' slope' of tlw (,IIIT('S on png(' 58 of the Appendix lit tlH' moisture
('ont('nl ulldl'I' ('onsi<lpl'll lion. diyidNI by fI, tht' sl)('cifie gl'uyity of the
wood 011 t hl' bnsis of tItt' YOIUllH' n t tilt' moist III'l' COil h'lI t UIl<iPI' ('011­
sid('mtion; thus:
D =d
•
~rl\('
fuetol'
~n chnnges
~m
pr'essUl'(' gl'UtiiNlt to
It
t
..l~mED -g1
(-",
(5)
tlH' diffusion {'OIlSt/lllt from
it
rpJlltivc YflpOr­
moistu17I'-('onL('nt gl'lldi<'nt bnsis per unit weight
of dl'Y wood, Ilnd tIl(> fl\(,tor 1. ('hnngc's tilt' luUN to 11 ll1oistul'(~ COII­
9
tent pN' unit yolullll' of s\\,oll('II-wood bllsis.
The bound-wnter diffusion COllstant dllJ is trnllsposN\ to thl' dl'sired
bnsis by multiplying th(' mt(' of ('Illmgt' of the moisture cont('lIt 011 It
volumr I>PI' unit. volume of SWOlll'II"'wood subslnIlC(' bnsis with I'Psp('l't
lotht' moist.ure content on n, weight {IN' ullit weight of <h'y-wood bllsis,
~.~. ~,
tl.m
obtnined from tIll' slope of the eurve of iitrul'(' 29 on lliwe G9 of
.
'"
'"
the Appendix, nt the moisture ('ont('nt UlH\PI' ('ollsidl'l'lltion. This is
multiplied by thl' speeific gL'llyily of the nc\sol'b('d moisture Ilt the
•
PASSAG~) Ot? LlQCIDS, VAI10HS, ETC"
~rHHOU()H SOFTWOODS
23
Illoisbll'{l ('011 U'll t Ulld<'l' ('onsid{"'lltion, p, '0 {'onv{'l't dw, ,,-lIieh is 011 It
hHsis, lo ti\(l units of.~ r whkh is on 1\ volllnw of wuh'I'
hllSIS, This \11 tUI'll is dh'id('d by r, HS ti\(l ("'088 s('rtioll to bl'uSNI in
tlw follo\\:ing ('f/ Ull tions is in t('I'ms ?f til(' ('/l'('cliv(' ("llIlsiNi Ii (:11 pilllu'y
{,I'OSS s(·{'lton of th(' ('llll wnlls oct'u pINI hy WH tl'I' l'Il tlWI' lIlIIn 11\ 1.('I'IllS
of til(' ('ross sN'!\on of tht' {'(Ill wllH itst'lf. 'Phis ,'nlt\(' is dividNI by th{\
srwl'ifi(' gl'uvi tv of IIw wood 0)) 11· bll,~!s of Ilw yol UIlW lit tlw moisl.lIJ'o
l'onll'nt. lIndt'l: ('ollsid(,l:ntion to ('01\\'('1'1. fl'OIll It weighl. of dl'Y wood Lo
Il yolunl(' of swoll('II-wood btlsis; thus:
wC'i~ht of wntpI'
•
,
D
I~qtllltio!ls
IC
,'.
dIi'
(.ll')(p)1
.lm ." 'Ii
(6)
flilllillll' to <'<llllltiOlls l. !tlld 2 (,fin 1)(> fOl'llHllllt ('d , tlsing
till' IlPPI'Opl'lnill dill'tlsion ('OllstHl1t fOl' ('iwh plitt, of
n",
tI\('
SII'UI'tIlI'("
nil O\(' S!I'Ut'l,UI'C'. PIll'ls inyoh'illg Dr W('I'(> lI('I\('C'
llIultipliNI hy DrITh:l'· TIl(' longilu<l i11111 dr,villg dill'lisioll (,Olls/nllt
I'P\" tiy(' t.0 I III i t d i I1IPl\sions ()f till' wood t h rou!!h lilly OIl(' III milllt Itt
rip;h lung-Il's to t bl' d I'yi n~ g-I'l\(1 ilm t is n'pI'('s(Inted hy 01(1 fo I' III uln:
\\'IIS lIsC'd fOl'
V,
nIP
(7)
+
AI"!)';])'"
I.
•
'l'IH' (,OIT('spollding tl'llIlSY('I'SC difrusion l'oustnnt is l'l'IH'('S('lIted hy tho
(ormula:
V"
0",
1
1'11/ ------ •
Oil),. +
/), '/)11'
I"
.
.
+ lm'1l. IS'l +Q, J
+~'" r,;.
-+ '1/11 ( [)'r)
'1,/
)
(It,
,
gin'n in table I, p. 12.
(/ITing, wlti('h is of rnlljor irnportlln('(' in drying pl'H('t.ic(',
The symbols uSNI in tlWSl' ('qulltions
'I'1'1I11~'~('r:;(I
(8)
111'('
will bl' eonsid('I'('d first. '['bt, stl'PS ill lh(, ('nl(,ll[ntion (01' the dl·ying of
wood with n :;woU('Il-yoIIUll(' Sl)('('ilie gruyity of O,:3G5 Ilt 40° 0, nro
g(\'('11 b('lo\\' (01' difft'I·NIl. mois(.IIl'('-('OIl('lIl conditiolls to ilIustmt.o tho
('(J('('t of ('U ('I \ of thl' fndors. '['hI' ('ulrlllllJiollS W('I'l' mllde fOl'fiYn
<litr('r('n t, moist ur(' <'on tl'n Is COIT('spond inp; to l'q1,1Il1 jll(,l'~n\('n t.$ of V,
thi' fl.'llctlO/lII! volt/IIl(' qf tilt' 8\\'011('11. ~'dl Wlll~ thllt IS oC{'UI)1('.d by wuter,
'['Ill' f()lIowlIlg N(llillIOnS lIr(' used III mnklllg the (~nlcll nttOlls:
\V'lwlI m=O.292
•
Illld r~O,2i7
D,~,':14,,)X 1O~5[ __.
1
0.200
. ]=0,444 X lO-1i
\00.' ..... +0... 0017.
+0.200 +O.OO();)
Q:()()n~.). O.OOO~:
0.000,)-+0.00000,)
+ o.ooon
0,014
24
~l'EC.l:r:NICAL
nULLE;TIN 020, U. S. UEP1'. 01" AGIUCUUrUUE
Wlwn m=0.205 lIud 1'=0.208
t[..),.'~~.:. a.o:t~_ .
D,=16.4X 10..
+O'OOO..9.3.
0.805 0.305 +0.00:37
,Q.OOO1. .,g.OOO()§
O.00058+0.000:n
•
]'"~()'376XI0-5
+o.ooom~
0.014
'Vhl'll m=O.laO lind 1"-0.1:30
;~~~ +O.OOO~(j.
5
Dt=18.7XIO ..
[
1..;;:-1
0./1;) n.II!)
.
5
. ] ::::O.a05XlO-
+0.0016
0.0001
0,OOO()2
0.O(lOG3 +0.000035
WIH'II m= o,nna ilnd
Dt::-';:21.SXIO.
fo
[.I.
I. .Oli
.
WhC'1l m=O
nlldl~
+O.OO()(i,g
0.014
r= O.O(i\)
131.2
+0.0(,,1 045.
. 1=0.410XlO-o
+ (I.()OO~_
1.00
+0.000::
~
• 'J
O.OO();.>S +0.000a8
0.0006/+0.000004
0.014
0
V''''''22.5XlO'''[''''.'l
1 a.'.I;i-+ O
•
. ]",.,().174XlO-O
"~-+
0.445 9..145 +0
•
O.(~~_~+ 0.000,,4
0.00071 +0
0.014
TIll' dl'\'ill~ dilrll~ion Ylllu{'s ]), l'hnll~(, but slig-htl.'· with II dt'crensl' ill
moisluj·(, ('(jl)tl'l\l; (lxl'('\>l nt Y(II'Y low moishll'(' ('ontt'nLs. This is
bN'llUSP til(' D. yuitH'S nn(\, ('ons('(pH'lltly, till' D./Vrc Ynitll'S inel'cns(\
nppn'einbly with d(l('l't'l1sing- moistul'(' ('ontC'llt down to ubout (j P('I'­
('(lilt ll1oist\t[{, rOlltt'llt nnd th(,l1 (\('('I·(,IlS(,. Ilcrnill.
This, in tum, is due
to lh(' fHct thnt lIw rnt(, o( dlllllge of TP!tlti,\TC Yl1pOI' PI'('SSIII'l' with
Chflllgt'S ill moistlll'(' ('ont('nt (p. 58) O('(,III'S in til(' SUIll(' fushion. EV(11l
though till' efl'pcth-p t1'llllsiP11 t ('('U wull ('Il pilInl'Y ('I'OSS sl'ctiQII d('('I'('IISl~'l
nppl'h'inbly with d('('l'(lusing moishu'(' ('.Qntpnl, th(' filet thn!. th(' l'l'ln­
lh'~ YI1.pOl'-PI·('SSUl"(' grndil'llt Pt'l' unit 1l10istUl'('·eollt('llt gl'fldil'nt is
st('('P('l' 11 t thl' Imn'I' moist 1Il't' ('Oil h'n ts l'ompl'IlSnt('s fOl' th(' fol'llH' 1'.
'PI\(' DI nlllH's Ul'(' ('ontrol\(>(\ ('hil'f1y by bOllnd·wl1lpl· difl'lIsion I1t till'
hig!H'I' moistUI'l' ('Ollil'IlIS 1I.11d by wnt('I'-\'np(lI' dill'usion Ilt till' low('r
1ll0lStll\'(, con t<'11 t8.
Fig-uI'(' 11 g-in-s thf,sl' YnltH's for tilt' trnIlS\,('I'S(1 drying diffusion
l'Oilstuut rdlltiy{' to unit dillll'nsiOlls of the wood plottcd ngl1inst thc
•
PAS~;\(lg OF LIQUlPS\ VAPOHS, ETC", T.ll Bonar SOFTWOODS
1ll0istUI'l' ('olll('tlt
•
ft)I: lht, wood
with 11
swoll('I1-yo\nn1l' sIw('ifie
25
gl'Uyity
of O,:3ti5, just; ('onsidl'I'l'd, nlld ftW wood wilh othl'l' SlW('ifie gl'ilYities,
li'itrul'(' 12 triYNi tlw IIY('I'Il"l' t 1'I111SYPI'SP dl'yilw d ifl'usioll ('ollstnnt in
I,(.{iltion to~ unit din1l'IISio~ls of' tht' wood' fOl~ wood til'it'd fl'om tho
1,0
09
~
~'
'....-
0,8 ~
..
,..- I - -
""-.; ~
I-..
~
~
•
~ 05
_."....
~
t::
~
~ 04
~ ~ ~
~
~ ~
~ O.Z
f-;
-­ .-
,_·t·-
~-,
~li
sp. CR.-O,S65
...
... -
.,-
-- V p:::::
1---.
~Vv:
i
V
-
V
Z
4
6
~
.
.-- -..
..
._--'
~~
-- ---­
8
-~
~'49
J'p.
~ oo r---
.--r---!tT
V
~
".­
,
I
I
I~ v . . . v
o. f--
~
~ 0.3 ~
.,
}f.
0.6
-
v
V
V
~
,J~>
/
~
~
j...,..~,.
V
~ ~ 0.7 :::-:
- V'
07.:--- .cr­
--1--"-'
.
1---
i---
o
I
,6 O
.-0
I""'
1
0--. .
CR, -0.80
.-0
~
10
12
/4
f6
18
20
2Z
24 26
28 30
MOISTURE CONTENT (PERCENT OF OVEN-PRY WEICHT)
ll.-Trnnsvcr:lc drying diffusion constants rclativc to unit dimcnsions of
I hl~ WOQd. for wood with different Hwollen-yohlllw specific grnvitics and Illoistnrn
contents dried at. ;,10 0 ('.
1"IOUltE
•
fiu('l'-sl1lul'ntion point to dill'Pl'pnL IW('I'Ug(' moistun' ('onlcllts, Thcf.,o
YHlm's \\"(,1'(' outnitll'd fl'ol1l til(' 11I'l'11 undt'I' the CUl'yes of figm'c 11
from till' fibt'l'-snlul'lltioll point to the yarious finlll cquilil)l'iUl~
moistul'e ('ontl'llts,
714::i::iO .'•. -17,·,-4
26
'l'ECHNICAL BULJ...B'l'IN o~o, U. S. DEP'l'. OF AGHlCUL'l'UmJ
•
1.0
j
I
P. GR.-O. Z5
0.9 ~
V
1--.•.
V
.~
l---' r-­
V
~~ .
­
-0
I
I
---.-
CIIL CULII TEO FROM
o -CIlPILlIIRY-STIWCTURE CONS/PERil TIONS
.-ORYING OATil OF MARTLEY
-- 1--1-,
I­
>-=.
~
t--
--.-
- •
!
1-,•.
~,
SP. GR, - 0.365 ..n.
I"
i·'
-
..-.... .
-0
f
~
I
•
SP. ER. - 0.49 I
.. ~
+--
•
SP. §.R. - 0.60
.,
o
o
2
­
•
-
..n
,
-'"
I I I
~
SP. GR. -0.80
4
6
8
10 /2 14 16
18 20 ZZ 24 26 28
EOUILIBRIUM MOISTURE CONTENT liT PRYING SURFIlCE
(PERCEtIT OF OVEN-PRY WEIGHT)
30
F[(1~lIu: 12.-·An~rngo trnns\'ol'So drying diffusion constants To\ativG to t.ho di­
mensions of tho wood, for wood with differont swollen-vohullo spocific gravities
dried nt 40 0 C. from tho fiber-sllturntioll point to clitferellt equilibrium surface
llIoistu ro COil ten ts. .
•
PASSAGE OF LIQUIDS, VAI'ORS, ETC., THUOUGH SOFTWOODS
27
The trnllRV(ll'RC dryin~ d in'usiou vnhH's in figur(' 11 nnd the. nvcl'ltgo
tl'nnSVl'l'S(1 (iI'ying din'llSlOn valut's in figUl'(! .12 vary ll'ss with moisturo
content for ,\rood with high specific gl'ltvities tlilUl 1'01', wood wit,h,
low specific gmvitil's, This is bccnus(l vnpo,' difl'usion pl'edomil1lttos
in wood of low SP('cWC gmvity, nnd vapor dill'usion is pl'opor'tionnl to
tit(' vnpol'-pl'('SSUl'(' grndil'nt rnth(ll' thnn to til{' moistul'e-<~olltl'nt
gl'ndi(ll\t" in which tN'IllS til(' diffusion is ('Xprl'SsNI.
~(nl't1oy (80) hilS l'xPl1l'inwntully dptt1rmilwd tho !t'IUlSVNRO drying
di/rusion constllnts I't'lut:ivo to unit dimellsions of tho wood for Scots
pille with It dry-voitmu' speci/it' gl'nvitv of 0,56 (gl'l'(~ll-volume spceifie
gl'llyity of 0,'19) lit difl'l'l'('nL 1ll0istUl'(' eontl'llts, His vnlues show n
sOll1(1whnt gt'pnlpI' d('(~I'('tlse in the difl'usion vuitlt'S with decrcnsing
moisture ('ontl'nt than tho t hl'ol'eti('ul vnitws just given, It is,
how('v<'I', p()sBibl<, to dmw 1lI0iStlll'l'-gl'udil'llt eurv('s tlll'ough his
(lx(wrinwn t.lll dntn thnt will giV<' PI'il('ticnlly linl'nr grndiell Ls OVOI' the
nu\<,p 1'01' whidl the eOI'1'('spon<iing theoretienl D, CUl'VC of figure 11
is q~tit(' f1nt. This shift in his gl'ltdil'ut eUl'VC, which is ontirely within
tilt' I'II11gt' of H('t'uI,'ney of his (I II t.lt, greutly improves the ngl'eement
b(\twN~1l his ('XIWI'illwntnl Ynlll<~S nnd till' theol'(lt;ku.1 vnlues,
AV(,J'ug(~ ll'IIllSYl'I'S(' drying difl'usion constnllts relnt,ive to unit
tlinll'llSiollS of tIl(' wood W('J'l\ clllruhttl'd Il'om ~lnl'tll'Y's (80) rnte~of­
dl'yillg datil JOI' dill'l'l'('n LSUl'fuc(~ moishu'('-ConLeut boundary conditions
by ('OllBidl'l'ing till' moistun' gl'lldil'llt nerosS the sections to be linenI'.
Jh't'llus(' of the fuet that Uw moist sid(\ of his sp('Ciml~lis WIIS not in
('(luiliuriuIH with u'lit 1·t'ln.tiVC "n.p01' Pl'l'ssurc, his equilibrium smfacc
moisture ('ontents tnkl'll from his gl'IHli('nt cmv('s were us('d instend
of llll' theorelit'1I1 Jibel' SlltUl'lttiOll point, for the high moisture-content
boulIdm'y eOllditioll.
U)(' I' points OIl his rllte of moistur~ loss­
cqttilibr'iulTl Yl1jlOL' eon('('lltrntion curVl'S w(lrc trnnsposed to rnte of
moistUl'(1 10ss-tlloistul'(' con tent curves by convcrting the concentrations
to l'l'lntiYt' vnp01'-]H'PSSUl'C tt'rms nnd then to moistme-contcnt tenns,
using the dtttit giYllu 011 pngc 58 of the Appendix, The nVl'l'itgo
trltllsY('l'sn drying difl'usioll eonstnuts D, were then cnlculnted from
the Sll'luly-stalt' difl'usion (l(luMion
•
•
o
D --. Q~-.
r-- [/(Am)
(9)
in which Q is tho rnte of loss of moisture in grnms per squnre centimeter
PN' sl'eon(\, (£ is the thiekness of the speeilllell ill centimeters, g is tho
nWl'ilgo spl'eifi<~ gl'lwity of tho sp('cimeu, nnd Aln is the chnnge in
1l10istlu'o content between tho two fnces in grnms per gram of dry
wood, '1'I1('s(' t'nlculnted vnltH's fOl' speciml'l1s- Nos. 1 nnd 3 are also
plottNI in figure 12. 'rho)' nrc in ~ood ngrcem,ent with the COl'l'es­
ponding th~\oreticnl vnlucs for wOOci with tho same spedfic gravity
(OA!) on n swollen-volume basis).
Thl;'! Ilvl'l'Ilge trnnsverse dl'~Ying diffusion constnnts nt 40° O. relative
to ullit (limellSiol1s of thc wood from the fiber-sntllJ'ation point to the
Oyen-dl'y condition nrc plotted ngninst tho specific gmvity of ,tho
wood in figure 13. These vnIues were obtnined from the complete
nl'en und('[' tho curves of figmc 11. VnIues cnlculnted {l'OIU the
drying dntn. oJ BIl,teman unci Hohf (6) for SitIm spruco are also given
in figul't) 13. III cnlculating the diffusion values given i4 the pnpel'
•
28
'l'ECHNICAL BULLETIN 929, U. S. DEP'l'. OF AGRICULTURE
of Bateman, Hohf, and Stamm (6) the final moisture gradient wns
used ratlwr thnn the e·tyt'ctive mcnn moisture gradient over the whole
drying period. Strictly spN1king, this would be COlT(~ct only under
steady-stnte conditions. Although the relative vnlucs are correct
0.8
•
.
.
\
\
CALCULATEIJ FROM
o -CIlPILLARY-SlRUCTURE CoNSIPERATIONS
e-ORYIN(; OIlTA OF BATEMAN IINIJ HOHF
\
\
~
\~
\\"'­
~ "'-..
~
~ r--­
o
0.2 0.3
0.4
0.5
0.6
0.7
0.8
SPECIFIC GRAVITY OF WOOD (SWOLLEN-VOLUME BASIS')
13.-Avl'ragc transverse drying diffusion const,ants relative to unit dimell8ions of the wood, for wood with difTerl'lIt swollen-volume specific gravities when dried at 40° C. from the fiber-saturation point to an oven-dry condition. FIGURE
fond, consequl'lttly, the conclusions ch'awn therefrom, the actual
diffusion values nrc too high. This can be shown to be the cnse by
calculating the drying-diffusion constant from the remaining evap­
orable water according to the method described later (p. 31).
•
29
PASSAGE OF LIQUIDS 1 VAPORS, E'l'C., THROUGH SOF'l'WOODS
•
The diffusion values giv(,11 i~~ table 1 of the paper of Bateman, Hollfl
and Stamm (6) were lWHee divided by the avcragn correcting factol'
3, 17 nnd by the sppcific grnvit;y of tho wood on a swollen-volume
bltsis to COIlV('rt il'Olll a gram per c('utimcter P(\!' second basis to a
square c(mtiuwtet, pPl' st'colld basis, Although these values fall
somewhat below the theoreticnl curve1 they 1'n11 on a curvc parallel
to it,
'l'l\(' efrect of chung('s in the (\t'ying tempel'atmc upon the transvcrse
drying diffusion (~onstnnt, l'plutiYe to unit dimellsions of the wood, is
giYl'1l in figul'(' 14, As ti\(' tempNutul'(\ incl'('ns(ls Ute vlI,por diffusion
3,5
I--
•
II
kC k\\
1\
\
If
~
[7 V
l7 I.-V
,-
80·C,
I~
--,
V i>--.
---
f--
.
~
"'"i'--<
~ 60·C.
t-
.r.
......... ~ t---
l-
t--- ti°·c.
-'"'
v
40·C.
zs'c.
-"
'l-- t-­
G 8
W n
n m
u u u u
°0 2 4 MOIST[JRE
CONTENT (PERCENT OF OVEN-PRY WEIGHT)
~
~
~
n
FIOUlm 14,-Tmllsvcrse drying diffusion constants relative to unit dimensions
of the wood, for wood with 1\ swollen-volume specific gravity of 0.365 all(\
ditferent moisture contents, dried at different temperatures,
•
becomes the pl'Nlominn,nt fnctol', bl'cause D. increnses morc rapidly
thall Dw, 'l'he pl'(mlilll' slutpe of the CUL'YPS Ilt the higher temperatures
is In.l'gely the l'l'sult of the 1l0ulilH'ar cOllvei'sion of the VU,POl''''pl't'ssure
gl'lldient to moisture-content gl'ndient tel'ms (p, 58).
'l'he UY('l'I1gc tranSVl'I'SC drying diffusion COIlstltutS relative to unit
dimensions of the wood between the fiber-saturation point and an
equilibl'iulU surface-moisture content of 10 percent were calculated
f!'Om the Itl'PIt undN' the curves of figure 14 down to n Il1oistu~'e content
of 10 percent n,ud from similar CUl'ves for wood with different specific
30
TECHNICAL BULLETIN 929, U, S, OEM'. OF AGRICULTURE
gravities, 'l'hes(~ values arc plotted ill .figure 15, The curves indicate
that the 1tV!,'l'fige difl'usion values increase apPl'eciubly with an in­
crense in telllpCl'ntUl'e, 'l'his incn'llse is, as previously stnted, greater
for wood with It low specific gmvity than for wood with It high specific
gravity because vapor difl'usion is greatcr in tho forlllCl' cuso, and
vapor dill'usion increases Illuch. more mpidly with increnses in temper­
atw'o thlln the bound-wnlc1' difl'usion (fig, 10),
•
~3,Sr---~.------.------r------r-----'------,------r----~
~
"< I..i ~
~3.0r-----~----~-----r----·~------+----f4-----~----~
~
CALCULATEO FROM
I
o-CAPILLARY-STRUCT(JRE CONS/OERATIONS
/
.-ORY/fIIG OHIl OF SHERWOOO I/NO COMlfIIGS
I
ARROW SHAFTS INDICATE EXTENT EXPER/- 1-,f---I----I---1.'-1
MEfIITI/L POINTS OEVIATE FROM THEORET"
ICAL VALUES
<.,
I
~
~
~ Z.S
~
~
::.:
I;)"Y,'
S! 2.0 t-----I------t----+-----I--,~~ "/-+------j------ir:------I
~
\J
~
~.
?
~ 1.5
~
'"
~ /.0
~ •
t------I----.-t---.:>.£---t-----t­
~
">::
~ O,Sf-...J.l.=--+----+-=~q-----::J~
l<J
I.:>
<:to
~. 0 U~~±==t=J~----L~
~
ZO
}O
40
50
60
70
80
/JRr/Nfl TEMPERATURE r'l;.)
90
100
15.-:hemgc trnn!;\'cr$C drying diffusion constants relative to unit
dimensions of thl' \l'ood, for wood with difTen'lIt swollen-volume specific gr/\\'i­
til'S dried at di/ferNI!. t~ll\perntures, under rclative vapor pressure conditiolls
thllt gh'c 11 surfl1t~c-llIoisture content of 10 percent,
FWl"lu;
Tuttle (55), Kollmann (25, 2(]), Shcl'wood (35), and Sherwood and
Comin6"S (S6) ha:n calculntl'd tl'illlSY('I'SC drying diffusion cOllstnnts
rclative to unit dinlPllsions of tIll' wood from }i'ouricr annlysis (21)
consid('l'utions on til(' nssumption thnt the dill'lIsion lllw is npplicllblc
over the complete moisture-coil tCllt I'Ilngo and thn t the difl'usion
constant does not VIlI'Y with llloistlll'c <:outout, Tuttle made his
cnlculntions from ll10i'stun'-distribution data, whol'('us the other
investiO"l1 tors uSNI l'nte-of-cir-ying dn tn,
Tuttle (55) hns shown thnt the drying diffusion constant D cnllbe
obtnincd from thll distauce into the wood a. o at which the moisture
•
PASSAGE OF LIQUIDS, VAPORS, ETC., THROUGH SOF'l'WOODS
•
31
contl'llt nft.!'r tho time t is the fmction 8 ('1) of the initial moisture
content, thlls:
(10)
Th(\ ynlll!' of q COlT!'sponding to 8 (g) can be determioNi f!"Om the
probability intl'gral
.
2
8('1)= .J;
f
q
u
e-!3 3d~
(11)
with the liSt' of tllbks (28).
N l',,'.IIIl1n (81) hiLS shown how th!' diffusion constnn t ('IUl b!' (~nl­
ClilutNI f!'OIlI dJ'yill~-J'lIt(l dntl1 for n eOlltillllOliS sinh. He hILs dl'­
Yl'lop~·d n 1'l'IIltionship bdwN'n the fl'lldion of the Ol'i~innllwnpol'tl,Lh'
wnl('I' .E IH'ld by
tilt' dl'vim!
mntl'l'ini n.t time t, nnd :l}?,t,
•
J.,
a­ in which D is
tlw diffusion ('ollstnnt nnd a is til(' thickness of t.he sln.b, The rela­
tionship is l'XPI'PSSNi by n eomplil'ntl'{i ('xpn.nsion equntion which
conYI.'I'~es Ilt slldl tll'nt(· Uilit only n. fl'\\' tN'ms hnYl' to be us('d, Sher­
wood alld Comings (86) iliwe simplifil·d the relntionship by using
ollly one tel·lll. EXc("pt for very short (iJ'ying times, they have shown
thnt
•
•
(12)
in whieh (/. is thl' thicknl'ss of tlIP slnb 1\11(\ E is Lhe fraction of the
ol'igillnl (lvnpol'nblp wnl('I' I'pnlltillillg in til(' wood nt the time, t. Ko11­
munn (to) lIspd nn equation similill' to equnt,ion (12).
It will bt' of inh'I'est to l'ompnre thl' ('nk'ulnted nyernge drying
difl'usion ('onstants J'('\Min to unit dimension of the wood, obtained
by lIll'S(I in Y{'stigators, with tlH' tiwon'tieul IW(,I'U~t' vnlues culculnted
fl'om l'npillnry sll'Ul'tul'l' l'onsidl'l'u,tions, <'speeiuhy since the ynlues
('nlclIlntt'd ft'oIll drying dntu hnve been questioned hccnuse of the
nssulII plions Oil whi('h they nl'l' bnst'd.
Cltkuint('(i nV('I'ltg<, (iJoying difl'usion constnnts reln.tiye to unit
dinwnsiollS of till' wood, ohtnilU'd by Sherwood al1(l Comings (36)
from drying dMn for sugnl' piIll' with 11 swollen-volume specific
grllYity of 0.375, nrc plotted ill figure 15 togl,ther with the theoreticnl
"nlnl's for wood with 1\ swollen-volume specific gl'lwity of 0,365. The
n~n)l'ml'nt Itt nIl the tl'lnperatUl'es t'xcept the highest is t'xcellent.
h,ollnuUlII (26) hus culculnted the ratio of the drying diffusion con,...
stnnt ttt 50° C. to the yulue nt. 100° C .• from the drying datu of
Egner (10). He obtnined a rntio of 0.17. The theol'eticnlmtio for
wood with 1\ swollclI-yohmle specific grlwity of 0.365, taken from
rigul'l' 15, is 0.16.
Similar compnrisons between. the drying diffusion constants cal­
culntpci fl'ol11 cit'Ying datn and the theoretical values calculated from
capillary structure considerations are given in figure 16. In this
32
'l'ECHNICAL BULLETIN 029, U. S. DEP'l', 01-' AGlUCUUrUllE
2.0r---.-~-----.------------------------~
J.81---\-~
CALCULI1TElJ FROM
O-CIlPILLARY-STRUCTlJRE CONSIOERIlTIONS
• -ORYING DATA OF KOLLMANN
~- <--If)-ORYING OATA OF BAT£MAN ANO HOHF
!()-ORYING OATA OF MARTLEY
ARROW SHAFTS INDICATE EXTENT
EXPERIMENTAL POINTS' OEVIATE
FROM THEORETICAL VALUES
•
•
0.2 I - - -__-I-_ _
~~
O~----~----~------L------L----~
____~
0.2 0.3
0.4
0.5
O.G
0.7
0,8
SPECIFIC GRAVITY OF WOOD (SWOLLEN- VOLUME BIISIS)
FIG VllfJ 16.-:\ \'erllf!;e t mnil\'('n;t;' drying diffusion l~onstants rclativc to unit
diul('lll'ions of the wood, for wood with diffen'nt swollen-volume sperifie gm\'i­
ti('s dried. at difTl'r('nt telll!l('rlltur(';'; nndpr rrJuti\'l' vapor-pressure rOllditiolls
\\ hich give n snrface 1ll0islUrl,! content of 10 percent.
•
PASSAGE OF LIQl'lDS, VAPOUS, E'TC" THHOUGH SOFTWOODS
•
•
•
33
ensl' spl'cific gmvity Cllrves mthel' Uum tt'mpt.'rntUl'(' eUl'\'('s IUl.Ye
bN'n e1m,wlI, IlIdu(\('d nn' vnitlt's cnlculnlt·d from tlw dl'yillg dnla
of Bnl{'llllLn IUHI Hohf (6) fOl' completl·ly wlltel'-sllLumled Sitka
SPI'Ut'(\ dl'it'd nt yttl'ious t('lIlPl'I'ltttlrl'S, fl'om tI\l' sleudy-slnLl' dl'ying
dlitn of ~lttrtl('y (30) fOl' S..' ots pilH', Ilnd Cl'om tlw dl'ying dnJn of
KollmiLnn (ftO) fOl' tI\(' a \"(\l'I\ge of St'Vl'll slll'cimens of SPI'U('(' dl'it'd
nt ()3° C,' o nt' spl'eill1l'n of fil' dl'it'd nl 53° C" I\(\(I 01H' specillH'n of
pill(' dl'it,d at 50° C, l'nfol'!.unately. KollIll1ll1It did 1I0t give tho
slwl'ifi(- gnwitit's of his woods, so tWl'I'ngt' vuitll'S fOl' the species
W('I't' us('d,
In ligurt' l i tiH.\ tiwor('tien,l nn'l'Ilgl' tl;tLllS\'('I'Se drying difl'usion
('onsi.nnls r('\nth,(' to ulli t dill1l'l1sions of til(' wood IU'C pIOlt,NI in
l~lIglish units against thl' spt'eifie gl'lwily of thl' wood, t,ogetht'I' with
VlLhll's enleulalNI from unpublisll(,d dl'Yillg-l'Ilt(' datu: by LOllghborollgh
(Fort'S!' l'rodllels LlLbomt.ory, (1, S, Dl'parllll(,llt of Agl'ielllt.ul'(·),
A single \'nlul' (UPP(,I' Sitka spl'uel' "lllu!') WIIS ('tticlIlnLl'd by Tuttle
(55) frol1l lIIoislul't'-gl'lldil'lIt. dutu,
'l'he tl'llllSYeJ'Sl' dryiJl~ difi'usiou constnllts j'{·lntiv(\ to unit. dinwnsioJls
of Ow wood t'lllelllat{'d from d.rying dulu (fib'S' 15, lG, nllt! l7) nl'(', in
g(,I\(~.I'tII. ill l'x('l'll('nt ngrl'ell1l'llt with till' till'or('tielll Yllitll'S cnleulated
fl'olll {'upillnl'y structure ('onsidl'l'ntions, TIll' ngr('('JllPl)t not ouly
indi{'lltt,s th(' \'ulidily of l'qulllion 8, but ulf;o shows thllt Inrg(· vuria­
lions do nol ('xist. ill tht' ellpilllll')' stru{'lul'lll t'OIlStlluts tlmt. 1lJ'(~ l'fI'HC­
tin in {'oJlirolling rilles of drying of the hl·!l.I'lwood of till' vllriuus
softwoods, 1'he dllttt also indicllt(, thnt th(' two assumptions 011
whkh tltt, vllhll'S ('ukulutl'd from dl'}'ing dlltn nrc bns('d Ill'll nt It'ust
slIfljeientlv IIl'I'III'ttll' thnt t hl')' do lIOt CUuS(~ Ilppn'ciable (,ITors in the
l'uleulllh,d Yllittl'S, Thl' assumption thut difl'usion is dft'l'tiV(' nt all
moistuI'(' eonlt'nls will be consid('J'I,d luter, TIll' nssllmption that
tlH' difl'lISioll "!litH'S m'l' ill<il'}Wlld('nt of til(' llIoisluJ'(' contl'lIt of the
wood is shown in figul'e 11 to bt, l'ellsonubly uceul'l1te COl' nil but the
very light('st woods nnd for nOl'mnl drying sllrfnc('· bounllnl'y con­
ditions (6 pl'rCl'nt. moistun' contl'I\t 01' nbovt·), The 40° C, curve
of fjtrlll't' 16 Ilull thl' ('unt' of fj"ul'e 13 dl'yiate f!'Om l'uch othcl' only
for tIll' wry 10\\'('S( spl'cific-g~IlYitY vnitll's although thl' fOl'm('r
rl'pl'l'sl'lIts tIll' tWl'fng<' diffusioll vnl\H~s fl,dm the. fibl'r-salumtioll
point lo to Iwrel'nt moisttu'e content nllli till' Inth'r 1'(,PI'PSl'IltS the
a\'l'rng<\ from tIll' fibl'I'-stttul'l1tion point to the oven-dl'Y condition,
B('ctlllse of this it wns Ulll\('('('ssnl'Y to takl' into 11CCOlUlt the
bOlludttl'Y eonditiol1 diffl'I'('tI{'(,s ill compnring thee transverse drying
difrusion vllltWS enleulntNI from drying dnt!\; with the theol'(\ticnl
ynlues obtnitH'd from cnpilllll'Y structure cOllsidel'ntiolls, The duta.
ilHli{'utt' thnt the use of an'l'Uge diffusion Yllitws in pInco of nct.unl
yultlt's 1l<i('qulltt'ly represents the true conditions for the pUl1)ose of
cnicuillting dryillCT I'ntes,
C!\. Yl'rngl' tr~l1ns~'ersc drying diffusion eOllstants relnth'c to unit
dimetlsions of the wood enlculuted from l'nt('-of-<h'yillg dntu by Sher­
wood nnd Comings (S6) nnci Loughborough und Peck Q for n, number
of different hnrdwoods are gin'l1 in figure 1$, together with the
theoreticnl ynlues cnlcuInted from capillnry structure considerations
~ Lot'GIU1onot'OIl, W, K" ANI> PECK, E. C, U, S, Forest Prod, Lab" Madison,
Wis" unpublished data, [Il, d,]
7H:i:illo--n--:i
34
TECHNICAL llGLLETlN 020, U. S. DE1'1'. Or' AGIUCULTUltE
ZQ ....- - - - , - - - - r - - - - - r - - - - - - , r - - - - - r - - - - - ,
~/8~--4r~------~------~-------L------~----~
~
CALCULATED FROM
•
~
0
~.
-CAPILLARY-STRUCTURE CONSIDERATIONS
-ORY/NG MTA OF LOUGH80ROUGH :::::i /6 I----\--t--ARROW SHAFTS INDICATE EXTENT EXPERI­
~
MENTAL POINTS DEVIATE FROM THEO/?­
~ ETICAL VALUES.
~
!
~ 141----\+-----1----1---+---!----I
~
~
~ ~ /2
~
~
f--\-­
~ ~ 101---\+-\--­
~
~
,
c...,
~
~ I
~ 3;.:: 8 1---\--+-\---\
•
"t
~ ~
~
~
Cl..,
~
~
......
)..
6
'-I
'-I
<::;)
--J
~
~
q; ~
<:;:)
~
~
"'t
2
f-----­
OL---~--~---L--_~
_ _~_ _~
0.4
0.5
o-.i
0.7
0.8
SPECIFIC GRIWITY OF WOOD (SWOLLEN- VOLUME BIUIs)
0.2 0.3
17.-Avcragc t,rans:vcrsc drying-diffusion constants relativc to unit
dimcnsions of thc wood in Englh;h units, for wood with differcrrt 5\\'0Ilcn­
volume specific gnwities dried at differcnt temperatures under relativc vapor­
prl.'&!ure conditions which gh'c a surfacc moisturc content bf 10 percent.
FIGUItE
•
PASSAGl'! O:P LIQUIDS, VAPOHS,ETC., Tl:(HOUGl:I SO.F'rWOODS
•
35
2.0.---..--,.....,--.,....----'T'----------.
CALCULATED FROM
O-CAPaLARY-STRUCTVRE
CONS'/DEflATIONS
.-DRY/NG PATA
ARflOW SHAFTS' INDICATE
EKTENT EXPERIMENTAL
POINTS DEVIATE FROM
THEORETICAL VAL liES'
•
•
OL---~--~--~-~~
~2
~4
~5
_ _ _L - _ - - J
46
~7
48
SPECIFIC GRAVITY OF WOOD (SWOLLEN-VOLUME BASIS)
•
~3
lS.-A,,·erngc t,ransversc drying diffusion conetants relative to unit
dimensions of th~\ w(lOd, for wood with dilTerent swollen-volulllc specific gravi­
ties dried at dilTefl'nt temperatures uuder relative vapor-pressure conditions
which gh'e a surface moisture content of 10 percent. (Theoretical curves for
softwoods, points for hardwoods.)
FIGURE
36
'l'ECRNICAL BULLETIN 020, U. S. DEP'l'. 01<' A(UUCUL'l'UHE
for softwoods. A singlt~ value for onk was ('alculni!.'d from th!.' stt'n<iy­
stlll(\ dulu of Stillw('ll (54) ill tilt' SUIll(' mlmHt'I' us th(' YflItIt'S ('nlculnted
from tIlt' stpnc\v-stnt(' dntn of Mnrti<T (SO) (p. 27), The ngr(,l'/llent
bl,t Wt'('n lilt' ('xpt'riIllPntul 11111"<Iwoo<l Ylllu('s nnd thl' tJl('or('t.icnl soft­
wood Y!lllles is llItturnlly not so good as tIl(' ('ompnrisons ill figml's 15,
Hi. ntH.! 17, b('cllus('. of tlw difft'rt'()('c in CII pillnry st1'ud\ll"(' lwt W(,(,1l
softwoods lind hardwoods, '1'11(\ qunlitn tive ngTl'(,IlH'llt indicnt!'s,
ho\\,('\'('(', thnt Uw Clmtrolling cnpillllry dinH'nsions Ill'e, in g(,lH'rnl,
of the Bnlll(' O/"d('1' of 1ll1l1"r'Jlitud(" 1'11t' dutll nlso su~gt'st thllt thl'I'(\
is vt'ry lil,,'ly n gl'P!t('I' variation b('tw('('/I tilt' cnpillnry sirlwilll'lll
dillll'lISiolls of thl' Y!lrious hllnlwoods OHm b('L\\'(,l'll the YllI'ious
softwoods,
('nfol'lunn\(,ly, 110 dutil, IU'(' iwni\nbl!' CO/' til(' enpillnry stru('tul'(~ of
sapwood, 'I'll(' (,{fl'('Uy!' fm('tiolllll('ross S('(.'Oon of thl~ P('I'll1llJlt'nt pit­
n,ll'lllhmlll' pOl'l'S fOl' tmnsY('rs(' pllssngl' '11 is, ho\\,p\'el', Mit' only diu}('I1SIOIl thil.t would bt' ('x)(>dNI to vary more thnn twofold, It mIght
bl' un}'wlH'n' fl'om t('nfold to n lhous!\ndfold gl'l'atl'r for sapwood t1mn
fOl' IH'urlwood, 1£ it is nssulllNI t.hllt (ll is 100 Liull's us gl'put; fOl' snp­
wood IlS fOl' Ilt'nrtwood, tht' Il,\'(\rng(\ b'll.lIsv(>t'S1' <h'ying diffusion ('.011­
stnllt ('t\lt~tiV(' to unit dilllensions of tI\(' wood would be iIlCI'(~IlSl'd 2,5
liuH's in til(' ('IIS(' of wood wi th a swollen-\'ohllll!' spe('ific gmvity of
O,3()5lwing (It'i('d nt 40 0 C, from tilt' filwr-snt\ll'ntion point to the OVl'll­
dry ('ondilioll, If lht' (h'yillg W('I'(' l'nrrit,d out nt n higlH'r telllp('rn­
t\l~'e, th(' iIl('r('nsl' in V, dut' to nn ill('I'('ns(' of n hlllldl'('dfold in 91
would bl> still gl'ent.er, silll't' ilH'l'pusing q, ilH'rl'ns('s til(' pl'Oportion of
tin' diffusion whkh is Ynpor diffusion, nnd inl'I'ellsing til(' telllpcmtllrc,
il\('rPIlSl's \'npor diffusion ('onsic\prnbly mon' than it inerenses bOllnd­
wnt('l' diffusion (fig, 10), LOlIghbO/'ough hilS ('nIt-IIInted the Ilvemge
drying diffusion ('onstunt n·lnlh'(\ to llllit dimensions of the wood for
the sapwood of loblolly pine from rnt('-of-<lrying meaSllrem('nts Ilt
71 0 C, He founel it to b(' about lhree times the vnllle for the henri­
wood (fig. 17) dl'i('(l under the san1(' conditions, It thlls npI)enrs thnt
if I must bt' Ilhou t 100 tilll('S as grl'll.(; for lhe snpwood of loblo Iy pine ns
for till' Il('/u-twood,
Tnl.llSY('I'Sl' drying diffusion ('onstnnts rl'lntiv('. to unit diml'llsions
of tI\(' wood WI'I'(' ('nleulnll'C1 fox s('Y('ml /"('du('ed nil' pressur('s from
l'llpillnl'Y stnl('lul'(1 ('oll$id(~I'ntions, Dr is gl'('utIy in{'l'()nsed by a de­
('I'('USl' ill the 11.11' PI'('Ssurp (pquntiol\s 3 il.lld 5) wherell.sDl/lnnd the cnpU­
liu'y diu1l'nsions ur(' 111111 ffl.'(.. ted , As tIl(' pr('ss\ll'C is n,du('ed, vnpor
diffusion I\l'('ounts fOl' II grl'n.tl'r nnd gn'lltt'!" pl'oportion of thc totnl
diffusion, BN'/lUS(' of this the lrnnSYl'I'S(' dryiug diffusion constnnt­
1Il0iSttll'(' <:ont('lll ('lIIT('S giv('11 in figme 19 nssllme Il. p('culim' distorted
shnpp nllow Pl'l'SSttres with n Illllximlll11 cOITcsponding to thl' infl('ctioll
point of the 1ll0istlln' ('ont('nt-n'lllli\~e vapor pressure (.'UI'Vl'S (p, 58),
'l'hl' Iln'mge tmnS\'('I'Sl' drying diffusion constll.nts relll.tivc to unit
diInNlsions of th(\ wood fOl' diff('r!.'nt nil' pressu/'{'s obtniued from the
nn'll. under Ole {'ul'yes of figure 1!) b(~twl'en the fiber-sn.tUl'lltion point
I\nd the own-dry condition nrc plotted in figllre 20 agllinst the air
pr('88 II 1'(>. A \~('rnge lmnsY<'I'St' (h'ying diffusion constnllts rclntive to
thl' dimensions of the wood thnt Wert' cruculnted .from the drying
IllN1SUI'('Ilwnts of Bnt('lllnn il.nd Holte (6') 1l1nde under reduced nir­
presSUl'(' ('onditions 111'('. nJso plotted ill figum 20, Although the
ngl'('Nll(,llt bl'twt'ell the two cU\'yeS is not so good il.S might be desired,
•
•
•
PASSAm~ OF .LIQt:ms, VAI'OHS, ETC" THHOUGH SOFTWOODS
•
37
the, (.'U1'\,(,S do hn n' the SiUlW fOI'In. The filet Umt tJl(' ytllu('s cnlcu­
latNI fl'om LIlli drying dnln d('\TjnU, mol'(' nnd IlIOl'(' fl'om the theol'(~ticlll
nlhl('s us til!' pr('RSll1~l' is I"Nhl('('(1 is not slll'prising bt'l'IHlS{' 110 lul('qunll'
Illl'lUlS of swt'('ping U\(, moistl1J'e awny fl'o111 t h(, drying SUl'fnc(' WitS
5,0
p....." v
\
/
4,5
II
\
1\
\
I
1\
I
I
\
i\
•
\
V 0......... "\
Ii (
\.
/
l
)
/
0.5
/
'/
D-
(~
o
o
~
2
­
4
~.r-~
~~
o~
4~'f1.o...
~
I~
??
-~
I ~~
K
_.
V
..".,.­
~
~ "-.
~
r---- .............., "Q
iO­
r--
~
750mm,/lq
6
8
(0
Ie.
14
16
18
20
2Z
24
26
28
30
MOISTURE CONTENT (PERCENT OF OVEN-DRY WEIGHT)
FlOlTRE 19.-Trans\'('r:;e drying diffusion constnnts relntivc to unit dimension of
the wood, for wood wit It n swolleil-vO\Uln(, specific gravit~· of 0,365 nnd differcnt
moisture contents dried nl 40 0 C. lIuder different rccl\lCcd nir prc.."Surcs,
•
possibll' tl.nd it is bene(' questionl\bl(\ if optimum drying .l'I\tcs wcre
mnintnined. The ngl'l't'll1ent b{,twceu the ('xp{'rimelltal nud theOl'cti­
cld \'IlJU\'S is su{fi(.'ielltiy good, howev{'r, to indicllt{, tho gClleml shupe
of the curvc and to show thnt ('\'en under ns compl('tc n VtlCUUIll as
38
'1'ECHNICAL BULLETIN 929, U. S. DEP1'. 01-' AGIUCl.:LTUllE
possible (55,3 mm. of nW1'('ury lit 40° C,) unci with optimulll heat.
mpuL, (lI'ying I'Htps ('ould b(, illl'I'(,lls('(1 ollly I~ fl'w fold,
In the longitudinal drying of wood, us in till' simple longitudinul
difl'usion of !\ solute through swoll(11\ or unswoll{ll\ liquid-sntUl'nted
wood, the efl'et't of th{' ('ollul1l1niel\,ling pit-Jlll'mbrHlH' POI'('S and the
tmnsi('nt {'{·Il-wltH ('Itpilliwil's is V('lT SlI1ltll. Equlltion 7 IIllly thus,
for nIl pl'lIdi<'1I1 pllrpOS('s, 00 1'('(itll'Nl to
•
(13)
a r---'--. .----~
-~t
-<.~
CALCUl./lTED ;q'()M
o -C/lP!H~RY -STRilCTlIR£ CO:VSIOO?ATIONS
.-ORr/Na OATA 0;: BAUMAN ANO HOHF
1~
\
-"-,, --+ ..
!
"
I
-
;
I
1
,..,.
_~. .--"
'0>­
-...
.,
-,~,"
•
I
•
t--".
1.)0
•
.
zoo
I
. r-::--
300
,UR PRESS(:~~£
. -)
I
400
(trI'"
,
.,
I
500
600
Of: ,HEi?CIJRr)
"<;!
700
800
FI(H'ut) 20.-·A\'('rllg~' (.nln$\'pl'lil' drying difTusion COllstllllts reillth'c to unit
dinWIlSiol\iI of till' wood h('lwPt'l\ the filwr-:;lllurIllion point. and thc oven-dry
pondiliolls, for wood with n swolll'II-\'OltIll1c sp('pific grnvily of 0.365 dried nl;
-10° (", un(!c'r ditTt'n'lll n'c!uc('(1 nir pn'!'.'lllrl's.
LOllgituclinnl {1I'ying diffusion consln.ntsl'(·lnlive to unit dimensions
of till' wood W{"n' enl('ulnted for diff(~I'('nL JIloistUl'econt('nts and
swoll('n-yo!tllll(' sp('eilil' gl'nyities of tho, wood. AI'('us were deter­
mini'd IIn([('r plots of the diff(·rent sl)('('ific grlwit,y ('uryos from tho
fib(~I·-snturn.tion point. to yarious equilibrium surface-moisture COII­
l(\l\is, 'fhe' n "l'rng(\ (h'ying diffusion constants n'lntiYll to uuit dimen­
siolls of the wood det~l'Jnil\l'd in this wily are given in figure 21. The
IlVl'I'ngl' IOlln'itudinnl ((rying diffusioll vnlues in (:ontrnst to those for
tl"ll,l\8"('1'80 (Ir;\'ing inl'n';lse appr{,elably with It del'I'l'asc in moisture
('ontt1nt. This is dU(\ to the inel'l'ilS(1 in the ('('lillin' Ynpor-pl'{'sSUl'e
grndi('nt. Pl'l' unit moistul,t\ ('ontl'llt (:hllng(' as lhe moisture content
is 1'1"(\11('('<1 ({'qllations 3 nnd 5).
•
39
l'ASSAGE Ol~ LIQl'IDS, VAVOIlS: ETC., 'l'lIHOGGH SOPl'WOODS
•
10
9
~
"-
..,."
~
~
~ 8
~
~
~
>-....... ~
~ 6
~
;::;
::s
•
>-­
~
C::i 5
~
~
~
'\
~~
~
~
~ 7
l',4LCUU,THJ FROM
o -CAPILLARY-STRUCTURE CONSIOERIITIONS
""
~
\
.~
.....
§
~
3
-..
r- r--
._- - .- ­
\
\ ~
~
\\ \
~
0\\ _.
"­
~'\~
\
\
r--o...
~
c:::.
.....
~ '2
'~"
I
~I,
I"'~ "-
·~t·····~·
I
~~
"" 4
6
8
/0
IZ
/4
~'-.....
­
J'p
r---~
-0
~Il~
...~~~.- -0­
~
1'0---
::.;
Z
.........._ ~"'-" ~~'-'--I---i---
~
o
o
~o
~\
~ 4
'-I
.-ORYING OATA OF BATEMIIN liND HOHF
ARROW SHAFTS INOICIITE EXTENT
EXPERIMENTAL POINTS OEVIATE FROM
THEORETICAL VALUES
.
·-0.49
~~.60
I--r--. >:::= J P. CR. -o.lao
-0
-v
'"
16
18
20
U
Z4
26
Z8
30
EQUILIBRIUM MOISTURE CONTENT liT ORYING SURFACE
(PERCENT OF OVEN-DRY WEIGHT)
FIGl~UE 21.-Averl\~e
longitudinal drying diffusion con~tants relative to the
dimensions of the wood, for wood with different swollell-vo!ullw speeific gravi­
ties dried at ·JO° C., from UIC fioer-saturation poillt to different, equilihrium
surface
•
lIloi~turc
contents.
.
l10
'J'I<}CHNlCAIJ Bt:LL'ETIN 929, U. S, DEPT,
Ol~
AGHICUUl'UHE
}l'ow dntn 11l'O nvailnble COl' the longitudinal ell'ying of wood, TIlls
is bec!Luso wood is normnlly cut so thnt pmeticnlly nIl the drying
OC('lIl'S in the tl'nnsYt'I'se dil'oeLions, Further, most of the ayltiln,ble
dn.tn aro not for optimum (lI'ying conditions, Because of the fact
thnt 10nB'itudinnl drying is considombly faster tilitn tmnSYOl'se drying,
l'Xtl'OIlHlly high air vt'locitios havo to be used to take the moisture
llWI1y us fast as it diffuses to the sul'face, 13ateman nnll Hohf (6) al'e
pl\I'hups tlw only in vestiglttol's who lIsed adeq unto circullttion, 'l'hey
eit't'ttllttod 55 to .2,500 lito.l'S of nil' 1)('1' hoUl' OWlr an oxposod wood
slll'fnco of only 5,:~ cm,2 Cm'Yt's obtninNI by comparing weight loss
with the squnl'(\ l'Oot of the time for which tho loss wns computed
jndi('ntc thn.t optimum (h'ying WitS obtnint'd in all cnses nftol' the
fiest few minutl·s of (It'ying (6), From tilt' grndient dnta nnd l'I1to-of­
dL'ying dlttn, I>I't,,,iously (h~st'l'ibNl (p, 31), longitudinnl (h'ying difl'usion
c'onstnnLS .rt'lntive to unit dinH'llsions of tho wood Wel'O cnlculatod,
''''lLlups W('l'P also ('ltl('ulail'd fOl' (It'ying nt r('lnti\'l' vnpol' pressures of
0,20 and 0,50 (e(lllilibl'iull1 moistul'H ('ont('nts of 4,0 nnd 8.4 pcrcpnt,
n'spo<'li \'('ly) by (,Ollsidnl'ing the difl'usion constants PI'opol'tional to
the slo()('s of the 1ll0istUI'O loss-squltl'e root of time curycs, AU these
,',du('s 1\.1'0 plottt'd in figm'c 21, togethcr with the thcor(1Licltl ynlucs,
1'h~, Ilgl'ocment h(ltwt'{'n Lho (~xp(1I'imcntnl and thcoretienl valucs is
Slll'lH'isingly good,
Hntios of thc IW('I'age IOllgitlldinfl.l to the nvernge trnnSVOl'Se (!iITu­
sion ('onstnnts 1)(>1' unit dimPllsions of the wood will vnry with the
spe('ifie g'l'ltVity of the wood, the drying tempcl'lttUl'c, nnd the boundnry
('onditions, }~Ol' It 10-ptll'cent moistlLL'c-content boundltry condition
and It drying tompcmttll'o of 40° C" tho mtio will incL'cnse from 7.4
COl' wood with n specific gl'ltyity (swollt'n-volume bnsis) of 0.25 to
2;';,0 fOl' wood with It specific gl'ltvity of 0,80, As the 10nO'itudinai
drying dill'llSioll constttnt relative t-Q unit dimensions of the wood
itH'I'('ItSl'S I'ltpidly with It clecl'oltse in tho surface moisture con.tent
(fig, 21) and the cOI'l'osponding tl'anSYOl'Se value is lUtnlly afl'ected
by ehltng('s in the sm'face moi~tur<l content, tho ratio will increase
eonsidembly as the smface-moistul'e content is rcduced,
'l'Ill' t'x('l·lh'nt atrl'('t'nwnt btltwcpn tIll' drying diffusion constnnts pt'r
unit diull'.lIsion ottl\(' wood obtniIwd from theoretieal eapillnry struc­
tun' eonsidC'l'Ittions with vnJlH'S enlclIlntNI from (It'ying datn fOl' both
tl'nllSVl'rS(' lmd longitudinal drying of wood undet' various tempera­
ture, ]H'eSSUl'e, nnd sUl'fal'c-1l10istUl'o-('ontent ('Qnditions for a gr'eat
yal'it\ty of difl'('l'l'nt softwoods with diffel'ent specific gl'nvities, gives
(lxel'llent support fOl' the validity of tho tht'ol'etical considemtions,
Tlw ngn't'IlH'nt is, in fnet, botter thnn might ofilmud be expected for
sueh n. variable mnh'riul ns wood, Thc l'enson for this tlxcellcnt ngrce­
llIent is Itugt'ly thttt tit(' normnl varintion of the structural dimensions
of It softwood OtlH'l' thnn those d('lwuding upon tho spocific gravity,
witieh Ul'(' compl('t('iy accounted. for in the cnlculntions, is small or
hus a small t'fl't'et upon difi'usion, FOl' tllis l'cason the theoretical
CUl'V('S of figuI'('S 15, 16,17, and 20 can be used with a filiI' dcgr'l'c of
Ilt(,lIl'lH'Y in ('stimnting the dl'ying mtes of the heartwood of different
softwoods with difi'el'l'nt sp<"cific gmyities when drying under optimum
cin:uitttiion ('onditions at val'ious tempcratures, relative humidities,
ait' pl'essur~s, llnd boundary conditions, The curves can even be used
•
•
•
PASSAGE OJ!' LIQUiDS, VAl'OHS,E'l'C., 'l'HHOUGH SOlo"I'WOODS
•
41
in (\(lkl'll1illing tho order of mngnitudo of tho drying l'lttes for tho
ll(lltl'lwood of hlll'dwoods,
N l'WIllfUl (31), in his (,0Il1Iu,t'hl'11Sivl' mntl1l'matil'ol anolvsis of
difl'usion phellomenn, givt's llll'thods fol' calculnting dill'usion· YlIlucs
und~'r optimum dreu,llttion eOllditions from vnlut's cnlculll,tpd f!'Om
dnla obtnined undt'l' less C'ircuintion. Combining this with tho
theol'(llienl ('ui<-ulntl'd dill'tlE-ion Vltitll'S of th:s papl'l' should mako
po!'sihle'the fixing of (It'ying s('ill'<lules for tlH~ (It'ying of ilw heltl'twood
of vnl'ious softwood spN:ies until'l' nny types of (lOIllIlH'I'einl conditions,
PRESSURE PERM EABILlTY CALCULATIONS
SYSTEMS .""nEE l"HO~l GAs·LIQlJlI> MENISCI
'l'Ill' pllssng!.' of vil,tultlly .free liquids through wood undt'l' nn ('xt('rnnl
d!'i dng 1'01'{'(\ 01' inh'l'nnlell pilhu'y nttl'ltetionis ksssubjol't to fundlUll(lntal
nnnlysis lImn tlH' diffusion of liquids, vapors, 01' solutt's through wood,
'{'his .is (hit' to tlw fnet lhnt tho ('onL!'Oliing stl'UctUl'(l is the most yuri­
able Plu't 01' till' wood struetuI'e, Although Ulntill'mati('ol values with
pl'llelieul aignifil'IUWo ('annot be euieulntl'd, a fl'w, g('llel'nlizations
\'('gnl'lling the natuI'('· of the phpnollll'non nnd the l'fl'ectiv(' stl'llCture
ClIll bl' mlldt',
]~Wlll't (L2)
•
•
ho('\ shown thn,t tlll' mtn of flow of a liquid thl'ough a
('ombinlltion of l'omplptdy fillNl Cllpillul'il's nnd i1l1'gN: tubl's in series
undel' u, dl'linit<.\ hydl'ostatie lll'nd is Pl'llctieully thl' same as the mta of
flow through It seril's combination of tlll' SIlUl!) eopillnries without the
lllrg(ll' lube:;, 'rho ltu'ge ('ont1l'eting tubl's furnish a negligible pnrt
of the l'esistuneo to the flow of liquids und yltPOl'S, This is to be ex­
p('e\.NI fl'OIll tho How rl'lation'lhip of Poiseuille given in equations 18
to 20, p. 63, In tlll' ellsP ot' smull cupill!ll'Y tubl's the impnctturbulonce
efr(ll~t at, the ends of the enpillarips is n(lgligible us tho flow is strcam­
lint' (37, 38), Beeuuse of this no correction tl'l'1ll is neNled in the
(.q unlion.
In it sN'ies comhinntion of cnpillal'il's the mtp of liquid flow through
(l!1('h will bl.l lhe 8n.tlH' nnd henee the pl'l'SSUl'e drops tlll'ough enell will
lll' inv(lrsdy PI'opol'tionnl to the fourth POWPI' of thc capillary radius
divided by its It'nr''th, /,4/l, 01' inv('l'Sply Pl'opOl'tional to thl\ pl'oduct of
lilt' ('I'os8-seetionn an'tt of the capillary ttnd tho sq uarc of tho mdius
t1ivid('d by th(, INlgth, AI''.!./l, In a Syst(llll made up of equalll'ngtihs of
enpilln!'i('s with l'itdii of 1 and 10 units, respectively, eonnected in
sel'ies, tho prl'ssure drop through the larger capillaries will be only
0,01 P<'l'('('ut of tho totl11 PI'l.'SStl1'C drop, The resistance to flow through
tho IUI'''or tubes will thus be onl~ 0,01 percent of the totall'esistauco.
In the case of tho Iongitudmnl flow of water under an external
pressure tlu'Ollgh completely sattl1'lttcd wood with free water on the
eutmuce !1nd l'xit fnees, the flow will be tlu'ough a large number of
fiber c!1yities in parnllel, ench of which is in series with a large number
of pit-memlmU1o pores nud transient capillaries in the cell wall con­
ul'('tcd in p!1l'!\llcl. '1'he equation Jor flow through this system is
(14)
42
'l'ECHNICAL BULLETIN 929, U. S. DEP'l'. OF AGRICUL'l'URE
in whieh P, and Pm l'epreso.\lt the pressure drops through the fiber
en,vitics and the pressure dwp through the communicating openings,
l'cspectivC'iy, and the other symbols have the significance given in
table 1, page 12.
When the clLpilltU'Y dimensions effective for the longitudinal flow
through the heart,wood of a softwood with n. swollen-volume specific
gravity of 0.365 (table 1) nre substituted in equation 14, the equntion
rends:
53,000 P,=(3.0+0.0007)Pm
or
P,=5.7XlO- sP",
•
Prom this it is obvious thnt the pressure drop through tho fiber
cnvitics, ns well as tlll' resistance to flow, is nbout 0.006 percent of
thltt for tlH_\ commullielLtiIlg sLrueture. The fnet tlmt the second
term in the parcnthescs on the ('ight-hand side of equntion 14 is only
about 0.02 pcrcent of the fil'St term in the pnrcnthcses indicntes tlmt
the flow through the tmnsient ceH-wnJI cn.pilln.ry structure is only
0.02 percent of the flow through the pel'mancnt pit-membmne pores.
FOl' trnrlS\'Cl'Se llow the equn,t,ion is
Aml,P,=(Qf;2
+QLw) Pm
(15)
from which
or
2.5 X 10 10 P,= (4.1 +0.00035)P rn
P,=1.7X10- lo P rn
The proportion of the totnll'csistnnec toAnw through the fiber cnvities
is even much less than in the cnse of longitudillnl flow, while the portion
of the flow occurring through the trnllsient cell-wnIl capillnries is n
sml1H frllction of the flow through the pit structure, similar to the
cnse fol' longitudinnl flow.
Varin.lions ill the specific grlwity of the wood will have a negligible
effect upon the magnitude of the pressure pel·menbility. Chnnges in
the specific grll.vity of the wood will nffect only the values of A",
nnd lin in equntions'14 and 15. Severalfold variations in either of
these qunntilies will have a nC'gligible effect upon the location and
mngnitude of the resistance to flow.
Pcrnwabilitv of the pC'rmaucnt pit-membrane pores of sapwood
mny bc n thoiisand times as grent ns for henrtwood. The resistance
to longitudinnl flow tlu'ough the fiber cnvities may, under these COIl­
ditions, be ns high ItS 10 percent of the totnl. l!"'or transverse flow
the resistnnce through the fiber Clwities would still be negligible.
The proportion of the flow occlU'ring tlu'ough the trnnsient cnpillnries
in the cell wnlls of sapwood would be much less than for heartwood
in both stl'uctunl,l directions. In the case of liquids thnt cause less
swelling of wood thnn does water, the flow tlu'ough the transient
cnpillnries in the cell walls would be still less thnn the vnlues cnl­
culnted. The pnssa~e of n liquid through the cell wnIls under other
thttIl diffusion conditIOlls cnn thus be disregarded. The totnl resistance
to flow of liquids tlu'ough softwoods mny be considered as existing
in the pit-membrll,ue pores in all cnses except thnt in which 101lgi­
tutlinnl flow of liquid OCClll'S tlu'ough porous sapwood.
•
•
PASSAGE 01<' LIQUIDS, VAPORS, ETC" THROUGH SOF'!'WOODS
•
•
43
'rho rcsistance to longitudinal flow of liquid thl'ough softwoods is
much less Ulan. the resistance to transverse flow pm' unit distance be­
cause of the fnet that f('wer pit-membrane pores have to be travcrscd
in S(,1'1I.'S pel' llnit distance in the longitlldiunl direction than in tbe
tmnsvel'se direction, The ratio of the transvt'l'se to longitudinnl
resistance should be equal to the ratio of the average efl'eetive fiber­
cavity length Imd the avcrnge fiber breadth, which is about 100 for
thi.' Iwprngt' spt'cific gmvity of wood, It is for this reason that p1'es­
sun' trNttmt'nt of wood with pl'est'l'vntives is so much more effcctive
in the longitudinal than ill the transverse din'clion,
'I'll(' t'/fl'ctivelll'SS of the communieating pit structme not only
Varil'8 grcutly bt'twcon speci('s and difrer('nt specimens of the same
Sl)('cit's, but from om' annuul rinlf to allotlWl', or eVell within the samo
lumultl ring, This hu'go varintlOll of til(' structure which controls
flow aeeounts for the V{'l'y irJ'('guln:r lim' of advnnce of tt'eating ma­
terinls into wood tlll(lt'1' preSSUl'e permeability conditions in nll'tlu'ee
strllctum.l direeLiolls, Tht, irregularity ill the fiber direction is gl'Cntor
thnnin tht' t1'nnSV('I'SZ din'etions, This is priml1l'ily due to tho better
chance of hnving (,ither nbnormllJly large 01' nbnormnlly small open­
ings in the l'l'lntiwly fl'w pits that nrc traversed in series pC!' unit dis­
tance in the fiber direction as compal'l'd to the mnny pits thnt have
to be tl'lwel'sod in Sl'l'il'S pl'l' unit distnnc(' in the trnnsverse directions,
Then, too, clwcks across the pit membrnncs sometimes occur in the
last f('w snmml'rwood fib('rs Inid' down nenl' the l'nd of the growing
sNtSOn, '1'ht'sl' tl'nd to occur in s(,1'ies in tIl(', longitudinal dit'ection,
thus furt\l('r incrMsing the probnbility that longitudinnl penetration
will be more i1'regulnr than trnnsverse penetration,
SYSTEllS CONTAINING GAs-LIQUID MENISCI
In gent'ral p1'nctice the mOY(,ll1cnt of liquid through wood does not
occur in n continuolls liquid syst('m with free liquid on the entrnnce
and. exit fltces ns has just bet']l conside!'('d, When green wood is dried
OJ' dry wood is treated with a liquid or solution; nir-liquic! ':-:"'.1isci are
for111('d ill the wood which ndd greatly to the complicatiolJ of the
processes,
'Vhen a piece of compl('tdy wntl'l'-snturnted wood is dried in air,
free c-vaporntion occms U1ltil menisci nre form('(l in the pit-membrane
pores of the surfncl' filwrs, Further cva]>ol'ation cnn occur only with
nn nccompnnying reduction in Yltpor pressure sufficiently grent to
overcome the added l't'sistnnce to ('vnporn.tion cnused by the curvntUl'e
of the menisci in the \nrg('st pit-m('mbrane porcs, This reduction in
vnpor pressure cnn be cnlculnted from the size of the pit-membrane
pores, using equntion 21, p, 65, There cnn be n movement of the
vil'tunlly frt'e water in the liquid phase when wnter is being evapornted
from nli fact'S of the wood only when tll(' tension caused by the evap­
orn.tion is suffici(,llt to cnusc- the fibcr cn,vities to collapse, and thus
relieve the restraint to flow (17), The reduction in "npor pressuro
that will gin' a tellsion suffici('nt to cause collnpse can be cnlculnted
from compressive strength data and the swelling-pressure equation:
RT . )
P.=---ln(P
n1v o po
(16)
44
TECHNICAL BULLETIN 020, U, S. m~PT, O(~ ACIlICUL'I'UHE
whel'(1 P, is th(' swelling Pl'CSSUl'C in d,}'ll(,S per squal'l' c('nUmph'I', R
is the gas constant (8,316XI0 7), T is t1w absolute temp(,l'llture,
j.\I is Uw moleculnt, w(light, v" is the sp('cific volume, Ilud 1J/Po the
j'eliltive varol' I>l'essure of the sw('lling liquid, The internal PI'!'ssure
OV(1I' the lllgh l'('lative-vapOl'-pl'esstu'e range of 0,95 to 1.0 is nlmost
diref)tiy propOl,ti011al to the vapol'-pressurc depl'l'ssion, bdng 13,5
atmosphercs pl'\, reduction in relntive vapor prl'SSUl'e of 0,01 at room
templ'ratUl'lI, The elnstic. limit for the comprcssive stn'l1gth perpen­
diculnr to the gmin (or gl'el'n softwoods is about 500 pounds per
sq Uti 1'(' inch (16) oj' 34 ntmosphl'I'('s, This COIT('sponds to n reIn tiV('­
vnpor-pl'PSS\IJ'e reduct,ion of 0,025 nnd n cnpi\1nry radius of 42 ?rip
(l'quntiOll 21, P, (5), Although this cnpillllry rndius is above the
nVI'I'uge> nnd IllOSt prolmble mdlus (p, (5) I it is below the mnximum
vnlu(' for w{'stel'll white pine, A liquid-tension collnpse could thus
ON'IlI' in this wood if it w('l'e completely wntpr sntlll'llted only in the
fibers which !lnd commllnicnting pit ml'mbl'lu1l's with no pore exceed­
ing 42 mj.l ill mdius, Such fibt'J's mny occur h('l'o and there in the
sti-uct:lIl'e of some woods, In no cuse, hO\\'I'Yl'1', would nil fibers be
('xp{'(~tNI to nl{~(~t tlwse l'equu'('m('nts, This ngl'('l'S with the fnct thnt
in woods subj('ct. t,o this form of collnpse, the collnpsll OCCUl'S nt mndom
throughout the structure of tllC wood (17), The mO\T~ment of the
vil'lually fl'l'!\' Wltt('l' in tho liq uid phlls~ ill til(' drying of compl~te1y
wntcl'-sntUl'n.ted wood will thus be limitl'd ent.irt'iv to cllses wh~re some
colll1pse of tho wood occurs,
•
.
Nntul'IlI gl'l'('n wood is r ,,'ycr eompll'le\y fil1N\ wit.h watel', although
some of Dill filwl' en.vit.ies mny bt' eomplel~ly filled, The filwr envitil's
of ~I't'{'n Sttpwood on the av~rnge rn.rely ('ontain mOI'(' thltn thn~efourths the amount of wnt('r l'l'quired. to fill them, nnd gre~n henl't­
wood fib('I' envities contn.in much l~ss, Pl'Il.eticlllly all the fibCl' cnvities
thus eontnin considl'l'nble air, 'Y1H'n evn.pomtion oecUl'S from aU
thl' surfacps of Eouch wood, tIll' virtually fl'l'e wntel' cnn moyo in the
liquid phnso iIi a manner gl'llphically demOllstmted by Hnwley (20),
'1'('nsion S(,t up in the pit-membrnn(' pores of tile surfnce fibm'S, due
to the evnp0l'lltion of water from mcnisei whi('h arc formed in them,
cauSes til(l flow of liquid wnt(,I' from the int('I'ior fiber Cllyitil's if the
contained nil' bubhl('s hnvc nppl'ccinbl~T Inrgl'r dinmetcl'S thnn the
pit-nl('mbl'tlIl(' pores fmm whieh evnpomtion ocelli'S, In this cnse
thl' intl'rnlll l<'l\sion thnt. is set up is rl'ii('wd by the cxpn.nsion of thn
nil' bubbl('8, As drying contimwc;. difl'usion of wnter vnpor nnd
bound Wlltl.'l~ will OceUl' from til(' interior of tho wood, causin~ a con­
tinunl inwnrd moyellU'nt of tIl(' wel line, the line of trnnsition bctween
the \Tirtullllv frel} nnd the hound. wntl'!:, It is shown on page 56 of
UII.' App('ndix that the fiber-satul'Il.tion point corrcsponds to al'~lativc
\Tapor Pl'pssure of about 0,99, This uwnns thnt the tension of the
vil-tually fl'l'e wntl'\, nl the W('t line would be 13,5 ntmosphel'cs, The
tl'nsion might lo('ully bl.' doubl(' this vnlue in the cuse, of fib('rs thnt
eonluil1ed no pit-m('mbI'llIle pores I.'x(:o('ding the nVl'ragc in size,
An adequate t('llsion is thus provided for n.pprccinble liquid flow to
the wet line,
The Il1t't'hnnism of the liquid flow will, in gel1ernl, be ns follows:
In a sel'i('s t:ombinution of fib,,!, envities contnining equnl-sized air
bubbl('s, th" flow of liquid tOWIll'd the wet line will OCClll' fil'at from the
fibcr cavity nelll'cst to the surfnel', be(:nuse the distnnce of flow nnd
•
•
•
PASSAGE OF LIQUIDS, VAPORS, ETC., THHOUGH SOFTWOODS
hon(l(~
•
•
•
45
thCI'{'sistllncl.' will bo h1Rst. This bubble will expand, ns flow
takl's plll{,(\ \lIlUI it pntctknlly fills th(' fibt'l' ellvity, '1'ho hubblo
nwnhwus will tlwn tend to be \>1111('(1 into one of tilt' pit odfit'es. This
will il\('n'I\Sl' t 11(1 ('UI'vuhll'(' of tilt' buhbl(' to UH' point. t.\lIlt till' 1'('­
siSttt.lH~(·, to ful't.\Wl' I'Xplltlsion ('x('peds the n'sist,nn("(' t.Q l'xpnnsion of
tiw nil' bu bhh, in tlH' n£'xt. fibel' ell \'ity~ Flow will Hum ooeul' from
t.his 8{'('OlH\ {jhl'!' ell\Tity until Ihl' hubble IJl'lu,tielllly fills tho fib('l'
('Iwity, ll('('lIuse of the il'I'('guhU'it it'S or Uw fibr.·r-{·Iwit.y SUl'fu('l's,
UH' buhhll'S will new'r (~ollfOl'ln to tll(I sUI'fue(', silH'l' in doin~ so t,hl'
('\lI'\'lIt,III'(\ would bll in('I'('IISNI to 11 VIlItW gl'l'l\tPl' LllIln tlln,t, of UH' nil'
hubblo in 1l1l0tll(ll' fibct' envit.y in t.he sel'it's ('ombinnlion, Th(' WI\.I('I'
in tlHl HN'ond fibcl' {'I\.vily frolll t.hl' W(,t, lil\(~ ('iUI, OWII pnRa through
("hnlllll·ls bdw{'('l1 the bllhbl(~ I\IHI till' fib£'1' Willi of thl' fil'st fibl'l' ('ltvity
from the Wl't Iinl', rl'his will, of (,OUl'$(', in(~I'l'lIsl\ tho I'Psistlul('l\ 1,0
liqllid flow but will not Pl'('V(,"t it.
Tlw Ilil~ hllbblt's in the Jibl'l' ('Ilvilil's will, of ('OIlI'Sl', \'Iu'y I'nlldomly
ill sizl' so thnt flow IIllly O('('lI!' fil'St, from n lib(,I' ('nvity nn t1PPI'(Willhlc
distlllH'l\ in from thl' \\y(\t lim'. This bubbll' will, how(\\,('I', hlWl' to bo
sufli('il'IIUy lurgel' lhun a bubbl(\ in 1\. Iihl'I' ('I\\'ity IIM1' tho W(,t lilw t.o
mnkl' liP fOl' t.\1(1 difT('I'ellel' in flo\\' r(osi::;tnn('(' oVC.1' the two distllllces,
As dryill" pl'O~I'I'S!'I('S, t.hl' ('\""\(,(' of II hllbbl(\, in n fibel' clwiLy Ill, 1\
cOI1.<:i(II-l'n1,I(' dtslulu.'<, in fl'om 11tH wet lilH', losing its wat,N' by l'xpnn­
sion of It ('OlllttilH'd ail' lHlbbl(· lwfon' thl' SIUlIC O(~(~urs in a fibl'l' cavity
!H'IlI'I'I' till' W('(, Ii Ill', bpcollH's illl'I't'ltsillgl~' I'l'moto, This is ht'{'nusl' of
Lhl' gl'l'nlpl' pl'ohnbilily umll'r tltl'Sl1 (:onditions t.ltat the wntl'l' will
hlWI' to lIow through mOl'll nhCl' l)nvities thn,t eontain prn.cticnlly com­
pll'tdy ('xpnlldl'd nil' bu bbll's, It is also ]>ossi\)\(' fOI' flow to occlIr in
Isoll\iN\ plt~et's in It (\il'(,(ltion opposite to the moistur'o gnt(liont bC(ll\uSO
of 1\ I(·~s('l' rl'sisilUwt' to flow, On the n\'l'I'age, howpv('r, flow will bo
Lowal'd Lhe W(.t lim' nt which (wnpol'l1tion is tnking pln('!.', with n pl'O­
dominant t('ndl'IH'Y for the wnter Ill'l\rest the Wl>t lille to move first.
'[,11lI Cnet t.hnt tlill vil'tunlly free wllter Cltll IIlOVU ill the liquid phaso
illlllLLul'Ill gl'l'l'll wood Itnd thl\t it Cl\llllOt mOVl' in the case of compleLt·ly
slLtumtt'd wood without Iwcompllnyill~ collltpse under tension set up
in (\t'ying', R('('Olmts for th<" diffel'l'll('e botWl'()It the moistm'tHlistdbu­
tioll CUl'VllS obtuill(,d nftll!' pnrtinl (\t'ying of wood in the two conditions,
'l'lw moistul'll-distl'ibution ('lll:VO giVl'1I in figure 22 is for 1\ spocimen
of tiitkl~ spl'uce thnt WitS almost completoly fillod with wnter by all
ILit('l'IIII,l(I vtlCUUIll nnd Pl'pSSllro trcatnumt (6), The 1ll0isLure-dtsLri­
bu lioll (,lII've giVl'll ill ligure 23 is for IL nnt.ur'nl greon specimen of
the Snlll(l wood (6), The moistllru-distl'ibutiQIl eurvo in figuro 22
shows a shnrp l)l'cnk nt the fibl'r-sntumLion }loint because of the 1'0­
strktod motion of the virtunlly freo wllter, wherons the curvo in figure
23 shows 110 such bn'llk. If tho nil' could hlLve been completely
rmllov('d from the specimon of figure 22, tho moisture-distribution
(~ur"e nboVl' the Hbot'-sl1tumtion point would havo followed tho vel'ti­
clLI dot,tcd curvo to the cOlnplotely satumtod condition. Tho fmetion
of {)vltpol'llted moisture that would havo beon lost in this caso is tho
1L1'@ A dividt'd by the nroa A+B+C+D. Be<!n.use of tho fnct thn.t
there WIlS. It littlo nir left in tho specimon, a smllll Ilmount of movo­
Illl'Ut of liquid witter did OCClll'. Tho nctual fmetion of the (\\'I\por­
!tbln 1Il0isLul'(\ lost is IWllCC. \'(~pl'()sellted by tho Ilroa A Vlus Itl'en B
dividod by IHCIl A+Bi-C+D. H the liquid wlltcr had beell able to
46
'!'ECHNICAL BULLETIN 929, U. S. DEPT. OF AGlUCUL'1'URE
24°~--'-1"----"""II --"--'-1t-"----I....----.----.-
- - -r - -V"
-F__~~
ZZO~n+~~~~0~R~/~G;IN~A~L~M90~/~~~=V~R~£~CO~N~T.~Ef.N~T~__
•
I
ZOO !
'i:::.'180
~
I
~
~
~
160
~, ~ ::,.;
~
140
~
I....
~
'4J
IZO
A
~ ~ •
~
I....
~ 100
I-.:
~
~ 80
~ !:?
~
60
0.1 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6
OISTANCE INTO WOOO FROM DRYING .fURFACE (em)
FIGURE 22,-l\foist~listrlbution curvo obtained after drying water-satumtcd Sitka sprnce ror 259.5 hours
III tho 1'\IIgcutlai dln'Ction at 40' C. and 0 percellt rolnth'c humidity. AreOl ~~~!C+D-rmctlon or
Are~\~~~~~+D-fraCtiOn or
X:~~c:t~t~6¥D-frnCtion of c"apornble moisture lost If there were
e''llporable moisture- lo,>st If there werc no mo,'cmcnt of liquid water:
e\'llpornbIIlIllOIStllre lIetuully lost;
free mO\'em~lItof liquId water.
•
PASSA(;F} O~' LIQt:IDS, VAPOUS, ETC .. THHOlJGH SOF'l'WOODS
•
47
moYl' fn,dy nbon thl' fib(,I'-sntlll'lltlon point, th(' 1Il0islul'l'-disll'iblllion
<'lU'\'l' ill this Will' would hl\.\'(' bp(m n ('ontinllnlion of the moistul'l'­
dist.I'ibulion ('\II'Vl' belo\\' till' fibl'l'-sltllll'itlion point I\S is shown by
nnniogy with tl\(, moistlll'(' distribution gin'n in figul'(' 23, 'rill' fl'H.('­
tion of (wnpomhk moislltl'(' thnt would hllYl' bN~n lost iC till' liquid
wnl,(It' 1110v'NI fl'(I('ly is thp sum of t.he Ill'cns A, 13, lind (I, di\·idot\ by
th(\ iU'('ll A+13+C+D,
'l'lwllt'lIIl\1 nlld thl'ol'('tieal nlOiStlll'l'-distl'iblllioll (,lIl'ns in figlln' 22
would .J'Nlilil't\ dill'('I'l'llt l('ngllls of t imp to h(' I'stnblislwd, In till' (,IlS11
of fl'N) liquid mo\'eml'llt, fl'N' \\"11('1' wOllld ('ontribute to Uw 1Il0iStlll'O
60
~
~
~
~50 f--- --TI )..
I
~
I
I
I
I
~
~
<:)
40
<:)
~ JO
.!S . . . zo ~
~
~
...
~
~ /0
~
V
"
'"
~
....
....;:;
/
I­
jV
".....
•
-- --- f!.N!.G.'N.!I!: M!~r..U!! fo.!'TE,![ 1--- -- --
II
/
II
o
o
O,Z
0,4 0,6 U
I,D
I,Z 1,4 1,6 1,8 Z,O Z,Z Z,4. Z,6
PISTANct INTO WOOO FIlOM DIlYING JUNFACE (em)
Z,8
FlOt'IU; 23,-MQi~hlr('-dil't
rii!lItioll. Clln'c obtained after dryin1; normal green
SHim !;pru('(' for 3.75 hours in the tangentiul. direction ut 40° C, and 0 percent
rclntiw hlllllidil y,
bdo W tI\(\ filwl'-sn tUl'ntion point by moving into thnt zone and bc­
ing bound, ~u('h motioll would tplld to kl'('P the llloistul'l'-liis­
tl'ib uUon ('UI'\,(, bdow tIll' Iilwl'-suturntioll point ut It higlll'l' level so
tim Lit 10n(7('I' liull' would b(' lWtlli1'l'(1 to IIHnill the llwd (l'iVt'Il, Tho
rQYt'I'Sl' hohls t1'l1(' in 111(' ('USl\ Whl'I'P 110 Jl'(~l' movement oCliqui<i wll.tcr
OCt' III'S; lllluwly, thll t n shol'tl'l' time would b(' l'l'quin,d to nttnin tho
mOl stun' disU'ibu tion gi\"('n 1I(I('l1l1s(' no mOYl'l1l('lIt of CI'l'(\ wnll'l' O(.'(,UI'S
into the ZOIU' bi.'low th(, fiI)I'I'-SlItlll'lltioll point, thus t('nding to mnin­
tnin thllt purl of th(~ {'UI'n' lit It low('\' level, C'olllpnl'nUVl' mtl's of
dl',Ying JOI' lhe difl't'rent conditions thus ('HUllOl be cuicuiu.tcd from the
COlli
•
48
TECHNICAL BULLE'l'lN 929, U, S, DEP'l', OF AGIUCULTURE
areas iu figure 22. Sueh t'ompnmti \'(~ rnLes cnn, how('yel', he ('nieulnted
from the dntn of BnLcmnn, Hohf, nud Stnmm (6) fOl' the normal
gn'l'll nud pl'tH'Li('I1Uy snturnted wood by eompltI'ing the fl'llt'tions of
(,ynpornblc wnh'r lost nftel' the snmc timo of drying, After 3,75
houl's' drying, the gl'Ct'll wood lost 0,124 of its evapol'nblo witter,
whel'('I\s the pmdieully wntel'-sallll'ntNl wood lost 0.0978 of its cvnp­
ol'nble WItteI'. The fraetion of eyu.porable \\,IL[<.'I' lost 1)('1' unit of time
is IH'IH'(' gn'ntor fol' wood ('ontnining some nit', although the actunl
amount of wiltel' lost mny be h'ss. It wns shown by Bateman, Bohf,
nncI Stumm (6) thnt the. slLme difl'usioll pel' unit 1l10istuI'e gmdiont
was obtnined fol' tho tangential drying of the gl'e('unnd the pl'lldielllly
wnter-sntul'l1te<l wood. It is the stN'per moisture grndi('nt, in tho
elLse of gl'l'('1l wood umintllilwd by liquid wnter How, that nt'counts fol'
the gl'(,ll.t(lI' l'('itLti vo .mte of moistul'c loss,
The fuet lhnt no brenk is ()blnillt,d in til(> 1ll0istu1't'-distribution
('urns fol' the.' dl'yitw of most ~'1'l'('n woods, wldeh ('ontniu appreciable
ILmounts of nil' ill thet>filwr t'llyities, indicutes thnt the moistul'c grndient
bdow the Hber-satul'1ltion point must control till' rnte of free wnter
moV('nH'nL nboyc till' libel'-sntul'iLtion poinL. If the free wnter moved
fllstel' t1l1ln Lite bound wut('r nnd water yapor below the fiber-satum­
tion point, the moistUl'e eonll'nt lIenl' the wet line would tend to build
up, 'fhis would )'('quil'l' thnt the nil' bubbll's in the fiber t'lLyities near
the wet lin(' be und(,1' compression nnd decrease rnther thnn increasc
in size, Under such conditions flow would t.end to be rcyersed. The
moisture 11l0Yl'lll('nt aboYe the fibel'-slltm'utiQll point, though not in
itself a diffusion plH'nolUenon, will thus be controlled by the diffusion
be,low tJw iibl'r-sntul'lLtion 'Point nnd will nppenl' ns if it were n diffusion
phenolll('non. It is for this rel1son thnt Tuttle (57), Kollmmm (26),
Shol'wood (85, 36), and Loughborough were nble to consider the
<h'ying of wood It diffusion phenomenon oyer the totnl moisture­
cOlltentl'nnge (p, 31),
•
•
TREATING PROCESSES
The b'cnting of wood with pn'sel'Yntiycs, fire retardants, nntishrink
dll'lnknls, 01' ehomicllI sensoning Il~l'nts cnIl be accomplished: (1) By
diffusion of the trelLting mnh'rinls lIlto gn'en wood by sonking in nn
nqll('OllS. solution or pncking dry ehemiclll nround the green wood; (2)
by replll('eTlwnt of the wntt'r in green wood with Iln aqueous solution
under n hydrostatic pn'ssurc or l'lectrictll potential; (3) by cnpillnry
I'ise of the liquid 01' solution into dry or pnrtially dry wood upon
immersion in the solut,ion; or (1) by supplementing capillnry rise with
the use of iL trcll.ting cylinder by applying n vac.uum to the cylinder
containing the wood, running in the trenting liqllid while maintnining
the ytlcuum, n.nd then npplying prcssure (so-cl1lled full-cell proccss),
or forcing the liquid into the wood against I1n intcrnnl nil' pressure
(so-culled cmpty-c.ell process), The fu'St of these methods is purely
a diffusion phenomenon, The second method depends upon pressure
permenbility, while the last two methods depcnd upon n combination
of cnpillnl'ity I1nd pressure permenbility. When wood is trented with
a WItter-soluble solute by processes 2, 3, and 4, provision must be
made for the diffusion of the solute into the cell-wall structure follow­
ing the trel1,tmellt of the cotU'Se cllpillal'Y structure,
•
:PASSA(l~J Ol? LiQl'IDS, "APons,
wrc" '!'UHOUGH SOFTWOODS
49
'.I'.11l' q ul'slion lI1igh t be l'nisl'll m; to why sO-t'nllt>t! oSllIot.ie lI'PH lillg
nWlhodl:l hll"(' not lH'Pll ('ollsidt'l'l'(1. ('lIL \\'ood, II II Ii k(·. gJ'owing plltllt
ilia lpl'i a Is, ('onll1ills 110 sl'lIlipt'nnl'ltblc 1)1('111 bJ'IUI('s (Illl'nli>l'ltllt's per­
111('ltul(' to WUll'l' but not to s(1111tcs) l'x('('pL lH'l'hups fol' I1loll.'('ules of
('olloidll.l dim('lIsiolls, In til(' lIus(ml'c of sueh s<'ll1ipt'I'IlI('nbk mClll­
bI'IU'.('S th(', 11Il£:nL oSIIH~tiy 1'I'N,~,lrl'(, dlllllgl' lhl'ougl~ It pi~et~ of wood
lHilHlfl'sts llst'll as It tldl USIOll j>J'N;SI,Il'(, ('hnngt'. '111l'l'P IS hen{'e 110
l'l'HI dislinelioll Iwtw('l'lt 1I1(\ sO-('HIh.·<! osmoti(' In'uLillg of wood ulld
1J'('Ittillg wood by lIll' simplt' difl'lIsioll Illl'lhod,
'l'lll' dill'l1sion'lIlelhod is npplit'ullt', l'X(,I'pt whl'1I nppli('d ns It IUul­
liph'-sll'P 1>1'0('(,ss ~4S), 0111.\' to till' Il'NllllH'llt. of gr('PII wood wiLh
wnt('I'-Holllb\(\ solules, 'rhe lIH'lhod hns lIot bl'l'lI ('xt'('lIsiveIy IIsNI
\)t'('llllH(llIlnllufnl'lIIl'('1'S, ill gt'II('rul, pr('[('1' ftlbri('nting thdl' pl'oduds
from (Ir'y wood pl'inl'to ll'('nllllt'nt" 'I'll(' PI'(H'('SH, too, is Y('J'y slow,
H IIns UIP dP/illlte\ nt!"Hlllag't\, howl'vt'l', of gh'ing d(~l'Ill'1' 1\.11(1 lllOl'C
ulliform tl'pntl1H'lIt in Ht'l'oss-lh(·-fi b('l' din'diolls 1I11U1 (,lin Lw obtnil1(,d
by nny of lll(, Pl'lll'll'ltlioll, ml'thods, l'sp('('itllly il.' thl' ('IIS0 of J'l'sisinnt
woods. For l'XtlllIpl(', wlllte ouk ht'lIl'lwooc\, ",hwh ('lUI be only SlIPC'I'­
Ikinllv tn'u.l(\d by IH'lll'tl'Hlion l1H'thods, ('1\.11 wlit'll gi'\.'('Il, bo Lrl'tlt.pd
to 1111)' ]lI'Ul'li('1I1 dt'p!h by till' difl'lIsioll tnC'tho<l, J~oughbol'ough (28)
found lllllL sodiulIl ('lIlori<i(' dill'usNI illto this matel'ial Itt sueh It mte
thn!. nl'tPI' 10 dIlVH' illll1Wl'sion III 4:>0 C '. it nUltilled It ("OIH'l'IILmtion
0,1 of tim! of til(: bath Itt It dt'pLh of 0,5 in('h frolll the ftwcs, RCiLdily
d('\('('lllbic n.moun\s of SHit \\'('1'1.' obtnilwd n,t, I\. tit'plh of 0,8 inell, In
:14 (\ilYS IlII nppJ'l't'iHbk IHllounl> of SHit, hnd difl'tIS<,'<1 to I\. depth of 1.2
in('ht·s, l\lthough sllC'h IOllg ll't'lltillg 1)('J'io<is wOlrld vel')' Iikdy bo
pl'oitii>ilin' 1'01' g'l'lIl'l'lll (,OIllIll(,l'cilti liSt' on 11l1'g'c' spet'iIl1('ns' b(,tlLuse of
till' gl'l'nL tllllk ('nvtl('ity thlll> would be ]'('quil'l.'d, tlwy nl'C 1I0t cxe('s­
siyely long 1'01' dmw piling of gJ'('l'n wood' with lity('rs of dry solute
bt,t WN'Il,
TIl(' di/1'usioll llH'lhod ill wltil'h th(' mnte'l'inl is llwl'(\ly ilUllH'I'S('d in
lilt' solutioll SN'ms ('omm('l'einlly npplicnbh' fOl' the {,t'l'nting of gl'{'('n
\"('1\('('1' dil't'cL fl'om the ('ullpl' Imin's, (ISlweinlly in till' (mst' ·of woods
thnt hlw{' R high gl'('l'n moist IlI'l' (,Ollt('Ilt. Stiunm nnd S('bol'g hnye
foullt! that ~lr.-in('h gl'('('Jl s\\'(\('tgUIUWlll'('I' tnlH's up nbout 30 pel'c{'ut
of t.\1l' dl'), wl'igh I> of tiw wood of n plH'llol-fOl'lllltlddlyde fPsin-fol'lning
mix fl'om it 50-pl'I'(,l'nt nqul'Ous solutioll !Lft(\J' 2 hOlll'S' imml'rsion nt
40 0 (1" whil(, simillll' %2-indl Wlll'l'l' tnk(\sup l.hc stnnn P('I'Cl'ut of
I'('sin-fol'llling ('onslillwnts in ollly % hour, DI')' SW<'l,tg'UIll cnnnoL be
(l'('nl NI ilion' rn pidly by t he' (:ylintil'r treating methods if time to open
lind ('\0,\('· I hI' cylindl'l' is indud('(1.
'1'IlP diO'usion melhod of LI'(\nting is tho only one npplienble to
dle'mien.l st:'Hsoning, nnd it .must be' nppli(ld to the gl'l'('n wood sinee
till' objl'c\. of tite il'PlltmNlt is to ('('dllce sellsoning dl'gmde (27, (8),
TIl(' tl'('nlnH'nt must also \)(1 in Ilel'oss-the-fib(·1' dil'ection becnllsc It COll­
('l'nlrntion gl'lldil'nt in thnt dircelion is tw('{'ssnJ'Y,
Of till' PI'('SSIIl'(1 treating n1('thod~, the 01\(' involving I'eplueellwut of
wnle'l' in gl'('('n wood with n solution is the' only one in whieh cnpillnl'ity
plnys. it mil101' 1'01(" 'l'bis prol'('SS is npplienble only ill the fiber
dil'~'('l ion. of th{' sapwood of s})('('it's W\;i('!l hl1ye a ypry high grcell­
mOlstu1't' C'onl('nt, O(,('I1I1Sp of thl' huge' l'psistnne(' to .rIow elllls('d by air
bubbll's .in (it(' Hbt\I: l'ilvilil''S. The pressul'es used 1\.1'0 insuHicient to
•
•
•
50
'l'~~~~ITNr('Al.
IWLLE'l'lN 020, l', S,
D~:P'l',
OF AOH1('UL'l'UmJ
to pllSS throllgh Uw pil-IlH'mbrlltH' pot'pS ('()ttlllIlIllh'uUIl~
b(·t\\'N'1l lht. fibl'l' ('Iwilif's (37,88), Ht'll('(\ llH' nit: buhhll's hn\'!' to
r('muitl in lhe·jl' I'('spt'dh'(' fibt'l' ('nvili('s. H(,('lllls(' of til(' itTl'gulnt:
SUI'fllt'(' ofth(' 1iJ)(,I' ('I\\'iti('s, tI,,·S(· nil' bubbl(·s ('!ltlllot (·ttl ofl' How
PlltiI'I'ly liS the' "lII'fll('l' [('Ilsioll of lll(l1iqllid tPllels 10 IlIllilltllin II tlIini­
IlIlIm l;ubbll' l'UI'VlltUI'I',
Liqllid is thlls ublp to puss nlong lht, ('hulltwls
1)(.twN'tl llw nil' hubble's I\JHltht' fibpI'-<'II"ily smfIl('('s, "Thl'll lh(' How
hils (0 O('('\lI' through 1I\1I1l.\' Sill'll ('hutllwls 'in sPI'h's, t he' 1'('Fist Iltw(' 11('­
('OIlW$ 1.00 high fOI'l 11(1 PI'Ilt'ti(,I1.l III~pih'lI tion of lIll' llH,!:hod,
'rhis llH'thod of I'('plllc'ing t hI' wnit'l' in gl'('('n slIpwood by Ull IUIII('OIlS
SOllltiOIl is tlw bnsiH of lilt' HOlldl('I'it' t1'('11 tillg PI'(WPSS IIlld nlso the
i'limp\cl ti,'p-luhp llH'thod of f('t(('(I-post 11'('111 tlll'nt dl'Velop('d by tho
l'ni(NI 8tutl's FtH'('st PI'o(\uds l.lubol'lltOl'Y.7
'rh(' HI('thod of (I'Puling wood by tnPI'('\Y fionldllg it ill tlH' In'uting
Iiqllid is tl)(l silllpksl of nll In'ntillg I>I'O('<'S51'8, but it is (','('n slowl't, t.hnn
difl'uSio.II' Tht' (,1I1'1~r st,lIg(\g of lWIWIl'fltioll 111'(1 fnidy t'l.l[lid wll('n HI('
liquid ",pts UH' wood, but bN'nusl' of til(' building up of n )1I('k Pt'C'SSllt'('
of nit: within tht' wood t1H'I'ILI(' of ('npilllllT t"iSl' will fnll 011' 11101'(\
I'Ilpidly thllll would ot1I1~.I'\\'ist' 1)(' l'Xlwd('(1,
8t fltIltn Ilnd Sp\)ol'g (ti3) found Ihllt sh('(!ls of lio-indt Douglns-fil'
\'(,1)('(11', ('ollininillg Ion (>PI'('('IlI ofwntl'l' 011 thl' hflgifi of Ul(I dl'y ,\'(·ight.
of lit!' \\'ood, took up 25 P(,I'l'Pllt of tlll' w('ighl, of til(' dl'Y woor! of a
ph"llol-fol'llluidphydl' t'psin-fol'tllillg mix in S holll's by difl'usion fmlll n
50-p(\I'('('nt Ilqll(\OIlS solul ion, Simillll' ,'('11('('1' wilh a tlloist\ll'(' cont,l'nt
of (i 1)('1'('('111 l'pquil'('(1:30 hOlll's to Inkp up III(' SIlIllC IItlIOllnt of I'l'sin­
fOt'llIing ('QIl'<tit\l('llts by (,lIpilinl'ity, DUI'illg till' fil'S!. f(·\\' minuh's the
dl'Y \'('11('('1' took up thl' solutioll fllslC'1' thnn did th(' gl'('('n wood, bp­
('IUlS(\ of lh(' initial Ut\I'('sll'lliIlNI ellpillnl',Y neLion,
'rh(' nntlll'lIi P('IH'tl'ntioll of dl'~' \\'ood ('lUI Lw tnnJ('l'illll,Y ni<iC'Cl by
hNlting UI(' wood priol' to imtll(\l'siIlg it, in till' unlH'nt,(·d solution, The
hNlt: ('1\ liSPS 1111 ('xpnllsioll of th(' nil', 011 ('ooling in tht' solution a
pluthtl ,'Il('\lUtll is ('I'('I11('d within t\.tp wood, thus nllowillg n fn'pl' ('npil­
IIlt'Y I'ist', This nwt.hod .is not to .1)(' t'('('01l lllH'tHI ('(I , It 0 Wl' V('l', when
dt'('PI)('Ill'tl'lltiOIl is (\('sjl:(·d, ('x('ppL in the ('lise of smnll spl'cimens of
r(lllllil'y tn'llf('d sp('('it'~ thut 111'(' short in lll(l Iibl'l' dil'l'dion,
'I'IH' tL'('lltllH'nt of dr~' or pn!'linlly dl'y wood with nn nqll(,ous soilltion
01' IIOlIll(lll('01l8 liquid, SII('h ns ('rl'osotl', (,iUwt: by llH't'l'ly soakillg 0['
\lsiIlg n ('yliIld(~t' tl'l'UtlJ1l'lIt ill whieh ('YIl('untiOIl is followl'd by tJ\(~ flP­
pli(,lItion of pn'i'lslIn\ iIl\'olVl'~ a ('ombillllUoll of t'!lpilllll'y l'ise and
liquid lIow, Unwll'Y (12m hns shown how the eombinntion of tho
sinlple, ('npillury rise l'C(lIntioll with Poi8t'uillc's /low Nltllltion, page
53, imlkntes thnL th(' p('ndrlltion in !(,I'ms of pilll('!' the depth Ot'
tlw "O!UU1l' ilhs(H'Iwd should it)('I'('nse pllI'il.boli(~nlly with increllsing
t iUll', ~l'h(\ P('(I('[ !'!ltion should nlso im't'N1S(' inv('t'S(.J:y liS th(' Sf( uat'C
!'Oot of the vis('osity of lhl' trNlting solution, lind dirc'etly flS the squaro
root of th(' nppli('d PI'PSSUl'(" li'mJl1 l'xpel'iml'ntnl dati\' tho timo
l'l'llltiollship hilS bN'1l shown to hold !'l'nsonllbly w<.'l1. .Mellgel' uvuU­
11\)1(, dntn nlso indi<'nttl thnt th<' vis('osity 1'(.lntionship hold5 roughly,
lIn Wll'Y (z(}l hilS shown (hnt the· pI'm'tI'll t ion S('('Il1S to vllry moro
lH'urly with th(' fil'st pOWN' of tite pn'ssllrp I'Iltlwr thnn with,the squllro
('11 liSt' IIiI'
7 \YUtl'" , H, :'.1., IINI'I:III.ISnBD
Madison. Wis.! HHO,
1111 1'0 U'I' NO, RUSS,
U, S, Forest Prod. Lab"
•
•
•
PASSAGE (>to' L,IQl'lDS, VAl'OH!;j gTe" 'l'lLHOI!OU SOPTWOODS
51
TooL This II(I hus l('nLnlinly t'XplfliIwd 011 tll(l bnsis of possihl!'
sll'('tehing of tI\l' pit-/l1PIII\)l'nne POI'('S II IH hI I' th(' highC'I' 1>I'('S811I'('S and
a subs('qllPnt illel'C'uSl' ill tit(' sil'.(' of tllll Olwnin!-,"8,
'1'h(, LI'('nt.IllC'1I Lof wood by lht, eylindl'l' 01' PI'('8SIlI'(' t.I'NI.ting l1H'lltods
Ims hl'C'1l sO thm'oughly dis('uss(,d by 1-.1n('L('I1II (20) lhnt, nO ntt('mpt
will bt' IIInde tQ giv(~ III0 1'(' d('Lniis ill this highly spN'illlil'.l'd lipid,
This llwol'('lielt\ Itllnlysis of lht' 1ll('IUlS of pllssng(' of 11111 l('l'inls
llu'ough wood should ('lHthll' lhos(' Pl'I'fol'lnillg' slI('1I OIll'l'IllioJls to
Ulldt'I'stnlld bl'll(ll' jusl whlJt lll(' ll'piltm('lIts iJlvolv(' fllld should !lid
lhem ill illl pl'ovillg tlll'it' 1Il('lhods,
•
SUMMAUY
An tLlllllysis of lll(l pnssllgp of liquids, VII POI'S, nlld solu\;('s t1l1'(>ugh
softwoods· ulldl'I' difrusioll n.llt! PI'l'HSIII'(' 1H'I'IlH'nbiliLy ('oll(\itiOIlS is
gh'l'Jl Oil UI(I bnsis or ('II pi 111\I'Y stl'lI('tul'n.l ('onsitil'I'u.tioJls,
l.gnol'illg lhl' pitSsug(' through ('('sin duets itlld I'ny (,l'l1s, it is showJI
thtl.L PIlSSltg(' is !'ps.tt'idNI to lhn t. O('('UI'I'illg t.h I"ugh th(\ fi b('I' eltvitips
ill R('l'il'S wilh th(1 pil ehn.mbC'I's Itlld pit Ill('m1.H'IU\I'S, with lhc' trlLllsi(lnL
('p11-wnll ('ltpi11nril'R in pttmlhll witlt lll(' pi L svsl dillS, Itnd thnL ol't'UI'illg
through ('ollLillIlOllS lrl\lU:lit'lIt ('I'll-willi (,1I.pilln.I'il's, The (Irrl'l~Liv(·Ilt'sS
of th(~ din'Pl'pllL pal'ts of th" SI,I'II('tlll'(> \'[\,\'i('s gl'('ntiy with vlI,rinlions
ill lhl' lI'PI1,lilig eondit iOlls. In SOIll(, ('I\S('S P[U't oil til(' si.t'lI(, LIII'(1 is
('lIlil'l,lv illl,n'pelin,
Tlw'dillll'lIsiolis IU\tI ('Xh'lIt of ('Iwh of lh('s(' ('ltpillHI'Y systl'HlS hn.ve
bl'('t\ dd.t'I'minNI by lISl' of llH'lholis whit'h l1,ulolllnlbdly give stn.­
tisti('n.1 tWt'l'tLg(lS WIU'lll'\'('I' possihh"
.
Eqllalions hlwl' IWl'n dpl'i\'l'd ftH' difrllsi()n lhl'ough wood on the
bm;is thn.t LIlt' dilrllSion is IInalognus lo 1'1l'l'll'it'all'ondll('(ion tlll'ough
til(' ('olllbilH'd Sl'I'il'S and 1>l\l'l\.l1 l,1 ('ombinntions of eapi11ltri('s, The
('onlrolling Sll'lll'Lul'ltl \'ttriILblt's. ollwl' lhn.n thosl' d(IP('lHI('nt upon tho
slw('ifie gl'l1viLy or til(' wood, ('iUIl'I' V!\lOY but slightly in tht' h(lll.l'lwool\
of dill'('I'(,lIt slH'('iNl, 01' till'se \'ttl'inLions hn.\·(\ It minol' ('freeL upon
ehllnging tlw d ilrusion \'n.1U1'8, Bc('n usp of this, till' CIIIl'uln tt'd
dil\\lsion VallH'H SN'1Il to 1.)(' pl'Iwtien.lly indl'l){Indl'nt. of sl)('ci('s, Thl~
dill'usion of It solutll into WItU'I'-satlll'ltt('d softwoods in the longi­
tudinal dil'('C'tion is 1).lmost pntirl'ly dcppnd(,lIt upon Lh(' I'fl'p('li\'c
filH'l'-tiwit y ('r~H\S st'dioll, TIl(' d ifrusion iII tIll' tl'nlH:WN'SP d il'l'e tiOIl
is primarily dC'll'l'mill('d by ttl(' eombir\('d ('ommullieatillg cnpi11ltry
slruetul'l' lwlw(I(ln till' fi b('I' (,lwili('S, .:\S a eonS(lq lWll('(', till.' IOllgl­
ludillill difl'usion v!tries ill\'N'Sply "'.ith ehnnges ill til(' specifi.c ~l,!t\'iLy
of tlw wood, whl'rl'll.s llH' tl'j\IIS\'Pl'S(' t1ifrusion y!tril's invers('ly itS n.
('OllIpl('x fUll(·lion of tltl' slweifie gl'll.vity, In the ense of tho dill'usion
of n. solute' illto wood f1\iPd with n. nonswellillg solvl'nt, tl\(, longitudi­
IInl difl'usioll is but s1i<rhtly ufl'('('tpd whel'('Il.s till' LmnSVer'S('. eli/rusion
is n.PPl'l'eilLbhr rC'liu(,('(f, \)i;eltllsl' the ('OIHl111111h'uting eltpilhu',Y sll'llC­
tu 1'(' Ill't"'{,(,ll fiber ('II. vi til'S is limi tl'd to pnssng<' t1u'ough thl' pi t
strnelul'l',
'rh(, drying of wood b(·low the flbt'l'-Sil.tumtion Jloint 01' the nbsol'p­
Lion of 1\. liq\lid from the \'11\)01' phns(' by wood is shown to be similar
to th(, difl'usion thl'oll~h liquid-fi11(·d wood l'x('l'pt thnt: (1) '1'ho
dur('I'pnt InminHs of tho\\'ood in 11, d.in'dion nt right nngles to tim
dryillg QI' absorbing gmdil·nt will be swollell to difrCL'(~nt dt'grc('s nnd,
•
•
52
'l'r~(,.HXl('AI:' BeLLE1'IX 020. r:, S, Dr~I'T, 010' AGHICl'Ul'l'm;
will II IlY (\ dilfl'I'PIIL ('npilllll'Y PI'Op('('U(lS; Ilnd (2) two
dilr{·I,(·!lt (YI)l'S of difl'u5ioll will lit' opl'('nti,'p, "1H.n\('I~', f~ bound-liquid
ditrusi<u\ thl'ough llw {'(III willis ulHI!'I' j\ liquitl-('(lIltl'llt gl'ndil'llt and
thl' dHI'IIS101l of \'nper through lll(' ('OMS!' ('l\,piIlUI'Y stnletul'p lIndl'l' n
"UIHll'-fll'('ssul'(I gl'udh'nl. By ('on"(,l'tillg [0 n (,Ollllllon gl'ndit'nt basis,
till' (iol1lbilwd difl'lIsion COl' (II1('h Inll1inll IIns h(I(l1l pXPI'I'ss('(1 in It singitl
(,OIlS(I((IH'lItly,
.\t tll(l 10\\'('1' tl'1I1PPI'lttlll'P$ nnd higlwl' llIoisllll'P ('onl('lIts
til(' boulld-liquid I>lu't of lIw diffusion (ll'l·(\olllinu.l('s. whilc' at higlH'I'
tl'lll P('I'I~tlll'(IS. n t 100w'l' l1loisllll'P ('OIlLl'1l ts, n nd lllld(,I' I'(,d lH'NI PI'(lSSUI'e
lhl' "U POI' dlfi'llsioll (lI'('(lolllilltLl/'S,
A "('l'iLg(\ lIH'ol'ptielli difi'tlSioll ('onstn.lIls 1'(,lnLh'p to tltt' dinlC'lIsiolls
o( lll(' wood hlw(I b('(ln enII'uIM('(1 rOl' thp dl'yillg of softwoods wilh
difl'('l'pnt Sl)('('i!i{' gl'lwiti(ls ulld(ll' difl'(,I'('llt !>oulIdnl','" ll'IIlIWI'U(lll'P, Illld
I}('PSSUI'P ('oud i Units, 'l'" ('S(' ,'n,ltws {'Om pn l'l' fll nwnhl,,' wi tit d in'usion
"HIll!'S l'a\('ulntNI f!'Olll (It'ying t1ntll fOl' n lIUIlI\)('I' of difl'l'I'PlIt softwood
SPl'l'it s, Thc' dntn iudic·n.tl' 1I1il t lIH' ll\('ol'('(i('ul "ltlt\('S ('un lw uSNl
for (1t'(,(,l'lIlining til(' optimum (It'ying s('IH'dlll('s of (It I' hl'l\.l'!w()od or
Ynl'ious ~mft woods, '1'11(1 thl'OI'pUenl difl'usion yn.lu.t's fOl' soft woods
st'1'1lI to hold qutdituth'ply 1'01' hnnlw()o(ls,
'['Ill' pnRsngl' of n. tiq ult! t h rollgh liq U id-stl.t UI'HINI wood wi th fl'{'(\
liquid. 011 t.\l(1 ('uLI'nUN' tLIle! ('xit I'II('('S Ims bPI'1I ('ollsidl'l'('d by npplyiug
C'ILpillltl',,' !low Pl'illC'ipll'::;.
'I'll(' flow of liquid thl'ollgh til(' il'unsi/Illt
(,(·Il-wldl ('npilla!'il's in ptU'ldll'1 with til(' pit s.v~*'IllS is ill nil ('liSt'S
IH'gligibh" lilx('ppt in tlH' ('US(' of porous sapwood, PI'n.dil'lI11y the
Loln[ I'(lsistnn('(' (0 flow ('xists in thl' pit-Il1(lmbl'lllll' POI'PS,
'
TIl(' pnssng(' of II, liquid .ft'OIll OJ' illt.o wood UtH[('I' ('ondit.ions wl1('l'e
Iiquid-n.i!'llI('lIisd ('un 1)(, fOI'.llI('(l in thl' wood is shown to tw ('omplic'l1tN\
by sUI'fIlC'l' tpH::;ioll pl\('IlOllll'llIL 'l'\w flow of yil'tulI.lly 1'1'('(' liquid
itbov\" till' fH>l'I'-SII,tumtion point in tit(' (It'~'ing of nOI'IIIt1~1 gl'P('lI wood
is ('ontl'ollNI by til(' difl'usion occul'ring in thl' Will'S bl'low till' fibpl'­
sn.luI,ntioll poili l. '
'I'll(' ll'~'llll11l'llt of wood undt'l' (\W'(lI't'nt tl'C'nting ('onditiollS is COIl­
sid(\l'(I(L in thl' light of thl' th('ol'('li('nl finding,
•
('qllillion.
l
UTEnAT('RI~
(1)
•
errED
W. '1',
I \.la3, so~U} I'IHlIII,~:~lS
AH'I'Jlt'ILY,
IX 1~1I~: X-itA Y ,\X,\ l ..n';18 O~' 1'1l~1 S'l'ltlT("('UIU: OF
,\:-n~1.\I. HAIIlS .\Xl) OTIIEIt I'ILOT~~IX ~'lIIEItS,
l"ILrndny Hoc, Trans,
(2)
HAllIE",
H1l3,
2!l: 11)3'·211,
I. \\",
iIlUll,
1'ln: L'1l~:5r:H\'A1'I"t: TIIEAnn:NT OF WOOD,
n. TlI}oJ STIlUCTUTlE
\H"rll~) 1'1'1' ~n:llllH,\N~:1l IX '(,Il~: TH,\Cllt:lllB Ot' COXI nms ,\Xl> '('In:1 It
In:hNl'lON TO Tllt:I'EXE'rl~\TIOX (W (lABEl', l,lCjPIllS, ,uw ~'Ixgr,y
DlVllHm SOl,WIl 1:;"1'0 Gln:t:N ,\XU f;t)AS()Xtm WOOD,. l~orestr\'
(~lIart. 11; [12]-20, illllS,
•
(3) - - .
H115, Tilt:
I,
t:t'n:\'T· 010' STItUCTVItE OF WOOD "PON ITS !'I,HMEMllI,ITY,
Tin: THAClnllllS (W co:;,n'.t:1I0L"S TI~lIn:IIS.
A 111(' 1', R~·. Engin,
A,,~()(',
(4) - . -
W3S. C&I,I,
('11('111,
(5)
B.\nK,'~,
Proc, .16: 83il··853, Hill",
WM,I, STHt'('1't' In: o~' IIlGlI'flll pLAXTS,
30: .I(},,·H, iIlus,
Indus, find Engin,
W, W,
HI38,IU;C};XT WOIlK ox TilE :'t1()1STt'IU; IN WOO» 1110 lU:l,A.TION TO STHt,:-;OTIl
ANIl SlllllXl\A(lH.
lOt. BriL] D(·pt. Hd, nlld Indus, Ih~$l'l\rch,
I<orc.st Prod. Hc::;, Spec, Il.pt, 4, 35 pp" iIlus,
•
PA~8AGE Ol~ LlQl'.LDS, VAl'OnS,E'1'C •., 'U1HOltGH SQF'l'WOOUS
;r.
H., HOHt" .1. P., ANI) ~hA~I~I, A,
Ul30. ~·N\I)\lIt}(,TI(l:\.\!. DHYlNO OF WOon, radII:;. IUHl Engill, Chcm,
at: lLi)O- \li)·t, illlls .
(7) CAOY,. I •. C., ,\NlI "·1I.1.1,\MH, .1. "'.
!!lao. ~\OU:l'l·I.All Dlt't'I~SION IX'I'O WOOD. .10\11'. Phys. Cla'llI. 3!l: 87 '102,
iIIus.
B,\'.l'tlMAN,
•
53
(8)
1)1'~IA~SKI, A,
11108. 1'lIHll
\lit)
Dlt't'l!SIOX
IN
I\olloid Ztschr,
KOLI.OIDEN MBDIU:.f.
3: 210212.
(m
F.
\) t·XI..I 1',
\\'OCllJ fH'IIS'I';\Xrtl ,\:-."0
• Agl'. HN;, 2: ·123 ,128,
101,1.
IHJNfll'I'1' nt,
.,
(H))
(to
112)
Til H 1'01l0SI'I'1' Ot' WOOIl.
,JOlll:•
h,
",(:Ntill,
1fI':\'I'IIXOtl 'l.l'\l Kt::-.":-."'I'~\S \l1~1I nn'rl\'I'IGKtl\TSII\~\\'t:n!'l'H: UI 1l()1.­
Z}}R:-.", VOlt AI,I.t1~1 IX t'(('I\'('B:-." 1101,7. WXIIIU1Nll I)\~H '1'\t(l('KXtl:-."G
('X'n11t1l \ LIl
IH:S
t'Mlt:HS;\'I"I'1(11':-."(1:;I'('XK'I'tlS.
l"Ol'schllllgsh('l'i­
('hll' 1I0lz, lll·rt 2, n 1 pp., ilhl::1. 1\!.'1'1i1l.
]0; ItH'KfI(l:'{, 11.
l:'c'mll'n, II., A:-."U (1 0 u'l':nJ 11 , H.. A.
I !l~{7. 'l'lnl I't:ll~nJ.\ 1I11,I'I'Y Ot' WClO\) '1'0 1,((H'lDS ANIl 1",\C'TOItS ,H'n1('~rIXG
'('1m 11A'I'tJ (It' t'I,OW.
:\linll, Ag\'. ·\o:xp\. ~ta. T(II~h. Bill. 122,
·12 pp., ill Uf' ,
EW.I\l'I', A. ,J.
lHOo. '1'lIt: "Ht'~::-1'I' (H' WA'I't;H I" 1'ltt;t:S. Roy. Ror. LonrlOIl, Phil. Tmlls.,
103.!.
n.,
~l'r. It 1!l8: ·\lSi), ilills.
( 13) FlU"", A,
1\128, ('lit)", OIFl I:s'TI1H~I(('t:I.I.,\It-ItXt'~It: Ilt;1l ;\tll.I,~ltl~\IIHANgN.
()('ut, CII('IlI. C:l·~l'll. ·\(i: ,1·14·150, illll~.
(I,D J.'H1·;Y- \\'YS:::I.I:\'O, A.
H13U.
IH111 .\I·PH \T'
n~llt I't'I.,\NZI.I('lIt:X ZFlI,I,\\'XXlltJ.
Prolopinsmn
Her.
25:
2li I· 300, 1II1ls.
llin
•
t'Ilt1ll DIg H(\X'!'Ot1X!nIt,THlS('lItl "t:lI~n:S~H'NG l)tm Sl1IlMICHO­
SKOI'IS(,lItlX \tXtr~\t1 I:\' la:HI'STsl'lIs'rANZ}lX.
Protoplmmm 27:
372-41 I, iIlIIS,
~Hi\ nllt~}:XILIl.I" ,,'. I..
Ul3n, S1'llt:XO'I'1\ 'I'llS'I'S I'F1Ul't:X\)lrt'l'" It TO Tllt1 OltA IN (H' TlMlnlll AT
\'A Itlnt'S. Tt:~II'.}"IA'I'\·lnlS ,\ xu ~IO\s'rt·rn:rO:-:'l'g;':TS.
AlIst.rnl.
\(l37.
('(]\lIH'il ::-;~·i. nnd IIl(\U:5. Rl's., ,JOllr. Il: 26fr-27G, illus.
(t7\
1\138.
(,()1,1,,\1'::;1~ XX\) 1'1'8 11I~~1O\·.\1.: !io~n: It I,CJo)X'I' IXVgS'I'IOA'I'IONS \\'1'1'11
t:1TAI,YI'1TS In:n:\AXS.
liS)
(:IlIt'FI:\.
.\1Isll'll!. COllllcil Sci. nnd Indus. Hes.,
Pmtl, 75, 20 pp., ill us.
,J.
n.
HI HI,
110HIlI'11tF1U I'ITS I;': IH)t'(1J"IS F'IH.
A !i'('\'IlY Ot' 1~111~ l'OSI','IOX Ot' '1'ln:
'\'Ol\lli IX ~lO\'N'l'AI:\' ,\l'W I,OWI.ANI) HI't1Cms IN lU11,,\'I'ION '1'0
C'IlIWflO'l't! .1'1~;':F:'I'IlA'I'IOX.
Jour. Forl'st.(V 17: S 13-822, illmi.
H12.l.
~'\'n'l'lIt11t :\'O'l'R ll:\' '1'11(, I'O~ITI(JN Ot' 'rill> TOIl! IN 110Hlmlt(oJIJ 1'I'I'S IN
In:I,;\'('IO:\ '\'0 I'tJ"B'I'IlA'I'IOX (H' I'lnlfjl~IWA'I'I\'ES.
,JOlll', Forestry
,)<). S<) S3
1201 1\ \ Wl.I~Y. r.~)?' - , .
11l3\. W()(lI)-I.IQrlll nEJ.A'rIONS, P. S. Dept.
iIIus.
(211 I Nnt:ilsOi.l., L. n., .\NP ZomH., n..r.
l!113. ~IATm:~L\'I'I('AI,
(22) KA'I'Z.
(23)
•
(24)
;J.
'I'IU:OItY
Qt'
Agl'.
Tf'ch. 13111. 248, 35 ))p.,
InJ,vr eONU1'c'rION.
168 pp.,
mUH.
Boston.
n.
1\J2.1.
itOI''I'(H1NSl'EK'rROSKOl'ISClIE l'X'I't:usecm·NON:-." umm IlM; \\'F:S~:N
IH)H (ll·~:I.I,l'Nr. In: I Sl'US'I'"XZl-:N .nm 1.~IN FAS~JItlllAGHA~IM
(unn:x. Phys. Ztschr. 25: 321-326, HIllS.
t\130.
'()AS l'R(JIlI;t)~1 DNIt Qt'l,I,I,\'NG DI>H ('I;;r.INI,(JS~: t'N\) 11IHBH DBHJ­
\·A'n~.
('('IIt1lo~f'('ll('lIlil' 1\\2): 17-30, iIlus.
1\133.
TilE L,\\\'S Ot' SWf:I.l.1XG.
Fl\radn~' Soc. Trans. 20: 27!l-2!)S, illus.
54
(25)
(2(i)
TECHNICAL IlULLE'l'lN 020) U. S. DEptl'. OF AOnICUL'L'UUFl
K()I.J.~I,\Io1N, F.
1\)35. 11I,C'IINI<:llIl'C!n; \'lml'O[.OI'XO IH~II KUNiW[,I('1I flN 1I01.Z'I'ItO(,KNtlNG.
Forsell. tluf d('1\1 (l('b. des IllJ,!;('lIiPlIrw., B('iluW' (i: 1 (i()-·l74, ill us.
Ul3(i.
•
~llN Nt'lt',,::; n;IU'MlltJolN ZI'H IIEIUWIINt'NO I)E:lt 'I'UOCKgNZI'111' A~[
IIlmll'lI~l. IH;H 1I01JI'Z'I'IUJ('KN1·NG.
Forseh. auf dem Geb. des
"r.
Inp;l'lli('1lI'w" Bl'ilu!{l' 7: 113··1 Hi, ilIlls.
(27) TAH'GIIIIOHOI'CiIl,
K.
]\)37. <:'IIi,l~IIC"" I'ln:-'I'UNA'I'~"':N'I' Sl'lmLlS SNASONI*1 01' LAUGI, 11'gMS
A \'0 IDS. IH)nUAIH1.
Anwr. LlIlll\)('rnlllll 300!): 0(j-(\7, illlls.
AND
(28)
'l03!).
(2!l)
('III·lmt',\I. SI':M,ONINO (JI' OYE:rt('t'P O;\K, South. Llimberlllun 150
(200m: 137 140, ilhlR.
\L\eLI'l;\N, .1.
11)35. M.\Nt'AI, tJlo' 1'111;8 I::II\'NI'I \'1,1 '1'lnl;\'I'~I"N'I' 0.' woon BY l'ltESSUltB.
l'. [4. nl'Jlt. A!{l', ;\[isc'. Puh. 224, 124 pp., ill us.
~[.\It·I·I.gy, ,I, F.
l(J2(\. ~IOIS'I'I'HJ'l .'\On:~JlolN'I' 'I'll HO 1'(1I I WOOD. 'I'Hi, R'I'IMIlY S'I'A'I'I". lOt.
Bdl.] D('pl. Hei, und [lI(lIls. HI'S., Fo!'('st. PI·od. Ups. Tech. Pnpor
2, 22 pp., iIIllS, n.
N'I~W~I'\N,
A. H.
l(Ja2. '1.'1111 IlIlYINCl
(H' l'OIlO":'l :'lOI.lDS: DJIo'J'I'SION ('A I.CITI.NI'roNS, nn'FU­ SH)N AN!) f\\'!tIo'.\('!·) 1':~lISSI(lN 1~(ll'A'I'IONS.
Cooper Union Bul., (32)
Elll.!;ill, Hl'i. HI'r. ii, 42 pp., iIIus. PIIIl,I.II'S, E. \V. ,J.
103a, ~IOn)~Jlo:N'I' ()to' '1'111': 1'1'1' ~mMIlH,\N~: IN (,ONIFJo.HOI'S WOODS, WITH
SI'I·)('L\i. In:Jo'I~llI':N('g TO I'ln)S~!H"A'I'lyg '!'JtNA'I'MBN'l'. Forestry
7: [I0UI120, ilit.!R.
v
Rl'l I'!o1H, O.• J.
10aO. WOOD 1·'llI~mR. ,lour. Forestry 28: 533-541, illus,
llla·1.
STIII'("rt'Hl; (n" 'l'IlB em.T, WAI.I, OP WOODFITl}]RS.
l'apor Indus.
1Ii (3): liS 1Sa, illtls.
(a5) SllBHWOlll), T, K.
l\l2\). TIJlol OHYLN<1 (H' 801.ms. I. II.lelUS. and Engin. Chom. 21: 12-16,
illus.
(3(;) ' - " - ' - '\;-/0 ('milNOR, E. \Y.
1!)35. ~n)K Il;\NI1.~1 RI'RII1\1 IZYl~S'I'IYA. VseSSltyuznoyo Tcplot.ochllisohes
["0\'0 1111't. Xo. 8, Aup;., iIIus.
(37) !:hAM~I, A, .1,
1028. 'I'll}} S'I'U\'C'ITHl': OP 80F1''''00DS AS H1,Y}]ATolm Ill' lJYNA~IIC PHYSICAl; ~IJol'I'1I01l!;.
Colloid SYlllposium l\lonog. 6: 83-108, ill us. New York. (38)
11)20. TllH ('o\l'll,I.AIIY i'\'rHl!C'I'1!UE OF 90F1''''00D5. .Tour. Agr. Ros. 38: 23 1i7, HillS. (30)
102l). 'I'lm l·'llnlH-:'lNl"'U,\.'I'ION 1'011'1'1' 0.' WOOD AS OTl1'AINED ~'UOM EI.EC­
'!'UI(',\I.
(,IWIII"
(40)
CONIl\,("I'I\'I'I'Y
M}]A8t!UB~mN'rs.
Indus.
and
Engin. .\llutyt. Ed. 1: O,I··!)7, iIlus.
1\)20.
1'H-)N:'lI'l'Y OF WOOIl 5 I'll S'I'A NCH, ADSOIU'1'ION BY WOOD AND .1'EUMEA­ JlII.ITY 0.' WOOl>. Jour. Ph~'s. ('h(>lII. 33: [308]-41'i, ill us. 1031.
A Nl)'" ~n;"1I01l }'on D}l'rl,U~IlNING ,'HE l'UOl'Olt1'ION OF' 'rilE 1.ENG'l'H Or' A 'I'HACII1JI.D 'I'IIA1' IS IN CON1'AC'I' WI'I'H U,\ YS. Bot. Ouzo 92: (41)
•
101,,107, ill liS. (42)
1032.
AN })1.tlC'I'H1CAI. CONIlt'C'J'tYITY ~IE1'1I01l FOR
EPr'}]l"I'IYl, (''\!'II,I,AltY DDI}lN510NS 01- WOOD.
30: 312·B2ii, ilillS,
1934.
Et'F};;('1' Or' IXOIWANI(' 8;\[,1'S l'PON 'rIIB SWEI.I,ING ,\ND SlIurNKINO O~· WOC)D, Jo\,r. AllIcr. Chom. Soc. 56: 11!l5-1204, illlls. D}]1'ERMINING THE Jour. Phys. Chem. (43)
•
55
l'ASSAOl<J Oli' LIQUIDS, VA POllS, :I-:TC., 'HIHOUGH 'SOF'fWOODS
(44)
•
(45)
1035. SIIHll'lKUHI A:-IO SWNI.I,ING O~' WOOD.
27: ·\01·106, illwl •
Jndus. lind Engin. ChcllI.
1035. '1'lm 1':Jo'n)('T OF
(,IIM~01':H IX 'I'll}; ~Ql·II.IIlHn·~1 HBI.A'I'IV1~ VAPOR
I'll JolHH \ 'II!'! I'I'Ol'l 'I'IIB (,,\I'll,I.AIlY S'I'I\l;(l'I'I.1JU: 0'" W(l(JIl. PIl\'sics
0: 33·1 3·12, illllS,
(-16)
(47)
•
H)3!l. VOI.I.OIII CIJ}J~1H;'J'II\, OP (,1·JI.I.l'I.OSIO
:'Ilisc. 1'111>. 2·10, UO pp., illus.
MA'I'11IUM,S.
U. S. Dcpt.
Agr.
1038. ~'''I,n'l ••\'I·I()l'IS OJ.' 'l'Inl \'01D \'OI.l':I(}l O'~' WOOD. Indus. nnd Engin.
('h('lI1. 30: 12S0-12St, ill US.
-
,\XIl HAXHl~X, L. A.
IH35, ~lIl'1l~II)\IX(I WOOl) HIIHlXKA(11-: ,\X.1> SWHr.r.IlW: Ulll'l,,\CINO \\'A'I'BH
1:01 wnon WI'I'II NO:ol\'OI,,\'I'II.1-l M.\'I'NIIIAI.g, Indus, and Engin.
('1\('11\, 27: 1·180 US·I, i\lus.
(M»
- - - Al'Ill IL\:-Isf!:oI, L.•\.
1\)37. TIn) 1I():-IlllNU FOII!'}J 01,' ('gl.I.l"1.0HJ(' ~1A'I'I')HlAJ,f; ~'()I! W<VI'l'll! ("'I!O~(
8 1'1·:e 110'((' \'\lI,\!~J11 AXD 'I·JnJH~I"I. I>Nl'A), JOltl" PII\'s. ('hell1. 41:
(50)
- - - ANll I[":-ISI'::-I, L. A.
lU3S. Sl'IIPM'l':-IW\'Nll n:IISt'S {'.\I'J(.I.AHY-('ONIlI~XS]'JD WNI']~n IN WOOD.
JOIII'. 1'Il\'I~. (,llPlIl. ·12: 20n·2l·1,
- - _ . ,\NIl LOI'I1 IlIio 110 1'(1 11, \\', K.
1\)3·\, '1'1I1·;1I~J()J\Y:-l.\~IJ('H ()I~ 'l'In: SWBI.I.IXO O~' WOOll • .rOUI'. Plws. OIll'JU.
t 007 lOin, Hitls.
(51)
'
30: 121 132, illus.
(52) - - ANIl 1:'hlllOU(l, H. ]\1.
103,1. AIlSOI!I"I'ION ('OMI'In:HHlOX ON (.'};(.I.l'I,OfnJ
~IIMl:H'ln:~nJN'I'5 IN U}lNZI,XB.
.\:-11) ·WOOll.
Jour. Ph~·s. ('h('III.
.
J.
ImN51'I'1'
31l: .133·,142, illm;. (53) - - - ,,:oIll l:-\}:U01H1, R. :'Ir.
] \)3\), IU:SIN-'I'IllM'I'],J1l I'I.YWOOI). Inclus. and Engin. Chell1. 31: 897··902,
Him;,
(54) SfI11bl~'rNIJl"1 S. ~r. C'.
1\)26. '1'111, ~1()\'}:~nJN'1' tW M(llS'l'\'IU,: WI'I'II Hl~~'Bln)x('JoJ ~I'O '1'1~IllBn S)MSON­
1:010. lGt. Bdl.1 nt'pL l:-\ci. and Indus. Rcs., Forest Prod. nes.
Tech. l'n\lN 1, 211 pp., ilills.
(55) '1' C'l"r J.}\ I" •
lU25. ,\ ~1,\1'IIl~~INI'l('A I. 'l'IllWUY 01·' 'l'ln: UItYlNO m' WOOD. .ToUl" l"rnnklin
lnsl, 200: OOlHiI·l, illus.
(56) WII.SON, '1'. It. C.
1932. S'I'Ill,NO'I'II-)IOIS'I'\'In: InJI.A'J'WNS }'OU WOOD. U. S. Dept. Agr.
T('ch. But, 282, 88 pp., ill liS•
•
•
APPENDIX: COMPILATION O:F PHYSICAL AND STRUCTURAL
DATA USED IN CALCULATIONS
FIBER-SATURATION POINT
Water is held by wood either as surface-bound or capillary-held water wit.hin
the cell wnll, or ns virtually free water in the cell cavities. 'l'he varJor pressures
of the water held in the avernge-sized fiber clwitics in a softwood will be reduced,
IlS u result: of tho curvature of t,he menisci (equation 21, p. 65), by only 0.01
percent,. Even at the tap!)rcd fiber ends the reduction in vupor prefisure can
hardly llxccod 0.1 percent. The coarsest ellpillury structure in the water-swollen
cell walls is, undoubtedly, below microscopic visibility fiS it is necessary to use
mOf(1 drastic swplling ugents or disprrsing agent.s to make the internul structure
mi<~roscopicalh' visible. This would nlC'an that no capillaries in the watel'­
8WOllllli cpll ,,'nil exepcd 0.2,.. in diumetclr. Thrse maximum-sized cell-wall
capillnrips will rrduce the vapor pressure by about t percent. ~l'hern is thus a
rntlll'r nbrupt, brenk in the cllpillarity effed between the IrIlIlRicnt; cell-wall
capillllri('S and the lIIicros('opienlly visible cnpillnry structure. This brenk in
capillary siz('s is somewhat bridgNI by the few largl'-~ized pores in the pit nwm­
branes that, nre microscopically visible (2, S) but brcuuse of thrir small volume
they are rclat,ively ineffective in all but liquid-pllssnge properties. Both the
surfllce-bound wntl'r and the water hl'ld by eapillnry forceR within the fine structure
of the cell wnll arQ thus held by forel's sutncil'ntly g-rt'llt to oi1'tinguish their effects
from those of thl' water in the grosser capillary structure which is virtually
fn'{'. Because of this discontinuity in the distribution of capillary sizes, a number
of the wood properties sho,,' discontinuities in their relationships with changing
moisture content.
The moistllTc content at which this discontinuity in wood property-moisture
content relationship occurs is known ns the fiber-saturation point. It can pcrhaps
be best defined as the moisture content of wood, in pcrcent. of the oven-dry weight,
when the cell walls are saturated but no Yirtually free water is present in the
grosser capillary structure. It hns sometimes been defined as the mdisture
content in equilibrium with saturnted water vapor. Strictly speaking, this is
not correct liS 1111 capillary structure depresses the vapor pressure of wllter someWhllt so that under this dl'finition the fiber-snturation point would correspond t.o
the completely water-filled strueturl'. According to the first definition for the
fiber-saturation point, it will correspond to the moisture content in equilibrium
with fl. relative vapor pressure sOIllC\vh('fe between 0.99 and 0.999. In practice,
how('v('r, the extrapolation of the rellltive vapor pressure-moisture content
eun'{'s to unit rl'lative vnpor pressure from rehttive vllpor pressures below 0.99
gives a value for the fib('r-saturalion point in good agreement with the values
obtnined b~' other methods.
The filwl'-sa(;uration point. of Sitka spruce Ilt about 25° C. in percent of oven­
dry wright;, obtain('d from the efTl'ct of the moisture eontent on six different
properties of wood, is given in the following tabulation.
Fiber
•
•
aulllralion
point
(percent)
Equilibrium rl'lative vapor pressure (extmpolat.ion to unit relat.ive vapor
pressure) (51) - - _________ - .. _.. _____ .. __ ____________ _______________
Shri~~Wl~~~~r~a(s~):~~l~:~-~l~r~_~I~~i~l:~~~~~__________________________
Taulj3ntial (39) - - - - -- -- ____ '-_ __ ________ __ ______________ __ ___ __
Rlldialo(3~6:~:=
=~=
Do. (56) ------______
_______________
______
___ ______
___ _____
=============
==== === ========
====
==========
==
Reat of wetting (extrapolation to zero heat evolved) (51)------_________
Adsorpt,ion compression of water (extrapolation to zero compression of
EI~~~1~ll(~~;l~~~th~tY-<"i;;i~t-ofd~~i;ti~n-f~~mlini;iir-l~-g-~f
~;-;;di~ct,i~fty:
moisture-content relationship) (39) _ _ __ ________________ __ _____ ___ _ _
56
31.
29
30
~g
24
29
30
29
•
PASSAGE OJ<' LIQUIDS, VAPORS,
•
•
~'HROUGH SOlf'l'WOODS
57
}'/ber
!a/llra/ioll
1'oi7l/
(/lercent)
StrclIgth (point. of deviation from linear strength-l1loi~lure content rela­
tiollsilip) (56):
bending:of rnptllre___ .____________________________________
Stut.ie
Modulus
"Modllllls of olnstil,ity_______________________________________
Pibcr strpi;S ut elastic limiL_________________________________
Work to muximum IOud_., __________________________ '________
Work t() clastic limit____.__________ ---------------__________
]mpnet bending:
i\ loc!ulus of ()In.sticit,y ______ __ _ _____ __ __ _____ ___ ___ ___ ___ _ _ _ _
Fiber ~tress at elnstic limit__________________________________
Work to clnfltic limit.______________________________________
('0 III prf!s~ion pamll('1 to gmi lI:
Maximum crushing fltl'ongtiL_______________________________
Coml)I'(~$SiOIl pl'rpellciieulnr t.o grain:
"ibel' strcs~ nt; elm,lic limiL_________________________________
Sh('IlI':
Avcmge radial aml tangelltinl._ .. ____________________________
Torsion:
l\loduhlH of rigidity_ .,___________________________________
Sill'!ll' stl'CSR nt elnstie limit,_________________________________
Ultimate shcar stress_____ __ ____ ___ ___ __ __ __ ___ ___ ___ __ __ ___
27
27
26
29
25
28
29
30
27
28
30
27
26
27
'l'h('f;(' \'lllue::; al'l' 1111 in v('ry good IIgrc(,llll'nt. Men!'lIrements mnde on different
sp('('i('s of ~oflwoodH vlU'~' i)llL l'lightl~', IlrIwtit'ally nil vailles fnlling ill the range
2() to 31 pl'rcCnl (45). Tile tilx'r-l'ntllmlion poiut \'lIlues III: difft'rent temperat.ures
u«('(1 in this )lubliclltion w('n~ obtllilH'd by extrupolating the moisture cont.ent­
r('lut ive vapol' pn'H;;III'(' (~urve;; of figul'(, 24 1,0 unit relative vapor pre~surc. Thcse
"aim's nl'(' ao.(), 29.2, 28.3, 27.2, 25.1, IIl1d 22.9 percent for 25°, 40°, 50°, 60°,
80°, nnd 100° C., respectively.
Bnl'klls (5) hns stated that; the fillPr-l'alumt,ion point has no real theorct.ical
significallce. He is eorreet ill his eontelltion on UlC basis of the definit.ion that
{,h(' fiber-l'aturatioll point is t,he moiHture content in equilibrium with unit activity
or unit relativc vapor 1)I'('1;sure. H is argument, is, from the author's viewpoint,
unfounded when tho fii)er-saturntioll point is d('fined as the moisture content
at which the cpll wnlls are 1;atumtcd, but no virtually free water exists in the fiber
cavil ies. The filwr-Hllt ul'!\lion poill" designlltes t,he break in the capillary size­
moi~ture conh'nt, I'l'lntioll~hip.
The diseonlinuity in the capillary size dil>tribu­
tion betw('PII tilt:' IUI'jl;psf; trullsient cell-Willi cnpillaries Ilnd the capillaries of the
microscopirlllly \·.isihlC' stl'u('tUI'C eIUISC'S an aPPII.rent. limit,ing value in the relat,ive
Ynpor PI'Pi'Rur(', ~hrinkllg(', IU'llt of wett ing, and Ildsorption compression-moisture
conll'nt I'l'lution!'hips, nlld It brellk or zonp of maximum curvature in the electrical
con(\ul'tivity and sln'ngt h-moisture content. rl'laUonships.
SPECI Fie
•
Elrc.,
GHA VI1'Y
OF WOOD AND 01-' WOOD SUBSTANCE
The $pcl'ific p;rtl\'il \' of wood, the mHo of the weight of ihe dry wood t.o the
weight of I\n equal volulI1o of watt~I', vMips con::;idombly for differcnt species of
wood and I\I~o within n Ringle spl'cieR. The specific gravity can be express<:d in
terms of the dr~' \'011llIle, t,h(' completely swollen volullIe, or the volullle at currcnt
moisture content. Til this publieation the specific gravity of the wood is \lsed
on bolh swollcn- and dry-yolume bases. On the swollen-volume bllsis the specific
gm\'ity of different ::;oftwoods vnries from nbout 0.25 to 0.80. On the dry-volume
basiS the \'alues are sOlllewhat larger. Because of this large variation, the cal­
culations will be IIlnde for the complete range of specific gravities. 'I'he property
v!\lues given in table I, page 12, however, arc for a wood with a. specifio gravity of
0.305 Oil a swollen-volume bllSis and the corresponding value of 0.406 on a dry­
vohllne basis, which was cnicuillted from the swollen-volume specifio gmvity and
the volumetric shrinkage on the basis of the fiber ca.vities remaining unchanged in
size Oil drying (44).
13eul\use of lhl'. ini('rIlal capillary structure of wood, the volume occupied by
air or water is included in the external dimension volume. It is obvious that the
58
TECHNlCAL BULLETIN 929, U. S. DEPT. OL,' AGLUCUL'l'UHE
•
OJ
04
P£lI1TJV£
05
Vll,'~'R
06
07
0.8
0.9
/.0
P/('(.J.!I/R£
24. '" J)(lHO rp t ion moisturc content-r('\ntiye vnpor pr<'s,~ure curves for
Sitka "PrlH'(' nt, di f1'l'rl'lIt t<'IlIpern(lIrl's, tnk('n from the rllltn of 1.oughborough (6ll. FIfll"IU)
•
wood substanCt'. its('lf. which oC('lIpi('s 1\ con~id('rnbh' smallcr volume, will h/l.ve
n con"idl'rnbl~' higll('r spet'ific gmyj(~'. The volume' occupi('(\ b\' the wood SII b­
st/l.nl'(~ hilS hl'ell (iNl'rIllIlII't1 by tIl(' amount of helium gus, wMer. or other liqu id
thnt: is displtl('t'C1 by the wood substance. \·n!t.les for the specific grlwity of wood
substnncc based on /I. volulIle obtained by watl'r displacement \'nry fro III about
1.50 to 1.:30 for difl'(>I'cnt I'pl'cics (.9, 40). These \"lilues nrc, however, too high
as wMt'l' is so strongl." held by wood that. the \\'ood is compressed. .HeliulIl g8S,
whk'h is not: c()lI1prl'i'~l'C1 by wood. gives a somcwhat; lower vnlue, 1..16, wh ioh lIlay .
be cOlIsid('rl'C1 to r('present the true sp<,cific gnwity of wood substance (49),
Com'III;:SSIO~
(w
AnSolllllw\\'ATEH
From tI\(' difTl'rpn('p betwecn the spet'ific volume (reriprocal of specific gravitr)
of wood slIh,;t:lI\('(' oilt:tillPd h,· 11('lilltll di~(ll:\('elllent alld hy water dispi:Lcernent,
UH.' CQntraction o('l'urrillg in the wlltpr held by the wood at the filwr-slltlirntion
point cnll be obu,illt'd (4[). liB). This Ilmounts to 0.031 ee. per gram of wood,
The compre:;sion occurs in the 0,306 gm, of water held by a grnm of dry wood at
the fibcr-lmturn(ion point Ilt 25° C. The volullle of the adsorbed water is thus
0.30G rninu$ 0.031, or 0.275 co., Ilnd the spccific gravity of the adsorbed water is
1.113. The ('omprpssion of the water increases with a decrcase in the lIloisture
('olltent below the fiber-satllrntiOIl poiuL. The water first adsorbed has a specific
gravity of about 1.3 (47",49).
FmEII T.E:"IGTH
'rhe len!-,oih of the fibers ill 1m)' spel'inWIl of wood yuries considernb\y, All
softwood SP('Cil':', howe\'er, ('()\'er about the same fib('r-lellhrth rnllgl'. 1.5 to 6.0
1lI1Il" 1\1Iclllvemgc about 3.8 nlln.
In table 4, fiber lengths determined by ill num­
•
59
PASSAGE OF 1:;1'Q(' 108, VAPOHS, ETC., THHOlrGH SOF'l'WOODS
•
bor of different Ilwalls an' givcn for se\'cra\ speeies of softwoods. 'Phe ngreelllcnt
betwcen the fib(!r lengths obtained by the c1iff('n'IlL methods is Ycry good. The
Ilvemge fiber (ength ~ee1l1S to vary bllt littIl' among t,h(: differellt. spccies. A yalllo
of 3.8 I1IIIl. or 0.38 C1I1. is lised LId the Il\'emge yulue in the calClIlations,
TAlILtl
4,-,-Ptller h'lIyth of sofl,lI)oods from diJJ('rent types of lIIeasurements
1
Over·
Direct microscopicuJ
Hydro' eOl1ling
,Electro-osmose
.tutl~
tlOII"
'"lpll·
lur~'
rl<o
Species
YeIlOIl"'I'e<illr, ,\tllsks.,.
Htlfhjl~lur t \\',\'ltl'ru
f)rnl~ht',llr
",. <' . .
IIl'llllork, Wl'~t(!rll.", ..... ~~ ..
l'ilw. Jlonllt.~ro....n
Mill.
3.3
a.S
a.s
Muxl,
mum
1\\'lIxi·
A(1II.
J\lll1.
4.5
5.5
.j.S
3.S
3.8
5.5
5.2
5.5
5.7
a.s
5.5
mum
i'lIlxl'
tuum
...\[1/1.
4.5
5.t!
4.9
5.5
5.3
I i'\('II'tlreuwuts otllt'r thun <lIrN'\ IIIlr"l~I'opk"lll'IuJllo)'cd ilitTvrvut meuuS thut uutomutlclllly givllslntls.
ticlilu \'erugl'~ uud ('xtrcull'$ ("r IlIIlU()II~ nf Ilbl'rS (S7, 8S).
En'ECTl\'E Filum-CAVITY LgNGTII
•
'The a\'('rn~e distallt'!;' lrl1\'('r,;('(1 by It IImt('riltl in pllS5in~ throllgh u fiber cayity
itl the IOllgitudillll1 direl'tiotl is not ouly d('pend('nl Ilpon the len~th of the fiber
but ulso on till' fiber oV('l'lup. Th(' fiLpr OV('rlIlP is upproximately one-follrth of
u fiber lellgth ut l'lich ('lid. 'rhus, in order for u matpriul to uch'ullce through the
filwr structllt'{', it will ('ntl'r ut {l.Il," p\1int o\'er the tibl'r ov('rlap ai, one end and
exit ut uny point ill the O\'prillp ut thp (1tll('r end. The,' Il\,l'ru~p path. would thus
11(' thrl'p-fourths of a filwr 1t'lll!;t h, 01' O.2S.j ~IIl, This will hereafter be designuted
liS the ctfedh'e fibcr-('lwit," 1('n,U;! h.
AVEIIAGE
NU~lBlm
OF FillEt{ C.H'ITIES AND 'VALLS IN SEnIES PER UNIT
L)ISTANCE IN LONGITUDINAL DIHECTION
Tlw uv('mjl;e lIumher of fiber eul'ilies t1'll\'pr,,('(1 in seri('S per centimeter length
ill the longitudilllli din\etion wit I he the re('iprocul of the effective fiber-cayity
leng! h or 8,5 fibel's Iwr Cl'ntilllctl'r. The nlunber of pit membranes or dOllble cell
walls tm\"llr8pd in SNips in (:he longituc!inul direction per cpntimoter will be sOme­
whnt. IC;;8 thun this, sinc(' no pit melllbraneS or cell wall will be traversed in order
that l\ liquid. \'apor, or dissolved mut~'riul IIIUY enter or exit from the open-fiber
cavitil';; which O('cur nt both ends of Il specimen, On the average, half of an
eff('('til'(~ fib('r I('nl!;th may be trtwersed ut ench end of the specimen without the
mnteril1.1 passing throllgh .11. pit 1I1(,lllbrnnc or ('ell wull. The ayerage number of
pitnwtllbran('s or c('11 \\'t\ll~ travcrsed in serics per C'cntimeter in the longitlldinul
dirp('til)il will thus bl' the average number of fibers truversed ,minus 1 diyided by
tho speCittl('1l Il'llgth.
AVEIIAGE NU)18En OF FIHEHS PEn UNIT DISTANCE IN THE RADIAL AND
TANGENTIAL DIRECTIONS
TIl(' number of fib('r;; travers('d Pl~t unit distunce in the rudial und tangential
din'ctions through swoU('1l wood ('un be rcndily obtuin(ld by counting tho number
of fibers in ('11('h of these dirp(,tions on photomi('rographs of swollen transverse
s(,('tions of tW()Wll lI1ap;nification. The magnification should be sutllciently greut
to \lIake counting easy but not so great 1\$ to reduce tho number of fibers on a
picture below the number in a complete annual ring,
•
60
TECHNICAL BULLETIN \)20, U. S. DEP'['. OF AOHlC'ULTURE
Photoillicro!l:rllphs 20 cm. in the radial direction IIlId 15 ('Ill. in lh(' tlln~ent illl
with a mllgnification of 50 times, w('re uSNI for d('tprillilling til(' lIullIbt'r
of fibN" Jler ct'ntilll('tt'r giv('n in tltble 5. Counts mudp in difTC'rpnt; parts of the
photomi!'rogruph:5 gave sllrpri:;;ingly COn$tallt "lIllies. Any onto count rllrely
d('villt(l(1 frolll til(' average of a considl'rable number of counts by lllorC t;hun
2 to 3 percent.
dire(~ti()n,
5.-Averuge lIumber 0/
TARLl:
fiber.~
1'l?r celltimeia
dtn'c/iolls 1
iIi
•
the radial (/1/(1 trIllY('nlilll
~----'-'-'--------
A \'crn~l' nllllllwr (If flhl-rs
})('r ,,'N) t iuwll'r
'I'nn~.. ntllli
Hlldllli
direction
AllI..~ktl ;i'1-IlClW-l,-tlnr.
....... ..
\'ort Orford \\'hl(,-.('\-<llIr .............. _.
Nortl"'rIl whllll·wdnr
nl1u~llI.'·flr
.• __ •. _.. ,..
~'Ir, hlllstllll .............. , .......
Flr.noble.... ....................
Fir,. n,d
. . . . . •.•••••••••••
Fir. 1',lt'llIusllVl'r
Fir, white
. ..........
H5
:\;12
3""
:100
3~S
21\5
252
Plnc. w,'st,'rn \\'hit~ (nllrrt\w rllI~sl
Sprlll~', blllck
Spr\l(~-, rl~1
00
..
..
.....
".
!
'l',uUllnick
25~
~.I(I;O()
f
!.
2;'", ~
I
I
";m i
2W
:1I Ii
2,,~
2."0
,...........
' . , . . 00. . . . . . . . . . . . . . . . . . .
. .....
S\lrllli>_ ~Itkll ('\lIrinall.. .. .... ..
SprllCt', Sltkll (<;()111\1"',51011 woodl
SpruCt•• while.......
.•.
i
2M I
277
3'.?:J ~
:UNliiock, wl',Stt!rn '~_~""""H"
.l.arch, \\'('stl'rn..
'"* ~ .. "-" .. ~-~
I'lno, lohlllllr· •••
I'lnl', l<l!lg('pol~
Phw, 10ttltl(~n(
~~ .... ., ..... r"
l'!tw, .'lIsh-rn whlt('
..... - .... '"
I'hll'. p()I1II(-r""'1
. ..... ....... ..
Ph'I'. shonlt·t\f
Phlt,', stl~ur
~..
Vlml , \\·t.'~t.lrn whitt" (brolld rlll~sl
H"llwllOd
illrl-i:tlOI\
.. ........
......................................_._..'\
300
2:15
:Ni
302
3.;0
2,S
:125
:103
t
1
.
;
,"
Hntio of
1Il1lnlll'r In
m-Hnl til
tnngl-IIt1l1l
dln-etlon
-100
:157
:1:10
:1()0
3117
270
200
247
a07
ar,:\
1.11
• !~1
• US
t.l')
,SO
.OS
.97
1.15
.!iO
.92
2Si
.S-.'J
:.11 .,1 (:1)
1
:.!'=n
I.' g.15
t
.01
.81
1. ItI
1.01
t O~
: 02
• \15
1.08
1.1·1
:12()
a07
2~tl
"17
3(}0
317
217
3:17
:140
:1:1-\
21l:l
30n
320
I.Otl
1. n.;
. 9~
I.Ofo ,1l5
•
- - - - - f -.. . -·--- - - -__
:105 !
':l1l7
) ll(l('nut'l~ tilt's..' r(l.lIlt~ w\'rt' l1lod~ from Silll!lt' IlhotOtlif(>rfl~nl}lhs for (Inch $I)t.l~~i(·s, with hUL two ("Xt'l'P"
UOtl$, th(t \ohws by 1\0 t1WUU$ n'pn\~~,mt thl"'- nn"nw(' for tIll' SIlt.'d(·s.
I .Fur silllllllclty n rOllnlt·nllmbt!r mcan Yllhw of :~10 hIlS bt'Cll m ..-(i In the calculations in this puhlklltiOll.
'1'11(' VUIUN; gi\'cn in tllhlc 5 IlrC' in Illl casC's I\.v('rng('s of Ilt, Icm;t two counts. The
table shows that til(' .IIuml.wr of fibers Pl~r ct'lltilll('ter ranges from 217 to 445.
'I'll(' Iw{'ragt' nUlllhers for the .radialllnd tangential dir('ctiolls ure practically equal.
The IIIt'IUl d('\'iation frolll this IWt'ragl' \'aluC' for th(' radial direct ion was 12 percent.
and for t h(~ tnngl'ntial din.'dion 10 p(-rc('nt. 1:h(' maxilllum deviation from the
1l\'{'Tage was 45 pNt'l'nt. The ratios of the number of fibl'rs in the radial to the
llllmh('r III fhl' tangcntial direction deviate pracHt·ally th(' sallle amount from
unit.y in both dirt'dions.
eilfortunaft~ly. 110 specific gTlwity data were a\'ailahle to dC'terminc th(' C'ffect
of spl-cifie gm\'it~' on the numbN of fihcrs per (,(!Iltilll('i<'r. In thp calculations
the llulllb('r:o of fibers per centillll'tpr ill thc radial and t.an~C'lltial dire('tioufl have
b('('u ('()u:;itil'rl'(1 ('(Jual. '1'lw round-nUlIlbpr lllcau \'Il.lue of 300 fibers per {'cuti­
Illcter is IltiNI in the l'al(,lllatiOlls.
:FIlACTIO:-tAJ,
Yom
CIlOSS SECTIO:-t OI'"TIlJoJ 'FWEIl CAVITIES
'l'hc fra\'tional clljlillury cross sectiou of tliC' fiber clwitil's can be calculatcd from
the srw('iti(' gnwity of thc wood und or th{' wood substance by assuming that the
l'Upillllry i'trllr:tuf{' in t.he longitudinul dirpetion is continuous. This assumption
is jllStifillhl(' bN'uu~e of til(' iHnllll proportioll of cross-(-npillllry strueturc in the
forlll of ray l'clls lind th;;> IlIrge fiiJl'r ll'n~th ('ompllrNI with it:; cross-sectional
dhulll'ter. The fr:l('tionul yoid cross sectIOn of ullY trllns\'erse section cut from
•
PASSAGE OFLLQl'lDS, VAPOHS, ETC., THROUGH SOF'l'WOODS
61
n cube of wood (If unit dilll('Ilsions will be prnctically icleIlti('ul, provided a sulli­
t'il'nth' Inrgl' lI\1l11ber of fibprs is cOIIHidl'rl'd to in~ure a stutistit'ally ulliform dis­
tributioll.. For this reason the frn(:tionnl yoid cross section alld the frllctionnl
void \'ultllHo will be 11\IIIl('rically equal as the former is ll\ultipliecl by unit length
to gh'c dIe latter. lIelll:c,
.4",= 1',.= 1(17)
•
([",+
g,m'ln)
g.
p
ill whit'h A", !llld V", art' til(' frtlt'tiollnl void filwr elld!.y ('1'088 scetiollund \'UIUIlll',
n·sp(·eth·l'ly, of SWoll('1l 11'(10(\, g", i" th(' s\>l·t'ifie grlwil,\' of til(' wood Oil Il swollel1­
\'UiUIII(' hllSi,;, (/. is Ill(' spel'ifie grll\·it.~· of the \\'ood 8U\);:;(IlIIC(', III is til(' fmctioll!ll
lIIoi;lture ('untent of the wood at the fiber-saturatioll point Oil a weight basis, and
p is til(' !l\'Ni\gc ::lpN'ilic gm\'iLy of the adsorbed wuter (47).
The I.e·rlll
l!;;: I'eprc-
SPlits til(' frnl'liOl\ of lhe \'olUlllC ot;e\lpil'd \)~' wood iluh:;tun('(' and !l... ~l tlmt. occupied
p
by udsorl)('c\ wall'r. WlINI tlw frnetiol11l1 \'oid ern:;" :"t'('lion of dr.\' wood is sou~ht,
gd ;lhould hp ~lIh~titlltt'd fill' g,.. In 1I1is ('lise //I is Z('ro; hl'!w(', til(' IllS! tl'rlll in
pllr('lItiIl'S(';I of I'qlllltiol1 l.i di"IlPP('lIrs. The frlll'tionni \'oid erosi:\-sectionul uren
of tI\(' ~woll(,11 wood wit h II SI)('t;iH(' gravity (swolll'n-volunw basis) of 0.3(;5 is
O.(i50 IIl1d lhe eDrI'('t!pomlinj{ \'ul\l(.· for 01(' dry wood is 0. i22,
A VlmAGg
CIIOSS-SEGTIO:\,AI.
AIIEA
01-"
Fllums
AND
,1·'UHm CAVITIES
'fhp IL\'('rIlge ('roilS-S('l'! iOl\ullll'l'll of til(' liht'r,; for swo\l('n wood cun 1)(' detNlIIined
dir('l,tly from the 1I\'t'!'IIj{e llllllli>N of fih('rs pN ('('Iltill1('t<'l' itl the rnrli II I lind tan­
gl'lltiul dir('rlion~. His thl' rN'iproell1 of the nlnnber of fibers in u sqllllrl'. centi­
nwtC'r of ('1'0"" s('('tion. Thi:; is Nlnnl to 1,1111'2 (1,111 X 10-8 CIl1.2) for wood with
n ::;WOIl('II-\'olulll(' ;lIlt'('iIi (' I{rlwity of 0.3(;5, In the cus(' of the dry wood the nUlIlb('r
or fiil('r::; Ill'r squllt'(' ('('llt iuwt('r is in('rNlsed us Il result of shrinkal{c of t.he wood.
The trtlllS\'l'I'!:,P ;;ill'inkuj{(' (lIpproxinmt('\\' th(. SlIln of rndinlalld tllngcnt.iul shrink­
li),:(') of the \\'ood. whh'h is prndil'llli.\- ('((lUlI to the \'olulIll'tric shrinkage bceuuse
of llw smtlll IUIl~it udilllli shrinkng(', is 10 PNccnt for the uverage wood with n
SW()ll('ll-\'~)llllll(, specific ~rn\'ity of 0.305.
Th(' Ilumber of fibers in n square
•
('('lltill1l'l('r of dry wood is therefore T~S times the number in the swollen wood
wh<'l'C' S is til(' frlll'tioulll shrinkllge. Th(' u\'('rage cross-sectional area of the dry
lib('rs is t IWl'I'flll'I' 1,0001'2. 'I'lIP u\'('rul{l' ('ro:;:;-s('<.'tional area of the fiber cavities
j,; ('qlml to thC' produl'l of th(' fruetiollnl void eross :;ediou of the wood and t,he
UV('rn.~l' cros8-sl'('[ionlll 11l'C1I of thc fibt'rs,
This gin's 722 I'~ for both the swollen
lind til(' dr,\' wood U41.
.\n<;Jt,\GE 1{,\I)\l':; 0 ..
Filum CAnTlES AND TIIICKNESS OF DOUBLE CELL
\\',\I,\-8 AND PIT MEllBRANES
In some woods the COr!ll'rs of !.II(' cross ;;;ections of t.he fibers (sec fig. 2, p. 4)
rot! nded marl' j hl\n in otlwrs, ;:;0 that th(' cross s{'ction is more neurly elliptical
or cireul:Lr in shupe; wlll'l'eas in other ('as('s it is more nearly rectangular or square.
III 1\lIy Cll;;e, 1\~"lUlling tl1I\( the aYNage fiber is circulnr whcn it actulIlly is a square
will iutrodllc(' 1m ('rro!' \\'(;,11 within th(' range of accuracy required to be compatihle
with \'lllue;; fOr otlwr pro pert i('s uf:'('d in the ('u\('ulnt.iolls. Becuuse it is lIIore
l'OIl\'('ni('ut to cOll;:;ir\('1' tht' \lll('r cl\\'iti('s as circular capillaries in the pressure
\ll'rme!lhility ('ail'lllations, tht' m'SllInption that the average fiber and fiber-cILyity
~'ro~s ~l'l't ion if; cin'ulllr will be made.
In this CUSl' the ILYcrnge fiber-cavity crosS­
';:l'('tionnl radius will b(' l'quul to the squarc root of the quotient of the nvernge
liber-eln'ity cro~~-sectionnl arca and 3.1416, or 15.21' for wood with a swollen­
"olume speeilic gmYity of 0.365. In the sallle way the avernge external cross­
;l('ctionnl radiui:' of the s\\o1\('n and dry wood fibet::; will be 18.81' and 17.81', respec­
tivel,\'. The ditfer('nce bet \\'('('11 the fiber und fiber-cavity rndii represents the
!l\'('I'uge thickn(';ls of the cell wall, I\nd twicc thi~ diff('rence represents the average
t.hit:kll(·~S of th(' doubl(' 1'('11 wall.
Thc !wl'rnge thickness of the swollen double
C('1l Willi for wood with 1\ SWOll(,IH'ulullle sp('cific graYity of 0.365 is thus 7.21'
und that of the dn' cell \\'all 5.2J.l.
The !Wl'rnge thickncss of the pit 11l(·mbrnne has been e:;;timated from micro­
5copit'ai llll'U:;llrell\Cllt.. This thickn('!:':; is not much grcat.er than the lllaximum
III'('
•
62
'L'EC'HNIC'AL Ul'LLETJN 020, U. S. DEPT. O~' AGIUCr:U\'UHE
n'solvill~
POW('I'
or
tht' l1Ii('r05('op(' nnd hc-ne(' ennnot h(' cl(,t('rmint'd with nny
The pit lll<'lllbrnll{' is. n eontimmlion of tht' 1i!1;l1in llIiddle
InH\dl!l. The middl('\lllll('lln eun h(, more r('lHlily focus('d nnd l1I('usllr('d thull the
pit lll('nlbrll')t' it~('If. H('('ulIs(' of this th(' lIH'n5I1r(,llIl'nts W('fP mudC' on the thi('kII(,SS of (h(' middle InlllPlin 011 tlll1~Nltinl ~edioll;;.
'1'hieknl'ss('s fIlngil1g from
nilollt 0,5 to L2}, Wt're obtnined, A vnlue of 1}, will bl~ used ns the round-figure
n\'l'm~(' \'nlue,
d('~n'(\ of necllmcy.
•
FII;\C'I'IONA[, AlmA OF Till': 'V,\U.s OF Till': li'llums COYlmED "'I"1T1l PITS
The fm<'tionnl nrNl of till' wnlls of the fih('r;; thnt is mnde up of pit chnmbers
cnn he (';;tillllltN\ fl'olll photolllkrogmpbs of trnllsnorsl' sr.·l,tions hy couniin~ the
11111l1hpl' of pits nne! (he numh(,!' of fibN"', und nlC'UHllril1~ th(' fmdiol1 of till' pit­
('hIl11lb('1' ditllll('ler \l'it.h TI';;Pl'ct to th(' filwr width. 'rhe pit chllll1b(,n; incrl'n.se ill
diall1l'tl'I' fl'Qnl th(1 Ol'itiCI' to the pit 1I1('l1\bmlll' (S('l' H!1;s, ,lal1d 5, pp. 0, 9), ('Ol1il('­
qU('I1Uy, Iln I\\'l'm~l' diallwtl'r is d('siI'N\ for t1w follo\\'in~ ('nll'ulllt ions, This hilS
h('('11 rsUllllltrd f!'Om photorni(,l'ogmphs of tmns\'('I'::iI' lind tan~(lnl illl s('('(;ions of
S('\'l'rllI IlU\l(lliticntions to be 'to}, for till' sprillgwood and 2}' for the' slIllIll\('rwood.
1f 5N't iOlI" \\'('1'(' ('ut IW!'OS" n iiitl~I(' wood Hbl'r ,l\l dl'flnit(' sholtint.('rvnls, the
mOo of the' Ilutnll('r of pits ellt to til(' total 1l1I1II\ll'l' of Cllts rnnd(' wOllld gin' the
rat io of thp 5\1111 of nil til(' pit-cluulIilrr diunwtl'n; to til(' (ol.tll Ic'ngth, Thl' snme
COllnt prinl'iplp IIpplirs ('qlllllly WC'IJ to a singl(' l'lIt lIer08" a hllncl\(' of flh('n; thnt
are di:::(dhutl'C\ M mlldom il~ OJ{' 1('lIl(lh clirp('(ion. ]n thi$ l'n:::(' th(' mHo of the
n\lmb('~ of pitR 5('(111 on 1\ (1'1111"\'(,1';.\1' H(,l'lioll di\'idNI. hy thl' tolal IIlIrnlll'r of fihl'rs
obsern'c\ 1(1\'('8 tl1l' ratio of totlll pit-ehalllh('r diall\etl'l's to th(' totnl fiber \ell~th
for tI\(' 1I\'('raw' of all tIl(' flb('rg.
Th(' Sllllll' s\'sll'llI of slIh"titllting II ('ollnt for II nl('II:<lIrillg l1lC'thoc\ to p;h'e Stll­
ti51it-1I1 rw'u\(i hilS J!n'\'iollill,\' h('('11 I\~l'<\ h." til(' lIu(hor 10 c\l'tC'rmillt, t,he propor­
tion of til(' 1(111/.(th of II wood lilwr thllt i:: in COli tile! with the rn\'s (41), Such n
IlIl'IWS of clt'\('rnlining til(' ('0111 hi 11 ('(\ pit opt'nin,1!; dinnwtpr-fih("r 1(,II~th rnt io is
c!C'lwndllbh, D11ly \l'hl'lI tll(' c\l'pt h of fOt'\lS dors. not ('xcet'd 1,11(' c1inllleter of the pits
{'(HilliN\. Thi" is trill' for tlw spriugwoocl pit" but not for tlw s\II11lllerwood pits,
Wh('fl th(' ",\"SIPIll su/.(/.(('st('d is u;o;('d. p('rllllps liS Illuch liS double the IIclllnl num­
ber of SIIIllIll('f\\'ood pits lila), b(' ohtl~in('(1. TId" is 1I0t of grellt signifiellnce in
dl'tl'rlllining th(l rrnetiollal Im'lI of til(' fibl'n: 1l1llc\P up of pits, b1lt it would result
in con~iclpmhl(' l'ITOI' in c1Nl'rlllinin,l!: t,lw 1I\'Prtl/.((' nUlIIbl'r of sUlllllll'rwood pits on
II lib('f, for tlw rl'l\$on thllt thl' SUlllllll'rWood pit ehll\l1h('r area is such a smllll
portioll of thl' total arl'u. '1'1l(' frat'lion of the surfuee nrea of sprin~wood fib('n;
thllt is 1I1IH\I' up of pit ('hlllllbl'rl" i~ ('qUill to th(' product of the fractio11s of the
l(lngtl! und brl'uclt h of thl' filwl' thllt 1" Illllc\e up of pit ehul1Ib('rs multiplied b\'
1I".!R to ehllll,!!:l' frolll n 1'qlllll'P to 1\ t'ireulhlr nn'lI lind to include til(' tllngl'nt,iul
wdl nl" thl' rndial rllr{'s, '.I'll(' :Wl'rnge "ltllll' for th(' S1I111111('I'\\'ood WIIS obtnitll'd
in thl' :;anw \\'I\Y, 'L'h(' frtll't iOJlallll'('u of th(' 1'('C(i0I18 lIS n ",hol(' t hnt is Illude liP
of pit {'IUllnbl'n; \\,11>1 obtllinpd h~' 1\\,(ll'I\gin/.( fhr nho\'(' \'ulll(,s in proportioll to the
nunll.ll'n; of sprin)!;wOOd lind ~1I111IlH'r\\'ood fibC'n; milking up the wood,
•
as
TAHl,I';
G.-f'rOl'tiOllo/
IIrl'(I
of the jibcr It'(1l/s made lip of pit openings
Frncllnn of ftb,'r 1(lJI~t,h ,
mOll,' up of pil ol','n· .
ing~
._ ."
$prillg­
W!lIl"
Larch, w~stl'rll
Pin~, mst~rn whit!'
l'ill~, shortt,'a[
Ilo
Piu,'", Wl''''U'ru whitf.,\,
f;pnu,",'t fNt
Spru('\~. ~Itka
0,
i!! '
:20 '
,. _,-
"~
.IS
12
,13
I
A\'~rn~".
mad(' up of pit 0[><'11- ; ·Fnlctlonnl
i1l~s
; arm of the
nuntb(~r
_ ..._. __ ..•_... ' fillI'rs l1I11d~ of pits pcr
sprln~­
, Ull of nit
wood
::prtng..
Sllmm('r" o[wuings
fibt'r
w(Xld
wood,'
_.__
Rlunint,lr..
wood
0,03 '
1
-
,
I
-.- -------1------1---
o.~Q
(H:
0,06
.07
.06
.06
..,'
,0-1
.:10
,0.'
.28
.32
,:12
.02
,05
.02
,16
,------- . -- -
..
•\ ,"('rngl'M '" .... _.._........... _.. ., "" ~'rncthm Qf ftlwr whllh
I
0,017 I
,012 "
,016
.015
,Oll j
,Oll I·
,015
,or.
,Oil
.07
":I.
~
I
2'.lO
91
152
137
91
99
122
"
_
_i _._
f
_ •• ,0(.1
1-·..······..
t Stm,'t' thl'~l' nh)~lIrt'l1h~nt:{ w,'n' tlHUIt' on 1'1 S;hl!!h' i')hnlOtuicrognlllh ror each Spt!cic.": ~tccpt short~eur pine,
they by UI) Ul~;\US n'pfl"\'ut unr:lg,' I';llu\'$ lor tho species,
•
}'Al:;SAGE O~' LIQ1.'IDS, VAI'01l8, E'1'(,'., 'l'lLHOl'GH SOFTWOOIJS
•
63
'L'h('sl:' \'IIIIl('S for >!('\'Nul difn'r(llll >!oft wood;:; al'l:' gi\'(,11 in lnhlt, 6, Th(' IIVC'rtlg('
nUmb('r of phs P(II' Hprin~wood fib('r wnll ('nil be' obtninNI frolll the PI'OII\Il'\ of
til(' fmdioll of thl' fill('r 1('1IL(lh 1\1I1d(' lip of pit ('\lIl1nl](lrs Ilild the IlV('rtlg(' filwr
1('l\gl.h, dh'ldNI by til(' Iw('rage pil (~hl(lIIhl'r' dituIlP\('r, Thl::; qllnlltitl' LinH'i! 2
Ai,,('':; (hI:' IW('rtllW 11111111)('1' of pils 1)('1' ::;pring''I'onc! fih('r ((nhl(' (il, A si'milar ('111­
('Illatioll (:ollid !lot. l)(\ III Illi !' fur UI!' sllll1l1l£'rll'o(ld b('('IlIl~(' of 11/(' dl'plh-vf-foclIs
('Ifl'et j\l~t, IIlI'ntioll('d. HN'I\II~(' (hN;(' 1II('II.Slln'II1('nts WNt' IIIlId<.' 011 1\ sinAI!.
photollli('rogrnph for ('Mil ,spN'ips wit II th(' l'X('Ppt iOIl of sitm'Upaf pill(', IIll'I> h\'
no !IIl'lliiS 1'('J)I'Ptll'lIt nl'I'mAl' \'jllll.I'S for till' ::;(JPl'h'""
1·'orlllllall'ly, (hiH st rlleturlll
fl'nt·llr(', wbich ('IUIIiOl 1)(' I'~lillllll\'d with IUl" npprN'illbll1 dl'f.(f('(' of IWCUruC", hilS
II millor ('IT('('l upon till' (·I.tt~lIlntintll',
'
•
An:ItAG1~ H·\\)\l!$ (W Plm~l \~l-:"i'l' Pl'I'.~h;)I\IIt.\~g POlms
'I'h\' ~il.(' of t h(, (ll'rnllllH'l1( oJlt'lIillj.(::; ill til(' pit 1I1i'lllhl'tllh'S ('jllt hl' d(~I('rllllll(~d
frOl1l 1I1('IISIII'I'II1('1I18 of (II(' pquilihriulI1 !l<'rtlWllbility of wood 8N" iOlls (0 l~iI' of
diffl' rl'lll rl'lnlil'l' hUII.li<iilil's, Thl' J!I'rll\('llhilit \' 11Il'IIS1Ir1'1I1('nts WI'!'!' IIIlld(' Ill'
d\·t(lrillillilll\" till' PI'PSHllr(' drops o('\'lIrrilll{ (hl'illtJ.\h (hI' wood ~('{'tioIl8 lUte! /\ ::;(lIllci­
nnll'llpillal'Y lulu. Wlllllt 1'(WIlN'tl'd in 8I'ril.·s. TIt(. \'P]m'i! \' of nu\\' of nil' ,lIrOlll{h
hoth I lip stlllldtll'e! l'llpillary t IIh(l and t Iw w!Jot! H('('ti(lit ('all 1.)(1 ('xprC$tiNI by
PotSPllill("" Hqlmtion:
J~e
\" ,= 1t""'("~
"I
0'1 c
.
(for a sllludllrd 1'lIll1l1llry r)
.. (f or I 1t('
\ ' Ie:=;: IIQ.1rr",·P
L\ I
,~Jl UI
I"
WOO( S\'dlOll,
(18)
(1 fI)
itl wlli<:h V, lind \'., ILr,· !II\' \'('Iociti!':l nf Ho\\" throllll;h (h(\ ('ILpillllr,v lind the
wood s('l'li(Jns, to lind 1'.. IIr(' tlw rndii of I \ll' "(lIndunl ('Ilpmal'l' nlld til(' 11\'I~rl\ge
ptTl'di\'(' rndills (\0 [)(' lIH1fl' (,XII!'t, thl' fUllrth ruot of th(' ILn,i'age' fOllrth pow!'r)
of th(' wood ('Ilpi\lllri('~. I. IIlId I", Ml' Ih!' ('orn'spolldillJ,( ]('lIl1;llIs and I'. !llld. P'"
tilt! l'(Jrn';;p()l1dill~ pn'::;SlIrp droJls, '1 is til(' d:;('o,;ity of tht' IIiI', n is thc' 1lIllIIb('r of
(,If\'('( in' 1'lIpilllll'iNt ill thl' wood ::;1'l~tiOIi ill J)1l ra II('I 11\'1' Ullit of truss sl,\~ti(ln, nnd
fJ. is lhl' ('Ifl'l'th'(' ('ross liN'liun of tho w(Jod ii]JN'inwn o\'('r whil'h till' IIICIL::HIf('lIlcnt
is IlIadl', nil (')(pr(':'s('11 ill C('l\tillll'll'r-lI;rtllll->'I'('ollll units.
\\'JII'n til(' Rtlllldllrd \'Ilpillurv IIncl lh(1 WOlll1 Iln' ('OIllll'('(('(1 in :;('riN:, lit(' volulIle
of nir pm;sinl{ lhl'ollf.(h ('/I('h ,i'Oldd bl' ('qUill if no l'xrJlln~i()n of til(' nil' oCI'lIrrl'd.
\\'hl'lI tll(' Ilr(':;S\l 1'(' drop throliAh till' wood nnd through till' slulldllrd cupillary
lire SIIIIIII ('OIllIJllfl'd to ntlllo,;phPI'i(' pr(';<..;ul'(', tho oxplln:;ion ilet:()lIIos l1egligihle.
l"ndl.'r tlt!':"(' 1'(Jlldit iOlls. or wh('1i t hI' \'a!tll' for t ht' prl'~l:illf('-dflJP rat io obtnined
h~' l'xtrILpulntilll\" tlw pn',,;,'ulr(' drop mUll-tntnl Ilppli('d prc:lslIre relnt.iom;hip to
z('ro IIpplil'd pn',;;:;lIrc is used, the equutioll i.:; IL.~ follows:
•
r. 1 p.
-l,. =(i.l~F:"
liT",'
(20)
Th(' rij.(ht-huud tl'l'lIl, t.lw stnndnrd prOH.'lur('-<Irop mtio, is l11ad(' up en! in'ly of
ull'IL.o;lIn'jlbl(' q\lIll1ti(II'S, "\1\ IIIP qUllulitips in t1w l('ft-huud t('rlll. urI' unknown.
11 willllo! ('hnllj.(1 with ('hlln~('s in rpllLli,'(' humidity un.lN~s ch(,l'king of the s()e!.ion
()C\·lIr~. :Iud I., will ChUII.l!;l' but sli){htly. The pr('sslIf('-drop rutio PeIP.., or the
lIlllntllLrd pr!·~slln'-drop mtio, is t1ll'l'l'fnr(' proportio!lnl to lhe fourlh power of the
1L\'NII!.!;I' ('tTI'I'ti\'(,' (':lpillury mdillK, IUHI tit" squllr(' rooL of thl;' pr('i!sure-drop ratio
is p,mporlionul tQ thl' !'Ih'l'live Cr()S8-S('('li()/~111 1L1'('n of t11(\ w~)od ('npil!nry systc.m.
I. he 5qulLr(' ront of til(' prl'sslIr('-drop rafl!) WILS fOlilld to mcn'l1$e 11Il('lLrly With
II d('Cr('lIi'I' in th(' 1Il0iSt.llf\1 ('ontNlt of t!w wood below II moi:<l:ur(' content of Ilbout
20 p(ln'('nl, whi('h is in NluiliiJrium wit h 1\ r('luti\'o. humidity of npproxilllnt('!,"
flO \It'rt't'lll UiJL This rC'llLlionship is showlI in figurc 25 .for thill rlLdiul lind
tlLlIgf'lltinl )«'('tjous of til" h('llrtwood of w(':'!(etn whi.k pint', Deviations f;om
this n,ltItiulIship II!. lIloisture-('ont('lIL \'ulll(,s ill I'qllililJrilllll with hight'l' rellLtive
h\lmidHit's tW(' Il{'('(ltlntl'd for by tht' condensation of lUoisture in purt of the
{~Om!~llllli{'lLtinll; <'upillnry strllrtllrr, thlls ('Hminntinf.( it US Il sourc(' of flow' ILt the
r('!lltl\'t'ly luI\' h~'dro:;tlltie prl'$slIr('s \lsNI t.o make the IUcn!mr('lllenf.$. As dis­
clIs:;NI 011 Jlll~l' 41, t hl' tmniii('lIt e('lI-wnll ('Ilpillllrit~s Me illl'fTecli\,(l for the flow
of liquid$ or gll..~('s lllldl'r pr{'S8I1r(', The flow ill ('n( ir('ly through fi!)t'r cllvities
lind pi Hn('ltIhfll!ll' por('H in sNi!'s. 'l'hl' lattor Illoll(' urc sumcr('IlU,\' small to
('(lnlie'nBC' wlltpr lit 1'(~llIti\,l' hlllliidit ips Il]lprl'cinbly 1)('10\\' sut IImUon; .llen(~l', the
pit-Ilwmhrnl)f' !Jon's nrl' pliminilled liS aourccS of /low ILS the rclnU\'e humidity
inen-jls('s frOlI.) 90 to 100 pl'n~('II!;.
•
64
'l'ECHNICAL DU.LLETIN 020, U. S. DEl'l'. OF AGIUCUUl'UHE
•
•
2
2
4
6
8
10 /2 /4
/6 18 20
MOISTURE CONTENT (PERCENT)
ZZ
24
26
28
FWt'ltl> 25.-EfTe~t
of rhllll~l'S in the moisture contcnt of tangential aud radial
;;('('liolls of lWll.rlwpod of wl'stl'rn white pine upon the square root of the equili­
briuUl pres:;ufl,-drop ratio.
•
PASSAGIil OF LIQl'lDS, VAPORS, ETC" Tl-IHOUGH sm-TWOODS
65
'rho l,ond('II$nlion of wnt('r frotH lhe vnpor phnso ill tint' cnpillurlN; is due to
the fnet that wllter in tlll'ro (,llpilluriNl .has e h1)duceci vapor prt'SSlIre, This
•
rclnUotlship is p;i\'('tt by 1(el\'I1\'5 equation:
r=
2ITM _ _
(21)
_'~_"c'
poll1'IIl(~ )
in which r is tilt' rildlus of IIII' ('Ilpillnry. /iii i,:; th(' vUlloI' pr('sslIrL' of h\llk wul('r lit
thl' ub;;lllllt(' l('III(l('rnt\lr(' T. p is lht' vupor PI'I'S;<Ufl' of \\'Iltl'r o\"('r til(' cupillury,
N is til!' p;ns ('UlIstlln(, ('(llml to 8,alO X 101 , IT is 111(, s\lrflH'P 1('IISioll,.11 th(' 1II0It'('­
ulllr w(·iu;lIt. I\nd P. Ill(' dell;;it\, of the liquid. nlll'xpn'ss('(\ in Cl'lIlinwt.(!r-p;l'IIm­
second uuits, From this l'«lIatioll it is possib\(' to ('1I1ClIlutc n cllpillllry mdius
ill II'h1('h lI'utl'I' will lI(lIl(\('nSl' ut ('IICh l'<tllilihriUIll r('luti\"(~ h\llllidit~' nnd ('or­
n'spolll\ill,f!; lIIoisture ('UIII('III of tht. \I'(JO(\, I t is thus possihle to d('t('l'Illilll' 1he
('iT('eli\'(; ('l\pilll1r,\' I'lldius for (:ut'h rNl\Il'lion in vl'lo!,'ity of How of Idr throup;h
the SI'l'lIOIU! ('HlI~('(1 1)\' th(' cllpllllln' ('OI\(\('tlSlltion,
In fi/);l1fe 2!i I Ill' mll' of n'chl{,tiOli of tl\(' \'l,lot'ily of flow per uni\. l'hlln~e in the
rndim; uf lll(\ ClLpillllriN; in whi('h ('ond('II:\lltion occurs is plotted 1Ip;lIinst the
\'apill:lry 1'1I(\(U8 ill millillli('rOI1R 111/).1 or IO-T ('IIl,t The ClIn'{'R whil'h Ilre of II
pr!lhllhilil~' typo rt'pr('~('l\t til(' plf(,(lth'l'II('sS u:; Il flll1('tioll of tilt' mdii of the
pil-Wemhl'lllw IJIII'l'S, Pon' radii bl'lo\\' 10 1/1).1 ill "izl' 1If(' prudielllly itu·(fed h'e
to fl.I)\\' for ,;(·(,tiolls t'ul, in NIt'll (If the' (hn'(' structural dirN'[iollil, The mrliul
lind lUIlp;('lltilll :<Pl'l iond both ~h'(' prneticlIlly t hc' :ml1l() mOil!, probllblc radius
trndius corl'l'sp(lI\(liu~ to IIIllxinllllll I\('ip;ht) lind 111('1111 I'al!ius (radius at which the
Iln'a of Ow I'un'\, is bi:«'('II'(\\, The 1I\'l'rIIP;(' \'Illllt' for radial lind tllll~l'nlilli
~N'ti(ll\R. 21-\.2 1IIIl, is of I Ill' ~all\l(\ (lrdc'r of 1I111p;nilu(\(' II~ tlll' a \'('rll/);{, \'1I11\('8 oh­
IIli n('(\ hy \'olllbinin,f!;IJI'(';>;surp p('rlll('nbilil \' lind l'h'c'l rO-ORI1IO!:,(' \II('IlS\lfl'lIlt'nls for
\llIll'r I\nn \\'oDd SPl'l'i,'s (P, Hi), 1n t he ('Ii.~l' of Ilw rllflUlI IIlId IlIn)1,{'lItilll ~l'ct iOIl:>
lltt' flow o( I\ir \\'I\S lhr()\I~h nt 1('lIsl. ;~O pit-lIIelllbrlllll' por!'s in st'rieS so thllt, the
prohability till'll 30 Inrp;('r (llll'l1ings will ()('cur in s('riC's is 1\1111111. [n Lhe cllse of
tllt' ll'llll:w('r::t' ::PCtiOll only four pit 1II('lIIhrt\lws W('rt' trl~\'('rscd ill serit's, thus
Illnl('rilllly illcrcnsing the probnbility thllt t\wre will bc series combinntions of
•
- - , . ._ _ _ _
-.-J
•
(0
ZO
30
40
50
60
70
80
CAPILLARY RIIOI(JJ' (MILLIMICRON.}')
l"lOl'RtJ 26,-Distributi(J1I of pore sizes in the pit. membranes ofwcstcrn white
pine det.crtuillcd in cllcll of tbe thn'l' structurnl directions,
'l'ECH~I(,AL RULLE'l'lN 020, U. S. DEPT. 0.1" AGRlCUL'l'URE
66
pit op('l\in~s con:;ldt'rnbly more ('Il'('(·th'c thun. tho IW('ril!(C for the other sections.
The \'uillcl! obtainNI \\'ith tht.' rudial nnd tnn~elltinl sections thus represent better
stntistieul Iwern~l' \'ulues thun thnt; obtnined from the trnns\'crso section und
hence will bOURNi in the enlculuUons:
•
E.'.'ECTI\'~~ FItAt:'fIO~AL CItOSS SECTIO~ 0.' PEn~IANENT .P11·-ME~lBnANE
POllf!S
Tho t'fTt'dh'c frllctionul cross s('t'tioll of the pertlmnent pit-mpmhmne pores
for both IOllgit,uelillul und lralls\'prs(' flo", \\'11$ dch'rlHined from (~Iectro-oslllotic
flow 1lI('nl:HIrNl1('lIts (37, 88). Wood. as well ns otil('r solids when ill COllt,uet
with 1\ liqUid. USSUlIIl'S lUI (·Jpdrit.nl dlllr~o with rt'Sppct to t.he liquid uS n result
of lit·h.'t'tiv(, nd"orpl!\lll of inns. WIIl'II un ell'ctril'ul putelltilll is nppliNI neross
n wul('r-suillrut('d wood s('Nion thut is imll\('rs('(l ill wuler, 1111 plp('t ro-p"lIlot ie
flow uC wnll!r O~t'lIr.S thn)ll~h the' :il·clinn. This 11011' through tho SCCtiOIl CUll bc
QXpr('ss(~d by th~ following cqulltiol\:
(22)
in whidl \', is the "o!uu\(' of flow p(·r unil of tinl(', q. is the fractional cupillury
L'n)SS sl'etion, Q. thl' t.utul l'rOS8 ~('ction O\'pr which the 1Il1'IlSUrl'lllent is mude,
U. is thl' npplil'(1 pot.Nltia! pN unit of thicku('ss, K is the di('I('~trio constunt of
til(' liquid,
is UI(1 1:'!('ctrokill('tiL' pot('lIlial set lip bl.'tl':een the wood nnd the
bulk of th(, wIlIN, lind 'I is til(' \'iseo:iit,\' of the wllter. 'I~hc equut-ioll shows
thut the mle of lIo\\' throu~h n IIniform capillary systelll is directl~· proportionnl
s
O.IZ
PrV\
I
~,JITKII J'PROCE 6.IINO WESTERN REOC£OAR
I II I I I
'.-11 LA.sIOJ Y£LLOW-CEOIIR 0
\ \
\
(
I
r
I
I
I
I
•
-
'.--,JITI(II J'PROCE 6 AND WfJ'TERN REDC£OAR _ X10_
I
"
1\\ \ V
~
I I I I I
IILIUi(1I YELLOW-CEOARox 10
I\~
\ '''\­
!t
1\\
\
~ ~
\ ~ \ ..........::
~.
o
o
O,Z
~
­
0.4
0.6
0.8
1.0
THICKNESS' OF J'ECTIONJ' (C M,)
1.2
1.4
27.~- EfTl:'rt of thl:' t hkklll'S:;\ of lrnnsv('rse f;!'ctions of Ritkn sprltce
W('stprn ,Nkl'dnr, !mel AJu:,ku y('lIow-c('dllr upon thl) clectro-oslIlotic lIow 0
\l'llt('r through tho seNions.
Ftm'RB
•
67
PASSAG}o} OF LIQL!lDS, VAl'Ons, ETC" 'l'HHOUGH SOl;VPWOODS
to tho frllt'Holllt1 ~'I\pillm'y cross !wl'lioll. Wll('l1 dilT('I'l'nt-J5iz~'d clLpillarips al'O
COlHll'C((·d ill ~l'I'iPl:I Iti; Is the CIt;;(' in \\'mHi. t. lIl' l'olullltI of floll' p()r unit; tillle would
be contl'ollNI (lnlir('h' bl' th l, size of lho smalll'st part of the cnpilh~I'\' (p, 41).
The capillar,l' cr();!s $('('(1011 of wood efTeeth'(, ill ('()lttrollill~ (·I!.'(·lro-oslilOli(" flow
throllf.,(h Il'lIllSl'erSe sediolls lhiek(lr than till' IIlI~xhIlUIII tilwr 1(JlIgth is Lhltt: of
the eOIllIl\Ullicntillf.,( cllpilillry strlll'l.IIi'(1 bl'tw{'('/\ the fih()r l'ILI'ities, A:; discus$ed
on p, '12, til(> !low of liquid Uu'ollf.(h the tl'llllsiP11t clIpillllri(,S in the swollell 11011
11'1111:; is 1I('ldif.(ihl(' itl ('Olllpllr!lion wilh nOl\' throllgh t.hl' p(·rlllnnl·n!. pi t... lIIl' III brano
porcli, '1'11l' I'(lllln\(' !)f (·It,(·t I'll-OSIlIOtiC flow I.wr ullit of time t.hrough tmllsl'et'so
sllt'lium; t.hi(·k('r (hllll till' IIlllxillllllll fih!'r Il'lIgth, 1IIId(\I' II dpfillit.e potclltial differ­
ence per IIl1it lhil,klll'Ii:;, h; thllS directly Jlrlli>\lI'liOIlIlI to Ull' eITt'c!i\'(\ pit-lIIclilbrlule
POI'(' ('I'():3~ ~1'l'tiOIl,
In figul'{'i:j 27 I\lId 28 till' 1'(·locitiN; of ell'cl.I'O-OSIIIOUc f1oll' Lhrou/-Ih tmnsvorHo
~cctioll:l of ~OI'(H'ul softwoods nrc plott.ed lI/-InillHt t.ho thit'kll('sS of the sections,
I~ol' II :R'C'(iOIl of infini«'silll,L1 thk'klll'/i.';, all tho /ibNS lire ClIl IWI'llSS t.lI'icl', lIIaking­
the l'ITl'('( h'(, l'upilltu'y ('rUH~ :;(Il~liull thllt of the fiht'r cnl'it i(IS, As tll(' thicknl'Si;
of tho 8N'liol\l:; is ill('I'('I\~i'(I, t h(l, IllllUbl'1' of fih('r ('Iwiti(':; thnt IlI'(' 110 IOllgl'l' Opt'll
at hot It ('lIds illl'n'ns(\:3 IilwllI'ly liP to the lllinillllllll fiLwl' It'tI~th (87, 8Sl. lip,\'oII d
this t hieklll.'HS it. is 110 IOllg(II' po:;:;ih\(, for the :;hortNlt, fiilt'I',; to bll OPl'1I Ill. both
('lid:;, lo'ihl'l'.ll'llgth 1'!tl:;S('1i al'(\ thllli bl'illf.( ('litnillnll'C\ IlS 1'l'glll'd8 ell'l'ctivelll't\:,j
01'('1' tlH.' (lUI'I'('d pnl'l of IIt(' f.(l'nph UIlLi! al tll(' lIlnXilllll1ll filwl' It'"gth t.here is 110
furlhl'l' (\OCI'I'II:;(I ill tho 1'('lotit,\ of 11011' pl'r ullit pllit'lItitd I!;l'Ildi(lllt with illcrclIsillg
(hit'kll('';'; of t Iw HPCt iOIlS, Tlw ('llll'tro-oi;1I10tknll~' d('tl'rl1liIlN.llllillilllulIl, averagc,
I1l1d IIl1lxillllllll fill{'l' Il'Ilf.(ths f.(il'l'lI in lnhll' ., II'NO dntprlllitH'd fl'OIll tho pl)ill\: oC
Illug(ill(',Y of t h(\ itH'lilwd stl'flight: lim' with thl\ CIIl'I'l', lho ('x(.rnpolnliOIl of tho
inclined strnif.(ht lilli' to til(' horizontal axis (87, 88), alld Lhe point of tallgellcy oC
thc) horizonlal line with till' 1,'111'1'1', ['('sp('ctil'l'ly,
In an t'llrlil'r pllblil'ation (88) lIw ('IT(I('tin' fmNiollal pit-lIwlIlhrnne pOl'O Cl'(}~S
S('CtiOIl \\'118 ClilCllIII(NI frOIll Ntlllltioll 22 Ilft.c'r dl'tel'lIIillillf.(.1 frOIll the illemllHc in
lhl' l'1('t'i.ro-oHlllotic n,locity Cll IlliN I hy drillillg fino holes of I~ knoll'lI Ill't'll in tho
sl'c'Lions, A vllluc' sul>jt'cL to Il'R:; ('xp(II'illll'nt.llll'l'rol' 1,'1111 be oIJtllilll'd 1J)'llXtClldillg
tI\{\ OXPCl'itucutai straight liuos in figures 27 Ilnd 28 to ZOro thickness, This
•
•
I
I
I
~PONOEHOSA
I
I
I
PINE
I
OOUC LAS·FIR
~. \
-'\fl
:-POtYO£ROS'A PINE X 10
I'( ~
V'
\~
-[\ I~
I
~, \~
I
I
I
lJOUCLAS-FIR X /0 \
\\ 1\\ -,
~
1\ \
\
•
o
o
I~
­
.'I'Y
~ ~q
\
O,Z a4
a6
a8
hd
I.Z
-1.4
THICKNESS OF SCCTIONS (C M)
FIG l'R~: 28,-" EfT('('\. of tho thickness of transverse sections of Jlonderosll pino
Illlci Dougills-fir IIpon UIC elcctro-oslllolic flow oC watcr throll gh tho sl!ctions,
68
:I.'ECHNICAL BULLETIN 929, U. S. DEP'l'. 01~ AGRICULTURE
limiting v(!/ocity is for a fractional capillary cro~s section cquul to that of the
fiber clwiti(1s of SlI'ollon wood, A,., which can be, eulcuiulod from equation 17.
Tho fmotional pit-Illombmne pore eross section effective in the longitudinul direc­
tion t'nn then be obtuilled from tho proportionalit.y of the two v('locitios of
(Mctro-oSlnotic flow to the COrrt'll!lolldillg fractionul cupillary cross S(lctions.
Tullio 7 gi\,ll~ these vah\('s for soveral dilforllut specios of softwood, using tho duta
of figures 27 und 28. Vulues for the r potentiul uro nl80 given. The effective
fractional pit-lIlelllbrlUle pore CJ'osssoctions anl nbout 70. porcont lower than
previously culcuitLtod and tho r potentials nro largor by this SIUlI!' amount and
prnctically constant for the difforent wood~. Tho avornge pil;-lIlelllbrnne pore
1'Ildius calculnted from the~o dntn nnd pre$SUrt~ permeuhility datu for wuter
pussing through wMoJ'-filled sectiolls was found to bo Hi lIIiJ for AllIllka yellow­
cedar und western redcedar (37',8S) whon the pit-lIlemlJmne thiekness was taken
liS l.0 iJ.
'I'h'so values nro IL little loss than tho valuo for western whito pino
!\(lterlllillod b~' lIlollSurillg tho oluUlge in prossure permeability to ait- of different
rou\tive Illlllliditicl! (p. 65). Becl\lisO ditfl'ront specios wero used in tho two types
of lIlel\SlIl'l)lIIellts, tho agrl..:)lllent is as good I\S could be oxpected.s
•
TAIIl.~;
7."" l~lTcctitll' fractional 1lit-lIwllllmlllc liMe cross s('cl.t()n.~ in longitudinal
direction /lnd cll!ciro-lIsllllllic da/(I (It .'Joo C. fro711 'wltt'ch Ihe1/ were obtained
---,
~peclo..q
I EII'ctru·(ISlllotlc
S "In
I·'mellonlll
PH (l I!Ill'rclII'lty
gm,:,I\~' o( f ,'old CI'IISS
soctlon
\\ood
(gm)
(Am)
,·~Ioc·
Itr t hl'ulIgh sectluns
\\,/111-
An h1l11\1.
tcshuul
thicklll'ss
IA Ihll'km'ss
llxct.!l!dlllg
the III1~d·
ilium libel'
leugth
_ _ 1_ _ _ _
y~llo\l'·l~"dllr. AlilSkll., .......
H('lll~dl\l'. w~stcrn .•••••••••••
l)ougl(\s~tlr •••• '" ............
S\lI'Ul~, Sitkll .................
.\I"o"'go................
0.4,12
.2UO
, tl2(i
.31)4
---- .... ,.._........
O.5iS
. i23
.49S
.710
w .. ______ .........
Ce. per ste. Ce. '/Ier sec.
0,100
.125
.002
..12.'i
0,000:15
.00053
.00033
.00081
.. _....... _.. _-_ .... ..._ ............. - ..
g lfcct.l "0
fl'lll'i.lonlli
plt·melll·
iJmne pOl'O
CI'OSS
51'ctlon In
the long I·
Iud I 11111
direction
Electro·
klnellc
potl'ntilll
of wood
~Igllinst
w~ter (r)
«(Ill
0.0020
.0031
.0018
.0040
0.0202
.0257
.02i5
• 0~'64
.0020 _0264
•
The nvcrt\F;e va\t1O for the fmctional pit-membrane pore cross section effective
in the tangential direction (0.00052) \\'1\8 obtnined from the electro-osmotic velocity
through thin mdiJ\1 sections (87, 38) by substituting the nverage value for r
obtained for the IOIlF;itudinal electro-osmose mcasurements in equution 22.
::iuch thin sections wcre used in th~'se mcasul'ements that thcnow through ray
cells afTeeled tho rC~llIlts for t.ullgcntial soctions. The valucs for'mdial sections
will t.hel'ofol'c be takt'll as reprl'Sl'll tnt:ivc of both transverso dircctions.
As prllviotlsly shown (p. 63 and fig. 25), the effective capillar~' cross section
of the pCl'nu\lIcnt pit-lIIcm\)rnnc pon'::; incrcases in size because of the shrinking
of the wood on drying (45). Tho values increa.se iincarly with l\ decrease in
moisture content. The l\\'erJ\F;o illcrease between the fiber-saturation point and
thc dry condition for wcste.1'n hemlock and westcrn white pine sections cut .in
each of the thrce different structural directions, is 37 percent (45).
RADIUS OF 'l'HANSIENT CELL-,VALL CAI'ILLAIUES EFFECTIVE FOH Ii'Low
The size of the trnnsient cupillarics in the cell walls can also be e.';'timuted, us­
ing cquution 21 and t.he moisture content-relative vapor pressure duta for wood
(fig. 24). Tho moist.ure contcnts, which are normally expressed 011 a basis of
the weight per unit weight of dry wood, have been trnnsposed to a basis of the
frnctional volume of the swollen wood substunce and recorded in figure 29. This
5 A later attempt was made to check these values from tlieoretical considera­
tions of clectrical-conductivity data (4;3). BeCUIJSe of Il. faulty IIssumptioll tha.t
a Il(.gligible proportion of the dectri('al conductivity of wood saturated with a
dilutc salt 50lutiol1 occurs through the coli wall] these culcuillted values are in
error by soveralfold.
•
PASSAGE OF LIQUIDS) VAPORS) ETC., THROUGH SOF'l'WOODS
69
wall done by 11l\lltiplying each moistur~ cont('nt v!\lue, exprcss('d as a fraetion, by
th(' specific 'gravity of wood substance and dividillg by Lhc dcnsity of the adsorbed
water (47, 49) to put on a basis of tho volume per unit, volume of dry wood sub­
stance. The swelling of wood snbstunco reprt~sents adding of the voluInQ of _the
adsorbed water to the volume of the wood substance up to tho fiber-saturation
point (44). Hence, tho fl'udionul voluIlle of the swollen cell WI\I\ occupied by
liquid is Lhe volume of liquid pOI' unit volul11(\ of the dry wood substullce divided
by 1 pltt$ tho volume of adsorbed \Vutt'r (fig. 29). Thul:!:
•
v=/l/O" ( .._1__.. )
p
(23)
l+~.uo
p
Wit h the aid of llw <lulu of figure 29 und oqulltion 21 the fmct,ionalliquici volul11e­
capillal'Y melius ('I1I'"e, Y, 1', shown in figure 30, wus obtained. Tho distribution
of capillury siz('s in the cdl wall Oll til(' busis of the yolumo incrcll1cllt. of capil­
laries )1('1', unil inert'Illont of the meiius of t hl'll(' cupilll\ri('s for 1\11 possible cnpillnry
r) obtniIled by gmphically eiHrOl'CnLiILting tho V,
radii C:/~'
in figul'o 30.
1',
curvo is also given
-:":-..
~
~
30
~ ...., 28
~
.., 26
co,.
<::>
~, 24
•
~ 2Z
'"
..,~'" 20
--+--1---1---1
4
•
FIGURE
6
{} 10 Ii! /4 16 18 20' ZZ 24 26 28
MoTftURE CONTENT (PERCCNT OF OVEN-DRY MiGHT)
30
.U
2!).-Rdationship between the moisture content of wood on a dry-weight
basis and on a swollen yolume of wood substance basis.
70
'j'ECHNICAL Bl:LLE'l'lN 020, U. S. DEPT. OF AGlUCULTURE
r-1--.Jr--._T_--.,-_-·_-r-.. . . ~-·.-1r-_-'--1,.'.-J"I--r=ib----'. ..."'_-:-_-:-_-:c----~_j;.;:
l',-J"'-+_-,'~-r-r-_.."TI---
I-+-t-+-+-j.-r~ ::y.-::-
~
~
,.~
009r--'
/
~~~
;i~
O,ll
0,18
~.-..
~
~
/
n::: l~l" --------f'·
::: ...~
I, [ I
--.+
~ ~ 004tit- t ., _.
~~
0,08 ~
I:::
~
i ~ iT r-:--:.
a06
O,OJ
~~
~
0,/4 "
::
~'"
~
•
0,16 ...
,1\
007
~
o.zo ...
/1--- - - . - ,'- -. -- -
~~008~"__-----7---·-~-t---~
:;j
I
1
/~
0,/0
o.oz
.if.!'
~
0.04 <.;
t'
~ ~ ~ttLI=tlJ[?:':J'---~""j'r_:_:,t-~···f:1=·=-f-:-f~-f-~-;";td:t:l:tdo.oZ
"'-
~
0.0/
00
:
I
I
I
I
Z
J
4
... ""---
5
6
--
7
-­
8
9
10 /l
11 IJ 14
CAPIlLARY IMPIII'; (WIlL/MICI/ONS)
IS
16
17
18
19
zf
1"lOI'UN 30.-Curve V, r, fracl.ionnl liquid volume-capillnry radills relationship
dd;'
{'alculat{'(1 frolll !,11l' cllLla of figurc 23 and cqunlion 21; c:lrve
r, distribu­
I,ioll of capillary :::izcs in the cell wnll of swollen wood, obtained by graphically
difTcrPldinLing {'Un't' 1', r,
. Equation 21, relating Ihn capillary radius and the reciuction in the relntive
vapor prN,surt', WM deri\'ed on the basis of the capillary radius being large in
comparison with molecular dimensions. In thel\e cnlculations the equation has
been used in the molccultu diIlien"ion range, so thnt, the calculations arc subject
to consic\('rnble error. The equntion most certainly cnnnot hold below a radius
eqllal to the diameter of the adsorbed molecules which for water is about 0.40
mil. The eurve il;l therefore dotl!'d below a radius of 0.40 mil. Although the
eun'c ll1a~' still be in error above this value, it provides the best basis available
for e«timating tht'se minute capillary sizes. The mean radius on a capillary
\'ollime basis of -1.0 mil obtained from figure 30 is similar to the value of 5.0 mil
{,~tilllnted by Frey-Wyssling (14, 15) from X-ray measurements on silver crystals
deposit.ed hi the intermicellar volume. One-quarter of the capillary volume or
area under the clint' is in capillary sizes lip to 1.2 mil, onc-half in sizes lip to 4.0
//tJl, and three-quarters in sizes up to 14.0 mJl.
The thickness of the double cell wall of two adjacent fibers is so great in C01l1­
parison with the pore radii of the capillaries that every irregular capillary system
extending through the cell wall from one fiber cavity to another must have an
appreciable portion of its length made up of capillaries with a radius as small as
the most prObable 'mine. The sizE' of the cell-wall pores is used in the calculations
only for determining the structure effective to flow Ulider pressure. As discussed
on p. 41, the resistance to flow of a liquid through an irregular capillary system
i" almost entirely controlled by the size of the smallest part, of the capillary. The
most probable radius may thus be taken as a maximum value for the effective
radius.
The molecules of Ule water, or other polar liquids .in which wood swells, arc
adsorbed on the surface of the wood capillaries with a force considerably greater
than the mutual force of attraction between the molecules of the liquid themselves
(49). The molecules directly adsorbed on the surface must, consequently, be
immobilized; hence the diameter of the molecules of the swelling liquid should be
subtracted from the above effective radius to obtain the radius effective for flow.
In the case of water the ccll-wall pore radius effective for flow will thus be about
0.2 mil.
•
•
PASSAGE 01" LIQUlDS, VAPOnS, ETC., 'l'II\{OUGlf SOl"'l'WOODS
E.lr't'I';C'l'lVg
I"Ht\C·I'IONAI.
•
Cnoss SgCTION
C,\l'ILLAIUgg
010'
71
TnANSmNl' CgI.L-WALL
TIll' ('I{(lcti vc fract.ional cross sec!,ioll of the transien t ccll-wall <lapillarie:3 is the
most dilli<lult 1,0 estimate of all the st.ructural properties. This il:; due to the fact
tlmt this properl.y is dt,pellclelll upon thc lIaturc uf tho capillary put.hs and upon
the blockll\~ (,tfect of adsorbNI lIIolecules.
Vl\rious t.vpes of assllmptions have bcen mudo .in an attcmpt t,o estimato the
effective cnpillary Cl'O~:l l'l'ction of Il1lllllbmnes, All the a:;;sumpt,ions, however,
involve Silllplifh'ntiolls Lhat are (,lItir('ly ul1tenublo for cellulose melllbmncs. Capil­
Inries hl\vc, in !;eneml, Iwel1 assumcd to ha\'e a uuiform bore, to extend only at
right anglps to the II11'IIIb1'lll1c fUC!'l:l, or to exlcnd at right anv;lefl to each o(,her ill
tl1(\ three ~t.l'uctural i1irl'etiolls withollt; interscl'l,ing (4£1). DunllUlski (8) is 0110
uf the few who have Il~H\lmed illtCI'scct,illg capillaries. He haH derivcd a relation­
ship fOl' the llff('div('. llapilll\l'Y cruss scction of n system involving packed SpilCl'!'R.
'I'hii:!, too, is ullt,cllablc fvl' lIut.uml cclluloHic lIl<:mbrnlle~ in which the long t.hrcud­
likl~ llIolrcull'!! 111'0 ori~nt,('d in lhe fiber db't'ction, A mOl'n logiclll aHHulllpt.ir.lll
l'l'(,llIS to \)(' lhut t,11t' coli WILli is lllllde up of idt'al l'egtl!ttr cellulose l'oeil:) with an
irdinit.o lonv;th with rl'spcc!, to t.heir Cl'o~S !;(,ct.ion. UrHlm' this IlSSlilllption the.
diffusion of a HolutH t.hrough the capillary liquid bctween the stl'uctuml rods will
bt' grl'nt,rr ill Ow tiber direction thnll nt'rw:ls th!' fibers.
In t'Ht illmlillJ,l the raUo of the fractionnl cell-wall areas effective for passnge
under diffu~i()ll conclit.ions in Ule longitudinnl to that ill the transverse direction,
Il.'; well Ill'; in tho cllpillary eomddemtions t,o follow, the nllltiogy between the
phcnolJltllllt of olpet.l'ieal eOll(hlet i vity alld diffusion given on pllge !) will bc used.
As a tirst; tlpproxinlIIt iOll, the gt'ulllctrienlly idenl case will be considered in
which the cell wnll is pictlu'('(1 liS made up of continuous stmight nOllconducting
1'0(\.', with n l:iqllllre cross :;(lCtiOIl dispcri:!l'd in nn e1ectricnl-conducting uicdiulll in n
perfcctlyori('lIled IlIltllnpr, The cro.';s section of such a system is shown in figure
31, 11. In order to HilJlplify t.he cltlculatioll$, the rods llIay bH assumed to be con­
centrat:ed in two plates t\8 shown in fi~lIre 31, B.
III Uli:; idl·tdiuod CIlRe the fmctiollal crO:5S scction effective for longitudinal
diffusion or l'l(~ct:!'icl\l conductioll would be approxilllutely equal to the fmctiona.1
volume of the systelH that conRist!; of ttll electrical conducting lIIedillm, Thnt is,
the (~ffl'cti\'t' cross Rl'CtiOll will lx, the sallie as the volullle because the length term
is unity, 'l'his will still be I\pproximately true for the cellulose structura.l units
which arc not continuous but nre very long in rc\ttt:ioll to their diameter.
•
"I' '-(J-SI)J ~
(I -sl)i
~~~~~~~
~~~~~~~
~~~~~~~
~~~~~~~
~~~~~~~
.....--..
r:t
I
~
+.
,-..,
~~~~~[?2l[?2l
~~~~~~~
•
(A)
...
J
r:t
I
~
.!.
(B)
31.-.11, Dingrmn of the crORS sect;ion of an idculizcd cell wall showing the
end "iew of the cellulose rod::; with capillary swelling I1!ediuIn surrounding
thelll; lJ, scpt\rt\tion of the ccllulose rodl:l from the swelling mediulll for simpli­
city of calculation,
FIGUIIE
72
'l'ECIINICAL BULLE'l'IN 0201 U. S. DEP'l'. Ol~ AGlUCUL'L'UHE
In the transverse directions the frnc! ional cross section ('ff('ctive for the passage
of solute or curr('nt will be determinl~d by the series comhirllLt:ion of the two liquid
plntel! (fig. 31, l:J), by nCl-:lceting the potcnti!~1 drop ncce~snn' to calise the equllli­
zntion of the solute or current in euch plate in n plane at rigflt angles to the direc­
tion of passlIgll of solute 01' current. This neglected corrcction hils been shown to
be well within the rnnge of expcrinlclltnl nccurllCY ill\'olved becnllse of other
npproxinllltiQlIs. The thickness of the plates ill the lIow direction will be (I -8,),/2
for the v()rLicIII pillte nnd 1- (1-8/)112 for the horizontnl pllll,(', ami the crORS
scction will be 1- (1-8 ,)lrJ for the v('rUclll pillte and unit,\' for the horizontal
plnte. In the serics combinntion the eff('ctivc frllctional tmlisvel'Se eross scction
will be
1
(24)
8.=
(1-8,)1/2'
1- (1-8/)1/2+ 1- (l-.'::/)lrJ
In rcnlit,\' th(' c('lhllose strllcturnl Ilnit" arc not Jl{'rfl'ctly oriented uniform rods
with (·qual SPIICinl-:" bet,weNt then\, ItS in fil-:urc 31, bllt. mUle I' n complex irrel-:Illnr
thrC'l\(llikll IIlI~SS with contacts hNe nnd t.lll're bl1l.wccn threads (1). Bquatioll 24
should hold equall.I' well, how(','er, 011 1\ stutistical basis if til(' dfeoUvo liquid cross
sectioll does not, I'MY appreciubh' from one point. 1\lolIg tho lengt,h to nnot,hcr.
The relntiQllship Iwt,wcen Slul\d St SllOUld thus be unaffcct.ed by variatiollsin the
s\)acing of the struetu rnl rods or Oven non pnmllelism of tho rods to onch other.
T 11lI aot,ulIl values of 8/ and S twill, hO\\'(wef, be grcatly nfl'ected by irreguillrities
of the capilillry structul'(' lind ul;m by the blocking effect of adsorbed molecules in
the zones whcre the distnlloe between the surfuce-lIdsoriJed molecules 011 adjncellt
cellulose ohnins is equul to or il'ss Umll the diamet.l'l' of the diffusing molecule.
The simvlest assuiliption to account for the irrel-:ulllritics of the cnpillary pnths
through the cell wull is that each path is made up of all the capillllry sizes alld
that the volullle of CIICit size clllss is in proportioll to the frnct iOIl this clllSs is of the
total liquid volullle of all. the trullsiellt cllpillllrics. The fructiollal volume of each
size of capilluri(·s ill thl' cell wull can be estimated from the
r curve of figure
rtf,
30.
•
•
The curve has 1)«)1\ broken up into compollent dd~ \'ersus r steps that divide
the area under tho CUl'\'e into four eCjuul parts.
Tho part of the curve where
~~
chnngl'S mpidl.\' with r has been further divided into sHlaller increments. l'nble 8
gives the dlltu for thesc in('I't'lI1cnts IlJl(I the reduction iIi effectiveness of the capil­
lary YOIUll\(l, duo to thc adsorptioll of n monomolecular layer of wllter on the
capillllry surfllces. It is u~sul1led t.hat diffUSing 1II0iecuies cllnnot approach closer
t.o til(> l'ltpillnry surfllce thlln thi~ valut'. ('olumll (I) gives the range of capillnry
rndii for ench inl'r('llIl'nt, ('Ohlll1n (2) the a\'ernl-:e capillar~' fndills for each capillary
incremcnf;, und colllllln (3) the change in capillllry radills within the increment.
Column (4) gives the correspondillg ordinate of the curve, dd·V. Column (5) gives
I'
the cnpillary volume for each increment of capillary radius obtained from the
product of columns (3) nlld (4), 'l'he SlIIn of these vol lime illcrements is equal to
0.284, the fmctiOllnl volullIe of the swollen cell-Willi substnllce that is occupied by
w!\ter, F. This vahl(' is in good ngrccment with the value 0.287 given in table 1,
p. 12. Column (0) gives the rlltio of the corrected to the uncorreoted volume of
cnch increment, calclllnt.ed from the reduction of the nctual capillary rlldius by
the diamet.er of all adsorbed water moleoule. ColullIn (7) gives the effective cap­
illary volulllc for each increment corrected for the adsorption of a monomolecular
Inyer of wlltcr on t.he capillary surfllce:;. The sum of these increments gives the
t.otal effecth'e yolume of wllt.er in the cell wnll. 'I'his sum would also represent
t.he effective cnpillnry cross section for longitudinal flow if it were not for the fact
that the major part. of each capillary Pllth is blocked because the effective capillary
diameter of the lUajor part of each path is less than the diameter of n water mole­
cule. This blocking effect would entirely prevent the passage of materials if the
capillaries were not intercommunicnting. In the case of intercommunicating
l'npillarics, llIlltcrials passing through the cell wall hnve to resort to a weaving
path to avoid the zones where diffusion is impossible,
The extent t.o which n lUaterial has to resort to n weaving pnth in passing through
the cell wall can be estimllted from t h(' fmctionlll length of n single capillary path
that is ineffectivc. Column (8), table 8, gives the cross section for each capillary­
•
•
•
•
8.-C'alclllatioll of Ihe fraclional c(Jpillflry cros,~ sec/ion of (I crlill'nil ejJ(ctice for dfjJl/l!ioTl or the flail' ()f 071 electric currer/till Ihe 10110;­
t1Hlifwl directioll, asslLminy OWl aile 1!w/ecl/lur di(//Ilfier of wlter molecules!s immobilized on the surface and thai (:(Ich capillary path
made up of (Ill capillary sizeS/II pra]lOftiOIl 10 their fracfirma/ volume i,l lhe cell u.'a/l a,~ (I tcho/e
TABLE
u
(1)
(4)
(2)
(3)
Arerogc
Ch,,"g~in
cupillar.­
\'OIUlli(' ,,:jth
mdlus
radius
md IUS trlJItl
figuro 2'J
T
Ar
~17Ar
(,h,,"~e
('"pUlary radl\1ll nUlgc
cupillar>'
cullilbry
(S)
(6)
Product of (3)
n'(·I~.I 10 un·
In
Ralio of cor-
i
and (4)
oorr~Cl(>d
yol­
(8)
(9)
U1
Ul
Product of
(O! and (6)
('apilbry
Caf,iIIary
l!'::
(!fOSS $c<:tion
lengt I (S)/{8)
(,=;:.4Y
~\t-rO.4y
rr'
~ 1,["':
O
c:
OMz.-------------.-'.:':.----------------------1
tfL:~~:~::::~~:~I::::~lJ
1.2-2.0. _______________________________________ -"
2.0-3.0....._______________• __________________ .,'
3.0-1.0 .• _••••___________...____________________
4.0-14.0. ______________...______________________
14.0-114.0__ ...________________________________ 1
m"
0.1
Itlu
0.2
J :I:
1. 6
2.!i
3. S
9.0
&1.0
,8
1.0
1. ()
](). ()
HK).11 '
O.ot/)()()
c1II.XlO·u
c
g;
,..
(mp,'
O,O:lit -­
0.012
.012
.012
0.040 :
,OOKIO
.012
.405
• 02'_~KJ
,(j'n
.01'iOO
.OOTIO
,IOJ.I
.rm
.700
.781
.91:l
• ()(1)(>O
•(JaM
• ()tJ)(l()
.or'(l00
, tL1!;OO
.012
.012
.1J.31
.017
.071
'rotaL--------·-------------------------·I--·--··---·-·· .. I.-.-....."- --1-'..- ., -'--,i---:;;4
.2S.'lI)
o.()I)fH$
.()(l221
.IM
.3fJ9
• ()()37J
• ()(}IS6
• 01.50
.0I5.'il
.&)3
.01330
.ot.>lSO
.07010
.9SS
~
-- -.,. '--'
~~, .... •.192.'11
C
'-=::
t-
~---,-"
em ..l
>
c::
urn"
~1'
~
(7)
.7850
~~~,
3.8(XJO .
S.OlOO .
19 GOI>(;
38 [000
~'t-I. LOiKJ
1201'.0. (K)(IiJ
35,21;
~.240
-­
....
.779
;;
.3SG
S
W
1.S:!\}
.4;2
.316
.112
.OH
.0'-'1
.001
46,124
"C
...
~ci
...
r1j
~
o
c:
o
::::::
I!i
Ul
oI':j
>-3
:ao
o
c
Ul
-:r
~
74
~rECHNlCAL BUI.LE'l'IN 929,
'u.
S. DEh'. OI<' AGIUCUUrURE
size increlll('nt, The cnpillarv volumC' «('Ollllllll 5) djvickd by t,he capillary cross
section (col ullin 8) ~ivt·" UI(' lotlLI 1('11),(lh of capillaries of each size clns!! (column 9).
The first two size mnges. which nrc totully inelf('ctive, repr('sen\, 92 percent of the
length of each path. A diffusing molecule will therefore have to tmvel, 011 the
•
1-&:U2
average, through
or 12.5 individual paths in passing through the cell wall.
Because of t.his t.he elfpcLive fractional cross-se('fion value just calculated will
havt. to btl dividpd by 12.5 to giw thp trUe plfective value. 011 this basis 8,=
0.0154, Ilnd from cqlllLtion 24.8 1 =0.0078.
In til(> clLleulnlimls on the drying of wood it is necessary to know the values of
S, Ilnd S, for llIoisf:\lre cont.ents below the flbeNHLt,umtion point. Values were
accordin),(lv calculated for the condiLions of threp-fourths, one-half, and oll!!-fourth
salllmted: This Wll.t; dOIl(\ by elilllilllLting the lnst incrPlllent, which makes liP
one-fourth of tim capillary vol II II\(', the last two increments, which make up one­
half of the capillnr~' volllllle, and the lust five incrpnl('nti', which make up thrce­
fourths of thl' capillary VOlUIlll', FIl('C('B~i\'('ly in the calculnt.ions. These values of
Sr ILlld 8 t IHC plo\.ll'r\ in Ii),(url' 32 ILgllini't. t.ht' JIloisture content expressed as per­
cent of the volume of the t)\\,ollell-\\,ood substance.
1(,
lP
15
14
/
~.
I
13
12
1/
10
"\
<::)
-'
-;
.­
r-"
...... 9
~
7
'q:
/
•
'--­
:>t
c.)8
/
V
-~.
_.
~
6
-
f-.
_
7
'-'
5
4 !--.
/
3 1--'
/
Z
o
o
VV
~
~~ ­
T
!..
I7
In
........_i'.
Sv
/
/
./V
7
L
~V
2
4
6
8
/0
/2 /4 16 /8 20 ZZ 24 26 28 30
MOISTURE CONTENT (PERCENT OF VOLUME OF SWOLLEN-WOOO S(J8J'TIINCE)
FlGl'Rt] 32.-Y!lriatiOIl of tht' ('fT('c\h'(' frllctiolllli transient capillllTY cross section
of the pell \mlll' in bot h the longit udinlll and i rIlnsverse direction with chanp:ps
in mlli~tllre content.
•
PASSAGE OF LlQ(;ms, \'APonS J E'l'C" ~'HnOUGH SOFTWOODS
•
75
'For ~ollv(,lIienc(\, Uti' ('fTl'~ti\'(' ellpillnrv ('r05.'; sN'lion of till' tmnsi('nt c('II-wILII
struclur(' e/Tel'live for pn$sn~(' of IIlllt,l'l'iui !.hrollgh wood in 1\ lrnnsvl'nw direct ion
il:l (H\'idf~d into t.1H' Pllrl \\'11i~h r('pl'(':i('nt~ continuous pa~;<ngC' throu~h cell wulls
aJld thllt which is in !;cl'iN! with the tilx'r l·IWitit'l'. Thl' proportion' of l'Ileh will
(h~lll'nd upon til(' speeific ~ravjt,· of tht' wood, 1'1\(1 fractionlll eross sl'ction of the
tmnsipnL capillllril's of wlIll'r-s\i,ollt!JI wood l'/Tl'cth'l' for the flIlS$lIgl' of 1I\0lccuk's
the size of the wntt'r moll'cul(, in till' trnnl1V('riil' dirl'ctions frolll (\1\(' libl'r clivi!.\' to
IInoth(~r, Q I, is equnl to th(' ILVl'rugt' rndius of til(' !ibN ellvit il'H of swoll('n ,,:oocl
divid<'C1 by the cOrl'('spOllding ('Xtl'rulll ril(lills of I,ll(' filwr$ timN! Ihe frnt'Lionlll
(lfTt'ctivc cross section of lh(' ::;wollt·n ('(,II willis ill tlll' lrunS\'ersl' tlil'l'cl ion; thut is,
QtczSrp, For wood wilh 1\ swollcn-volunll' SIl('cific gravity of 0,3(15, QI=O,0063,
In th~~ ;;('l'il'S combination of !ibN (,lIvitips lind c('11 II'nlls in t.hc .Iongitudinal
c1in'etioll, th(' 11IL:;I'a!.W through I h(' rpll wall is st ill in I h(' lrnns\,('ri)1' dil'l'('! iOll,
BerILll>'!' of til(' sloping c(lnlll('t il('l\\'('('n 1iI)!'1' clLdtips and cI'1I Willi 0\,('1' I,ht' o\'crlufJ
r('~i(lll, til\' l'fTc.'cti\'(' ('('11-\\,1111 capillary cross ;;I·ction Ill'l' unit (,l'OSS ;;N~lioll II('r­
IWlIdiclllar to Ull' fiht'ri:l will ht, cOllsidrl'nh\,r illel'('asl'd, This is i1111stl'llll'C\ in
!i~llrt' 33, VUI' i:!implificiltioll till' 0\' 'l'1I1P hai:! 1)1'('11 I!.SSllllll'd 10 ('onfli:;1 of II sill!!;h.l
pllll\(' with a width NllUlI to tht' avt'l'IL!-\I' liI"'I'-clL\'it,\' dianl!'l('r and Il \('lIglh ('quILl
to thl' slollin g (lvl'rillp 1\'11),(111, II f· z, of which II I:; ill(' ('ITN'tin' pllrt, This l'fTt'c­
th't· Il'ltgll ('Illl hI' ('II)('\llal('(1 from til<' I'xtl'l'llIll O\'l'l'1ILP It'llgt It of a fihl'r, which
hILS bf'!'!1 t\ssulIIPd to I,., o.tll'-folll,th of thl' !ihN Il'llgt.h, till' li!)I'I' lind fill\'l'-CUVit.y
dtllllll'tl'rs, !llId tilt' dOlllll!' <:(111-11'1111 thkkl\('ss 11\' .~ill1plt' g('OIlI('( dc cOIIsidl'l'atioml
of silllilnr Irillll~l('i'1. Till' pITl'\'liv\' O\'PI'lIlJ!,
linw;; (h(' fill\'r-\'lLvity dillllll'tcr
gin's till' l'fT('l'I h'p c\'I1-\\,1I1I url'a p('r !ib!,I': iLllcI lIli::, diddt'd b~' thc croHs-Sl'diolllll
111'1'11 of till' liht'r, ~i\'('s till' \'If('d h'p ('('11-\\'1111 ILrI'II (ll'l' ullit ('ross Sl't'( iOll, l?or
wood with Il SlI'olll'lI-yollllllt' spl'l'ifil' gmdty of O,3U5 thl' ('fTI'I'ti\'" ('('II-Willi urea
pl'r tlllit ('ro"" SPI'I iOIl is 13, Thi", (illl(,;; (lIP IWI'mgp l'lfl'('1 ivl' frut'! iOllnl CI'II-WIlII
t'ro,;s 1\('('( iOIl for t runS\'l'rsp (lnS~IIJ.(I', gin's 0,10 I for (h\' fm('t iOlllli cross section of
Ol!' 1'1'11 Willi ('fTl'l'tiw' f\JI' IOllgitlldillll1 pllssngl', Q/,
Tht' s\I'olll'l1 pit 1l1t'lllbrullPI:l \\'ollid Iw l'x(ll'etNI to sho\\' n pl'rlll('nililiLy IIlIell'r
diffllsion ('OIl!\i(.ions silllilllr to thnl of t hI' cpll wnll::, liS \\'('11 us n PI'I'IIII'Ili>i1it.y
through th(' gr()S:;I'1' PNIIIILlI('lIt ('npilllll'l('s prt'\'iom;l,\' ('onsidl'rl'e1 (p. 051. This
pI.'l'Il\t·lIhilit~, hns bl'l'1l nS:l1l IllNI , !IS II fir,,!' a\lprO'l:illlal iOIl, to 1)(' thl' :lalllC Il,~ thnt
of tltt' l'plI walls. 'I'll(' frlll·tiollal un'lI in\'oh'pd is (h!' Slllll of all the thill pit­
1Il!'IlIIJrnlll' nr('l1~ SlIrl'ounclin),( tlw torll::; for 1111 til(' pits Oil !In !lvI'rag!' !il)('r WillI
dh'ill('(\ by UII' art'll of till' 1I\'l'rngi' Hilt'r lI'ull. Tid,; should hc.' vpry silllilllr to
tilt' fractiolllli III'l'n of I hl' tllllgNl1 iILI wnll::; of t 11(' fil)('rH (,O\'('r('d by pits, q" (p, (j2),
bN'nllg(' til{' /L\'('rng(' pit.-I'llllllll)('r l'I'Oss-s('etiollal url'lI of Urn 1Il(lt'ring pit OIl('llillgs
L-; !Lbollt of the SlIlIll' IlIILg.rillldl' II~ tht' IIlllxillllllll pii--cluLllllx'r crm;s-sl'ctionnl
!Ln'n IllirillS til(' torllS IIrl'I\, 'I'he fl'lH'tiollllt pit-OP<'llillg arca, fI," will thlls be
II~NI n~ th(' fra{,tional pit'-IllPl1Ihmlll' UI'('I\ mill\lR I h(' torus arcll,
The prodllct
1["8,=1/,,,;:,,0,00011 will Hwn I'('prpl'('lll t.ht' frtldional (,1'0"i; 8t'('tion of the s\\'ollen­
pit lllPnlhrnnl's, ('xeitlsh'l' of till' IlIl'I.\pr )l('rlll/LlI('n( pit-lII('lIIhrlllll' pores thllt are
I'IT('('li\'(' for tht· pnsHngl' of lIl()h'I'lri(':! (h(' si~{' of th(' \\'lItl'r molecule, This \'lIll1e
1Il1l\' hI' ill (;I'ror br 1\8 IIII1l'h 1\;; 100 lll'rCl'nt.
Fortunatcly, it is only of secondary
illlj1ortnlH'(' in tht, cnlcllintions,
!/;
•
SnlllOLS ANn ]~QlT.\1'10NS
The intl'rpr\'tntioll of tht' symbol;; 118('(\ in fO':l11nlns dt'vclopl'd in this publica­
tiOll, I\S \\'(.\1 liS thl' CorlllullLs th('mf;(,I\'I'::;, nfl' glvcn here for the cOllvelllcnce of
thO:il' will) 11\11)' wh,h them for rend)' l'('fl'l'('11I:1',
SYMBOLS
A ,1'''" }'rtwlion!Ll void ('ross-~l'd i0111l1 1\1'('1\ of thl' fil)('r eayities of dry wood,
A", ='" Frill'! it'II:!1 void cross-sect iOlml nl'(,11 of the fiber ('Iwities of swollen wood,
n =Thicknl'ss of wood in centiml'ters at right ILngles to dirciltion of moisture
grad~nL
.
ad=A\'('rn~I' er();;s-;;I~l'fiolllLll\rea of dry wood fiill'rs in square ccntimeters, a,=An'ruge rro:ls-sN'tionn! arca of fiber Clwilil's of swo\len nnll dry wood in sq\lnfl' rPll tillll'tl'r~.
a .. AVl'rng(' l'russ-scctiolll\1 nrea of swollen wood fibcrs in square centimeters,
•
=
•
z '"
_.1....
[ _X_1m:.:.:.
8rm
if + Z =
!/
(¥i)l (z rr)Z
+
= (JIXr,)l+(zr)Z_ .l/X.!m
l
4 rm /
:I
8 rhl
•
FWt'lu: 33.-niil~rallllllntic sk('tch of oyerlup of two IOllgit.udinally udjuccilt
wood fibNS and lIw ll1(\ul1" of cu\<:uluting the ('ffectiyc cell-\\'ull urea for IOllgi­
tudinal plIssagl' of diffusing JIlut('rials.
•
PASSAGE 01<"' LlQ(;ms, VAPORS, ETC., T.£[ROUC::H SOFTWOODS
•
77
a o .,Disllllll'C hllo wood ill c('ntimt'tl'rs nL which 1\ spcciliccl fraction Qf tho iniUnl
lIIoistllr(' ('ontl'llt (''(ists, 1) \)r\'lll~ diffusion con:;(nn t. D, DiifU~i(l1\ t'OIiStilut clfl'clive ill the tiber dirt'cliOIl of wood per unit dimensiolls
of tl\(' wood,
D" _ OifTu:;!On COllstnnt PH tlnit (\iml'lIsious of bulk di/fusion lI1('dillm, D, DlIfusiull ('ollsttllll ('Ifeclivl' ill the !.rnIlS\'l'rSl' din'clioll of wood per uuiL (Ii ntl'll:liollS of t hI' wood.
D. Ditfu'lion ('Ollstnnl of waler \'I~p()r through wood pl'r unil dillll'IIHioll/i of
wood,
D",
Diffusioll ('onsllHlt of bouud walt'r through wood pl'r unit dilll01l8iolll; of
W(lotl.
Ii .; D('rl\'n\lVl' :;i~~n.
Ii, Dilfu~ioll ('oll~(nlll of WI~t('r \'lipor.
rl., nill'lI~i(l1\ Cnlll'tllllt. of I.H)lllld \\I~«.·r,
I~ E\'II\~()mhlu Wi\~('r ('xpr('l'~l'(III$ II frtll',tiUII of ori~dlllli l1I()i~l.lIn· ('(JIIII'II!"
U" App It'd pol('nllll\ pl'r \Hut lhielw('t\s 111 vult::;,
(' ,; BII~(' of IIl1t\lrlll IOj.(lll'ithms,
y-.SpN'if\l' grlwilt of wood (i1oy \\,l'ij.(h\~\"l)hlll\(' lit t('ill).
VII Applln'nt flpN'lfh' !!:nw!ty of w(lod :;UII"(I1I1('(',
fl" t'pN'ifit' gm\'ity of wood (dry wl\i!!:hl-dl'~' voIUIIIl'), II... t'p('('ili(' j.(l'lwit \' l1f woot! (dry w\'ighl.-owoll('n "OIUII1t'), II.. SpPl'ili(' !!:I'tldt~· of wood sllhsllllJCl'. If H(.llllh·(' hUlIlidit\' in vqllilihl'iulIl wilh wood. 1\ Dit'Il'('lrk l'lll1stlllll of liquid hi wood, /, Ll'IIj.(t.h of :llluHllll'd ('II!,i!1I11",' ill l'C'ntiIIlPfl'r:;, 1.1 A"N'Il!!:(' \hh'klll's;; of ((l\llll\, ('I'll Willi" of dry wood ill C('ntiml'll'rs,
l. ;\"('t'II!!:(' ('fTl'l'li\'(' filll'l'-l'/t\'ily Il'l1j.(tlt in l:('11 ti II ll' t('r;.; ,
I, A\'('l'IIj.(l' IilIl'I' Il'lI!!:th ill ('l'utill1('II'I':;, I.. An'ra).:l' t!lit'kll('l':; of (\ouhl(' l'pll \\'llllR of $\1'0\1('11 wood in ('!.·lIlillll'ters. lp ,\.\'l'l'l\!!:l' thit'klll'S;; of pit IllNIII>rIIIII':l ill t'('lItiml'll'rs,
L", L"nl!:th ill t'('lIti\l\l'tl'r:; of ('olllbilll'c1 pit-lI)(,lIlhl'llllt~ thickllcs:;cs ill series
thr llll l!:lt I.h(' s('('1 ion ill the {low (\il'l't'litll),
til is'lIllll'lli IOV;lIl'it1tlil slaw,
M • ~1(l1l'('\Illlr \l'l'il!:ht of liquid ill w(lod. /1/
~!tli~tl\n' ('outellt ill !!:mlll:l 1)('1' I!:ralll of c\r~' woncl, .\'
;\\·O~:l(\I"lI'1\ IIUIIII,('I' tn,on)'" l(Jla, 1\I\I1111t'r of 1\I0\('l'ull'S ill 11 ~mll1 molecule). /I
is'UI1lIl('r of l'fTl'I'th·(' eL\pilltll'i<~$ of wood sN'(ioll in pnrl1l1e1 per sqllare
('pntill1l'i.l'r.
IIf ,A"PI'IlI!:\' nUl1lh~'1' of Iilll'r CIWitic-S ll'lL\'('t'fll'd per centimeter in tho fiber
(\ir('('l iOIl.
II, AVl'I'lLI!:(' 1\\lIIII)('r of fi\wr:; tm"l'r~('d pl'l' ('('nOmeter in t.he mdilll alld the
1t11l!!:\'lItin\ (\in'l'tion):; thl"'\I~h 5\\'01\('11 wood.
II ... NUIIIlll'r of pllltll'IlI\lI'IUH':; or double ('('11 \\,l1l1s lmv\'rl;ed in serie::! per cent.i­
mNl'I'.i1l tlH' lill('1' (\Ir(,(,tioll,
"" ;\ t \I\!JsplH'r.ir prei(l:HII'(' ill lIlillillll't('rs of 1Ill'I't'ury,
"
Prc;;flUrl' drop throuv;h stulldnr(\ l'lIpil\nry ill (\\,n\'):; pl'r liqullrc centilllcter. /,', I'rl'l',-mrp drop through fiI.lt'r \'I\\"i(i('~ in Sllllll' units 1\;; Pm' I'.. Pn'li~lIrt' drop through fihN-to-fibl'r ('OIl1I11Ullknt illg stl'll('lure ill SlIlIIe
units I\l~ Pt,
1',:4\\,(.\litlg prN\:lIlI'(' ill <I),II('S per squl1l'e ('l'Iltillll'l.er,
P,•. 1'r(';;:;lIrl' drop Umlul!:h wood Iltnll'turl' ill dym'H per squl1rl' ('('nUnwter.
p \'npor pn'55111'1' of liquid in 1'(llIi1l\)riulII wiUI wood in Sl1me I1nits m; Jio'
1'. \'/\por \In'$sUI'(' o( !iquiri in l'llme utlils I1S p.
C) Hlltt' of 10;;;; of ll1(1iSlUrt' in p;mml' per sqllllre ('l'ntimeter Iwr !'ocolld,
QI Frndilllll\l t'rl1sR-s(,(,tiona!Ml'a of tl.(1 trnn;;it'nl l'ell-wl1l1 capilluries of \\'I~ler­
swollen woocl l'tTPdi\'(' for til(' pn:ISU!!:t' of molecules the size of the water
moll'l'ule ill tlw tilwr directioll frolll one fiber l'aviLv 10 unother,
Qo EfTI'('ti\'(' l'rO:;;H'l'rt iOIH\1 arl..'u of woor! section in s<llIaTe centimeters,
Qt.," }o'rt\('\ionl\l l'ross,sl'rtionul Men of th(. tmll>iit'nt. ('oll-wull cllpilll\rics of \\'ater­
SWO\1l'1I wood l'tfl~('t.ive for the plls:;uge of Il\ol('('\lil's the size of tho wnt.er
llIo!l'('\lle it, the Irnns\'ersl' dil'l'c(ions from Onl~ liber <:I\\'il"\' to llI\othcr.
11':",1'erl1l of prob!lbility intl'grnl.
'
qr" EITt'dh'e frucl ionul cr()ss-~('('( ionu\ urea of the permanent pit-mcmbrane
pon.':! for longitudillnl pal:lsugc.
•
cO;
'nJ('RXl('AL BeLl~E'I'IN 020. l,T. S. DEPT. OF' AGHlCl!L'rUH~;
78
q.. :,Frn('(ionnl l~nli\s-:o\('rtil)lInl Im'lI o( tlw trlUlRiC'lIt pil-lJ)C'mhmlll' ellpillllrit's of
"'iIt('l'-lm'ollC'1I wood for the pn5..',nge of molecules tho size of tho water
11101('('\11(\, I'xl'lll~h'(' of P('I'III1I1Wllt porl's,
1/. FmC't iOl1llll'ITI'{'t h'(' ('npillnn' {'rol<s-sP('tionnl 1lr('II.
If ,,:c; 1"ru{'lioIlUII\l"('u of llll1J.(Plltilil wulls of lib!'r.; e(lVI'rpc! h.,- pit!!.
'II""" EtTl'('tiv(' frlll'tiUliul ('l'll::IH,wrLiollllIIU{'1I of l)('rn1ll1l('1I1 pit-IlII'llIbrull!' pores (01'
tralls"!'!"::l' plk~::IIJ.(!'. /(,"",(1n8 rOIlF:lnnl tR.3HiXI07 1'!"gR p('rdpgrp(, ](('ll'ill), r= HndillS of l'upillnrJ' in ('PlililllPtl'l"R. r",,"lIndi,,::: of :::tllndnr<l ('lIpHlnr," in ('('nUn1('tel"R, r,/= A n'rtlJ.(t' rndius of fih('r!; of dt,\' wood ill ('('n I illl!'l('r:i. rf~-'A\'l'rug(' 1'lIditls of fih!'1' ('n,'iti('~ of :::lI'ol1!'n nnd dr.\· wood ill t'!'lItillleters r .. ~~;A"('rugl' rndius of fibl'rs of RlI'oll!'1I W(lod in ('(,lItilll!'ll'r>1. r" "" 1,:tT('t'1 il'l' mdi Ill:< of dHTli/ling purl it'll' or tnoleellll' ill l'ell t illll't er.;, rp=Av('rll):(' radins of pertlllLll('IIt. pil-nll'mbrnlle POI'('S of H\\'nllen 1I'0od in •
(~l'lItillw!.('ril.
r",""'Hudi'.:i of transient el'll-wnll enpilInries in cent.inll'tl'rs etTncUvo for tIow of
wld!'r,
8",";li'rm'til)llnl ('X 11'1'1 1/11 vo\ullldril' !<lIrinkn!-:(' of wood to ov('n-drl' eOlldifioll,
S,,,,,,FI'udiotllll ('ro;;:H'Pl'tiOlll~1 un'lI of Il'Ilnsil'llt 1'('11-11'1111 ('upilluri('s of wutcr­
slI'oll('l\ wood ('tT('('I.iVl' for lht, plIsslI~e of molt'c'llll's thl' size of t.he wnt('r
mol('('nlt' ill til!' fihl'r din'cl ion.
S,,,,;:'Frll(,tinnlll (~I'Oi'~H':I~l'ti(Jnul IIr('n of II'IlIISil'lIt ceil-willi I'l\pillllric's of II'lItl.'r­
Hwoll(~11 wood ('ITc'I'1 iI'(' for IIIP pIL'ii'ngl' of molecllies tho size of the wnt,or
IIIOI!'('u](1 III, ri~hllll\!-:I('s to filwr dir!'dioll.
'/'" AbHOlul(' I('mpl'mllln' (kgrN'!;\{c'lvin).
/::::TIIIII.' ill ;lpconds,
I' ',,", :\\oi;:1 Ilrl' ('on tent ill ('ubll. Cl'lltinlPt!'r p('r cubil' N'ntimeter of wood subs(.nllce
lIud IId~()rl.)('d 11'/1(('1',
\", "('Im'ity of III)\\' 1hrou~h /I ~t IIndllrd ('npillnr)' in NIbil' N'ntinllltl.'rR 1)('1' second.
\', '"t'l<wit~' of l'1l'ctro-osIIlO$P Ihr()\I~h wood sl'ction ill cubic centimeters per
;':('('OIHI. •
\'..
I"rtletiollnl ,'oid "Olllllll' of wood. VII
~" Hp('('ifh; I'(lltlml~ of ~lI'l'lIill~ liquid. V u,' ,'('I()('it ,. of lIow throu~h wood >'N'lioll in cubit· l'rllt inwl('rs Iwr lil'cond. X=" IlItl'rtllIlll'ngth of o,'('rillp in filJl1r dirl'ctiOIl in lIlierOIl$. !I='~ EtTN'!in' o\'('rillp 11'1I.L';th in. pllltH' of o\'('rll\(l in minons. z~:::lll('fT(,I'fil'p purl of O\'(lrlup I('n~th in plnll(, of oV('rlnp. fJ·~ Tl'1'l1l of prohllhility illtp~rnl. il IIJ('rc'IIIPllt si):n, iIHIil'nlill): I Ill' dilTl'rPIll'l' 1ll'\'wPl'nlillliling vnlues of tlH' propNt '" df'si~lIul('(1 br til(' s,\'IlIhol following.
l' Ell'ct'rokilll'1 Ie pO \(I II I inl s('t up 11('IW('PI1 I IH~ wood lind 1he bulk Iiquirl in volts.
" Visl'os!ty of glls or liqUid in pois('/I, r(lrtllll~ ppr crn(irnntl'r per second.)
o ., Hign dpsignlll ing 1\ fUIICtiOIl of till' 11I'ol}('rl,1' 1'l'(Jn'scnted by t.he symbol
rollo\\'ill~. Jl .
t'nIt of If'llgt h (I O-~ em), of h'ngth (\0- 7 C'1Il.), ". HuLio of t'irl'lllllfl'rf'nl'c to dillnll'lf'I' of ('ir(fl(~ m.I·1 Hi). p~"";;Av('mg(' /lpl'l'ifie ):1'I\\'il.\' of Ild1'orl){'c\ wllternl tlw tilwr-slLtllrtltion point. P.::::HPI'(·ific ):rtlvit," or till' liquid in titr l'lIpillnr,l". <I'=Surfllce 1(,IISiol\ of liquid ill dynl's (ll'r l'1'lI!ime\.ef. lIlJl .... rnit
EQl:',\T10NS
No.
I'q~O
1
12
H~hltfng-
F.Quat!on Diffusioll of Rolut!' through Iiq II id-~M.IIr!\t('(1 wood ill ..!...+
th(' tillt'r c\ir('l'tion Illld the D/ Do Am
capillary dilll('nsions. [
1 nOD
_l_._+~
q/+q", q.
+<l-A,.)S,]
+Q.!
l..
•
l'ASSA(l~J 01·' I.TQUlDS, VAl'OIlS, E'l'C., 'l'l1HOl1GIJ: 501"'1'WO{)I>S
No. l'!Ij(u
1Il'IUling 2 \2 \)UTusi(l1l of 8()\lIl(' throll~h
Iiqllid-sntlll'llt.I,'(i wood in
Uw \.\'IInSI'('I'8(' din'('tioll lLnd
•
tlio l'tlpilllll',\' dhul'lISiolis.
3
21
Di/fltsio(l or II'U/('I' 1'11[101', /('lll­
pC'I'ntlll'p, lind !)J'('SSllrt',
"
22
I }itTII!lion nud
ll':illsll·iu) ,
Ii
22
Diffusion of WIIIN 1'111101' in
Jl(ll'lllld unit!l nnd wood·
lIIol:;llll'(' ~llLdil'lIl units,
(j
23
DIlTIISioll or hOllud WI\IPI' in
tlol'uud
(l11i(s
ElIlIlItiou
D,~:;D"
,---1-+£..
11,8,]
II,
1+ -'-',-1-- +9 1
,
[
t
+~"'
"d,,,.,
11.
p
d. 0,220 (
ptu'!il'h' !li1.(·
II'"
/.•
'J' )I'7~ 700
27:3
/>"
1 )
=--­WI'(
N 1111'1/1'.
\\'(/u<l·
unit...,
lWei
l\Ioi~lIIl'l,\ ~l'IIdicnt.
7
23
()I'~ill~
•
23
])rdJlI-\' c1ilTu;;ioll I'ons/ nn t of \i'oml in til(' ll'IU1;;I'l'I~t' cI i­
I'(:('tioll. I\nd I hI' Cl\pilhLry 8
dHTIISioll 1'{)I\;;tlLnt (If wood in t h(' Hhl'l' lIil'l'(" iOIl 1\11<1 tl\(' \'lLpilinn <lirl\l'll­
!lion!l,
'
dll1l('llSIOIlS, [), "" D,,, [
1
D~/D.. +
JO
StNLd)-sll~t('
31
J)rd)l~
dilfl'l.lion.
diITu:;iol\ ('Ollllfl\l1t, dis­
(nm'(' illlO wood, ulld llIois­
tllll' rOIll('l\t.
11
31 Probnhtlit.\· in/.('gml.
12
31
•
Drdng
difTusion ('()lIslunt,
(;\'up<JtI\blr wult'r, 1~lld tillle•
11,,8,]
_+ Q,
__~. __ +~ l ..
_I
27 +C..
1It
,D,/D,.
(/)';)
"n"q... /),
\)
79
qp
80
'l'ECEXICAL Bt:LLETIN O!!O, U. S. DEl"l'. Ol~ AumCULTURE
No. I'IIg0
13
38
IlrJut/llg
~:<lUlltiOIl
Dryill~ diffusion eomHllllt, of
wood ill filwr dir£'t'l ion in
simplified ilpproxilllntl' form.
41
Prt'ssurc' drops rt'SUltill~ frolll
flow throu~h wood in the
fiber dirl'ctiOIl alld tilt, Cllpil­
\ary dinWl!siOlls.
15 42
PrN;slII'C drop,; [('suit illg' (rom
tlO\\' throll~h wood ill tho
lmml\'('rse direC'J ion and
the ('tLpillnry ditUt'!\siollti,
1(\ ·13
Hw('llillg' pressure;
pressqrc,
14
IIlId
D l",,- D,A,.. +D.. (l-Am)Sl
mllor
(i1
Fmdiollill \'oid \'olUn1l' lind
('rOHiH'l'('t.ioIlUll\!'('/l o( wooel,
lind tit(' SI)t'cific ~rtL\'ity o(
the' wood.
IS
1)3
V('locit)' o( flow, pr(·~sun.. ulld
l'llpillury I'IIdius fOl' singl('­
gillS'; cUllillar.\'.
10
1)3
\'l'lo<'il~' of 110\1', JlI'('S~\lI'l', Hlld
In'('mfl;l' ('upillary radius (01'
(I)
WI' III L
p.'"'_....:.
Mv"
17
II"
wood Rl,'clioll,
:20
!i3
•
Prl';;>:un' drops t.hrough gltl.~S
~'llpill:II'~' IIlld wood Spet iOIl
1(\ 1'1'1'1('5,
21
05
('npilllll'\' radiu1I lind
2<7' .lI yaJlor
r= ;~-R'I11;~~.)
prl's!:nir!' (Kllyin1,
22
!ili
2:3 G9
2.1 72
rp\ol'ity of
l'1l't'll'o-o:{I1l0Sl',
•
,',,,,,:S,85XlO-7( g_"qo~,;"Kt)
~Il'i"lllr('
con 1('11 I. 011 YOhlll1('­
frill') i(lll Hnd \\'('i~h t-fml'HOIl bl\,;('s.
v = 1'lJ!!!
p
(_1.. _ )
1+'1I~[?
P
'fmtHw('rse nnd longitudinal
cnpillnrity of cell Willis,
tL
s.
GOVERNMEtiT PRINTING Of Flett lU7
•