M . Kutilek
B R Y A N T , J . C , T . W . B E N D I X E N and C . S. S L A T E R . 1948. Measurement of the Water Stability of
Soils. Soil Sci. 65.
C E R K A S O V , A . A . 1952. Priruinik za praktiine radove pri melioracijama. Beograd.
H A I S E , H . R . , W . W . D O N N A N , J . T . P H E L A N , L . F . L A W H O N , and D . G . S T O C K L E Y .
1956. The Use
of Cylinder Infiltrometers to Determine the Intake Characteristics of Irrigated Soils. ARS-41-7,
Washington D . C . 10 pp.
H A N D B O O K N o . 60. 1954. Diagnosis and Improvement of Saline and Alkali Soils. U S Dept.
Agriculture, Washington D . C . 160 pp.
KACINSKIJ, N . A . 1965. Fizika poôvi. Moskva.
M A Z U R A K , A . P . , H . P . C O S P E R , and H . P . R H O A D E S . 1955. Rate of Water Enty Into an Irrigated
Chestnut Soil as Affected by 39 Years of Cropping and Manurial Practices. Agr. J. 47: 490-493.
—, and E . C . C O N A R D . 1959. Rates of Water Entry in the Three Great Soil Groups After Seven
Years in Grasses and Small Grains. Agr. J. 51: 264-267.
—, W . K R I Z and R . E. R A M I G . 1960. Rates of Water Entry Into a Chernozem Soil as Affected by
Age of Perennial Grass. Sods. Agr. J. 52: 35-37.
N E J G E B A U E R , K . V . 1948. ZemljiSta Juzne BaCke sa gledista navodnjavanja. Arhiv za polj.nauke
i tehniku, sv. 5, Beograd.
R I C H A R D S , L . A . 1949. Methods of Measuring Soil Moisture Tension. Soil Sci. 68: 95-112.
THUN,
R . , R . H E R R M A N N , und E . K N I C K M A N N .
1955. Die Untersuchung von Bôden. 271 pp.
Vucic, N . 1964. Vodne osobine íernozema i livadske crnice i njihov znaCaj za navodnjavanje na
irigacionom podrufju Bafke. Novi Sad.
Analysis of s o m e factors affecting the water vapour
diffusion in soils
M . Kutilek, University of K h a r t o u m , S u d a n
A B S T R A C T : The diffusivity of water vapour D w is considered to be a general characteristic of soil
moisture transport due to the diffusion of water vapour. Values of Dw were computed for various
models of soils from the equation
Dw = DA«PA ^
ow
where D A is diffusion coefficient of water vapour in air, a - emperica! factor (tortuosity), p density of water vapour, PA = P — W , where P is porosity, W- water content in unit soil volume.
It is concluded that two cases, different in principle, have to be distinguished when analysing the
diffusion of water vapour in soils:
a) Diffusion in heavy soils where surface active clay particles are predominant.
Water vapour diffusion is influenced by the change of geometrical parameters (e.g. porosity)
to a relatively low extent, and the mineralogical composition becomes the principal factor
affecting diffusion. A high content of strongly hygroscopic materials (e.g. montmorillonite)
brings about the decrease of the D w value by about 102. T h e influence of exchangeable
cations is reverse when compared with the influence on the flow of liquid water. The bivalent
exchangeable cations lower the D w value and the monovalent exchangeable cations raise the
D w value, omitting the possible change of aggregation.
350
Analysis of some factors affecting the water vapour diffusion in soils
b) Diffusion in light soils where silt and sand particles are predominant.
Since surface properties of these particles are uniform, the water vapour diffusion is affected
primarily by the change of the geometrical parameters (porosity). T h e range of the changes is
relatively small w h e n compared with the changes caused by mineralogical composition of the
heavy soils.
R É S U M É : L a diffusivité de la vapeur d'eau D w est considérée c o m m e constituant une caractéristique
d u transport d'humidité d u sol, due à la diffusion de la vapeur d'eau. Des valeurs de D w peuvent
être tirées des divers modèles de sols d'après l'équation :
dp
Dw = DAaPA -f-
dw
o ù D A est le coefficient de diffusion de la vapeur d'eau dans l'air, <x un facteur empirique,
p = densité de la vapeur d'eau, PA = P — W o ù P est la porosité et W la teneur en eau par unité
de volume d u sol.
O n arrive à conclure que deux cas, différents en principe, doivent être distingués quand o n
analyse la diffusion de la vapeur d'eau dans les sols :
a) Diffusion dans les sols lourds où les particules d'argile à surface active sont prédominantes.
L a diffusion de la vapeur d'eau est influencée par la modification de paramètres géométriques
( c o m m e la porosité) d'une quantité relativement faible, et la composition minéralogique
devient le principal facteurs affectant la diffusion. U n e forte teneur en matériaux fortement
hygroscopiques ( c o m m e la montmorillonite) a m è n e la diminution des valeurs de D w
d'environ 1 0 % . L'influence de cations échangeables est inverse quand comparée à l'influence
sur l'écoulement de l'eau liquide. Les cations bivalents réduisent les valeurs de D w tandis que
les cations monovalents échangeables augmentent les valeurs de D w , en laissant de côté la
modification possible de l'agrégat.
b) Diffusion dans les sols légers o ù les particules de sable et de vase prédominent.
C o m m e les propriétés de surface de ces particules sont uniformes, la diffusion de la vapeur
d'eau est avant tout influencée par la modification des paramètres géométriques (porosité).
L'étendue de ces modifications est relativement petite quand o n la compare aux changements
causés par la composition minéralogique des sols lourds.
I. I N T R O D U C T I O N
T h e m o v e m e n t o f water in an unsaturated soil is considered as a polyphase flow. T h e
mathematical solution o f this flow is enabled b y the introduction of the moisture
diffusivity (Klute, 1952), a n d the flow of both phases is expressed b y m e a n s of diffusion
equations (Philip a n d D e Vries, 1957). T h e v a p o u r phase flow is negligible at higher
moisture contents. H o w e v e r , the v a p o u r flow h a s to b e considered at l o w moisture
contents, for e x a m p l e during the second stage o f evaporation (Budagovskij, 1964). In
the extremely dry surface layers of the soil w h e n the moisture content has been decreased
under the value o f the hygroscopic coefficient, the v a p o u r flow is supposed to b e the
d o m i n a n t m e c h a n i s m of moisture transport.
T h e total liquid a n d v a p o u r diffusivity D w is:
Dw = DWL + DWV
(1)
where DWL is the liquid diffusivity, and Dwv is the vapour diffusivity. W h e r e vapour flow
is dominant, and liquid flow, negligible, w e shall consider Dw = Dwv. With regard to the
theories of the moisture transport in soils and generally in porous media, the vapour
diffusivity is expressed as follows (Philip, 1955):
Dwv = DG?£-
(2)
dw
351
M. Kutilek
where p is the density of the water vapour (g. c m 3 ) , W is the moisture content (g. c m " 3 ) ,
and DG is the diffusion coefficient of the vapour in the soil ( c m 2 ^ " 1 ) according to
Penman (1940) after some modification:
DG = DAaPA = DAa(p-^-\
(3)
where D A is the diffusion coefficient of water vapour in air at a given temperature and
external pressure ( c m 2 . s _ 1 ) , a is the empirical factor called tortuosity, PA is the air
porosity, P is the total porosity, and pL is the density of liquid water. Eq. (2) is analogous
to the relation between the hydraulic conductivity K and the liquid diffusivity D W L :
D^-KÍL
(4)
where T is the suction of the soil water. The vapour flux density q ( g . c m ~ 2 . s _ 1 ) is then:
q = -Dwv—
(5)
ox
where x is the distance in the direction of the flow (cm). Considering the adsorption and
desorption process, Jackson (1964) derived
ÔW
ô (^
oW\
— = -[DWy
— \
(6)
ot
ox\
ox J
and proved experimentally that diffusion theory is fully applicable to water vapour flow
in soils, and that good agreement exists between the calculated and measured values of
diffusivity D W Y . It follows from eq. (5) and (6) that the vapour diffusivity Dwv is an
important value characterizing the moisture transport due to water vapour flow in soils
under the action of the moisture gradient.
Since there is a lack of the experimentally determined values of the vapour diffusivities
and since our knowledge of the significance of the individual factors influencing the
water vapour diffusion in soils is insufficient, w e have calculated the values of D w i r for
various models of soils to get an information of the first approximation about this
problem.
II. PARAMETERS OF THE SOIL MODELS
The vapour diffusivities were calculated from the equation
DWV = DJP-^)^
\
(7)
PL/ÔW
Geometric conditions (Px a) and exactly defined materials (dp/d W) had to be chosen as
a model for the calculation.
As soil materia], w e have used the following soils and clay minerals of k n o w n and
previously published adsorption and desorption isotherms (Kutilek, 1962):
a) Clay minerals < 2 \i, alternatively saturated with N a or Ca: kaolinite, montmorillonite,
and illite.
b) A sample from the A-horizon of a loamy chernozem on loess, and a sample from the
A j-horizon of a sandy loam podzol on gneiss.
352
Analysis of some factors affecting the water vapour diffusion in soils
c) T h e same as item b), but after the oxidation of h u m u s ; humusless chernozem and
humusless podzol.
d) A sample of the medium decomposed highmoor.
The term dp/dW was determined from the isotherms in the ranges from 0.05 to 0.8 of
the relative pressure of water vapour pipo.
Geometric conditions were characterized in all cases except of item d) by porosity
P = 0.45 and by the empirical factor a = 0.60. These values were chosen for basic
comparisons though it is known that the value of afluctuatesgreatly being dependent on
porosity, pore distribution, particle size and shape (Penman, 1940; Blake and Page, 1948;
Hanks, 1958; Currie, 1960). In addition to the basic comparative geometry, alternative
values of P and a were chosen as to get a general idea of the influence of changed
geometry upon the change of the vapour diffusivity. For clay minerals, w e have compared
the influence of the change of the porosity from P = 0.45 to P = 0.50. The porosity of
highmoor was chosen to be P = 0.85 and P = 0.75. T o get more a precise picture on the
influence of the humus, we have compared diffusivities of a humic soil characterized by
P = 0.55 and a = 0.80 with the same but humusless soil characterized by the lower
porosity P = 0.45 and by the lower empirical factor a = 0.60.
The physical constants in eq. (7) were used as follows: pSAT = 1.631.10 - 5 g . c m - 3 ,
D A = 0.283 c m 2 . s _ 1, both at T = 19 °C, and p = 760 torrs.
D ( c m 2 <T 1 x10~ 3 )
30
20
10
0.1
0 2
F I G U R E 1. Vapor diffusivity D
(2) Ca kaolinite
j
0.3
w v versus
L
0.4-
0 5
0.6
j
0.7
|
0.8
P'Po
relative pressure of water vapor pip0 in (1) Na kaolinite,
III. DISCUSSION OF RESULTS
A . CLAY MINERALS
T h e resulting values of diffusivity D w v computed from the adsorption isotherms for the
wetting process in clay minerals at P = 0.45 and a = 0.60 are plotted against the relative
pressure of water vapour p/p0 in thefigures1, 3 and 5, and against the moisture content W
in the figures 2 , 4 and 6. The m a x i m u m value of D W Y appears closely at the monolayer
353
M. Kutilek
moisture. Jackson (1964) obtained the same result in loamy sand and in clay soil. T h e
m a x i m u m value of Dwv is reached in all cases in N a clay minerals, if w e omit the
possible change in aggregation. But noting facts ascertained afterwards on the influence
of the geometric parameters u p o n diffusivity, w e suppose that the change in aggregation
JO
f \
1I
1\
1 \
-
1
I
20
—
/
/
\
\
\
\
/
/
/
/
/
1Ü
A\
/ \ \
/ / \ \\ \
/
\ \
/
-
\
~
i
I
Q004
I
I
2
,
0.008
0 012
0.016
W(g c m - J )
F I G U R E 2. Vapor diffusivity Dwv versus moisture content W in (1) Na kaolinite, (2) Ca k
of kaolinites and montmorillonites will hardly suppress the influence of the exchangeable
cation, and that the strong aggregation process causing a rise of porosity a n d of the
empirical factor will probably not raise the m a x i m u m Z>^K-value of C a minerals over
that of structureless N a minerals, except of the ilutes. But w h e n comparing the diffusivities
depending o n the moisture content, w e see that near the moisture content where C a
0.2
0.4
0.6
0.8
P'Po
F I G U R E 3. Vapor diffusivity Dwv versus relative pressure of water vapor p/p0 jn (1) Na
(2) Ca Mite
354
Analysis o/ some factors affecting the water vapour diffusion in soils
minerals reach their m a x i m u m value of Dwv, the values of Dwv in N a minerals fall
below the D ^ - v a l u e s in C a minerals. F r o m this point u p , the moisture transport in
Na-saturated clay minerals—and similarly in Na-soils—will be probably lower than the
moisture transport in Ca-clay minerals—and Ca-soils—throughout the whole unsaturated
region.
D(cm 2 . s"1 x 10~3)
0.02
0.04
0.08
W(g.cm- 3 )
0 06
F I G U R E 4. Vapor diffusivity Dwv versus moisture content W in (1) Na illite, (2) Ca illite
T h e highest values of Dwv are reached in kaolinites, lower in illites, and the lowest in
montmorillonites, being in an inverse proportion to the specific surface. T h e difference
between the diffusivity in kaolinites a n d in montmorillonites is of the order of 1 0 2 .
T h e diffusivity values for the drying process were computed from the desorption
isotherms. These values were slightly smaller than those calculated from the adsorption
isotherms. T h e reduction of the m a x i m u m values w a s about 6 0 % in montmorillonites
and about 2 0 % in both the kaolinites a n d illites.
05
/
04
/
/
/
\
\
\
\
\
0.3
\
^ y
\
- ^
\
0.2
'
01
2^
I
I
0.2
I
I
0.4
I
06
I
I
08
P'Po
F I G U R E 5. Vapor diffusivity Dwv versus relative pressure of water vapor p/p0 in (1) Na montmorillonite, (2) Ca montmorillonite
355
M . Kutilek
The change of porosity from p = 0.45 to P = 0.50 caused an increase of D w v from 20%
to 25% in kaolinites, from 25% to 40% in montmorillonites, and from 20% to 35% in
illites in the examined ranges of the relative pressure of water vapour p[p0 from 0.05 to 0.8.
Increasing the empirical factor a from the original value of a = 0.60 to a = 0.80 causes
D W Y to rise by about 34%. If w e compare the increase of D w v caused by the change of
0.5
0.4
03
02
01
0 1
0 2
0 3
W(g.cm-3)
F I G U R E 6. Vapor diffusivity Dwv versus moisture content W in (1) Na montmorillonite, (2) Ca
montmorillonite
geometric parameters with the diverse values of D w v in different clay minerals, w e can
ascertain that the properties of the solid soil phase, or the mineralogical composition,
are influencing the flow of water vapour in clay fraction to a m u c h higher extent than the
fluctuation of the values of the porosity and of the empirical factor. W e also expect the
same influence in heavy soils in general.
D(cm2.s"1x10""5)
02
0
4
0.6
0.8
P/Po
F I G U R E 7. Vapor diffusivity D w v versus relative pressure of water vapor pjpa in
(1) chernozem at P = 0.45, a = 0.60,
(2) chernozem at P = 0.55, a = 0.80,
(3) humusless chernozem at P = 0.45, a = 0.60
356
Analysis of some factors affecting the water vapour diffusion in soils
B. HUMUS
Values of Dwv in chernozem at P = 0.45, a = 0.60, and at P = 0.55, a = 0.80, and values
of Dwv in the humusless chernozem at P = 0.45, a — 0.60 are plotted against the relative
5 —
4
_
/ ^ \
3
y
\
\
2
1
i
i
i
i
0.02
i
0 04
i
i
0.06
i
0.08
Wlg.cm-3)
F I G U R E 8. Vapor diffusivity D w v versus moisture content W in
(1) chernozem at P = 0.45, a = 0.60,
(2) chernozem at P = 0.55, a = 0.80,
(3) humusless chernozem at P = 0.45, a = 0.60
B
7
6
'
/
\
/
\
5
4
3
"
/1 / /
1 /
//
\ \
\ \
\ N \\i
/ /
1/
If
N
2
\
S \
2 "»
1
1
1
0.2
1
1
0.4
1
1
0.6
1
1
0.8
P'P0
F I G U R E 9. Vapor diffusivity Dwv versus relative pressure of water vapor pjp0 in
(1) podzol at P = 0.45, a = 0.60,
(2) humusless podzol at P = \ .45, a = 0.60
357
M . Kutilek
pressure of the water v a p o u r p/p0 in the fig. 7 , a n d against the moisture content W in
the fig. 8. V a p o u r diffusivities in p o d z o l a n d humusless p o d z o l are represented in a
similar w a y in fig. 9 a n d 1 0 .
0 03
0 02
Wfg.cm- 3 )
F I G U R E 10. Vapor diffusivity D w v versus moisture content W in
(1) podzol at P = 0.45, a = 0.60
(2) humusless podzol at P = 0.45, a = 0.60
/-\
1
1
/1
/
\
\
\
\
/
/
\
1
\
\
\
1
3
-
2
--
\
\
s
N1
y—^\
~~—---~-~2
1
i
0.02
i
i
,
0 04
F I G U R E 11. Vapor diffusivity D w v moisture content W in
(1) highmoor at P = 0.85, a = 0.60,
(2) highmoor at P = 0.75, a = 0.60
358
i
0.06
i
i
0.08
W(g. c m - 3 )
Analysis of some factors affecting the water vapour diffusion in soils
The soil h u m u s causes a decrease of the m a x i m u m diffusivity provided that all geometric
parameters are kept constant. But if w e consider the positive influence of h u m u s u p o n the
aggregation of the soil and so u p o n the probable rise of both the porosity and the empirical
factor, w e d r a w the conclusion that with the presence of h u m u s the m a x i m u m diffusivity
can reach or even exceed the m a x i m u m diffusivity in a humusless soil. F r o m fig. 8 and
10 it follows that after reaching its m a x i m u m value, the diffusivity of the humusless soil
falls below the diffusivity of soils containing h u m u s even under the unchanged geometric
conditions.
C . TEXTURE
F r o m the comparison of Dwv-\alues
in the figures 8 and 10, a n d from the computed
values using the adsorption isotherms of K u r o n (1930) o n various fractions of quartz,
w e conclude that the increase of the clay content will cause a decrease of the diffusivity
provided that the mineralogical composition of the clay fraction will not change. However,
the changes in the diffusivities in sands till loams due to the changes in texture or in
mineralogical composition of the clay fraction are not so great as to suppress the
dominant influence of geometric parameters.
IV.
SIGNIFICANCE O F T H E
W A T E R V A P O U R DIFFUSIVITY
T o be in the position to reply to the question of the significance of the water vapour
diffusivity, w e must compare the diffusivities of the liquid and of the vapour flow. This
comparison, however, has to be considered as a preliminary one due to the uncertainty
whether the liquid diffusivity depends only upon the soil moisture or if it depends upon
the moisture gradient too (Swartzendruber, 1963). The liquid diffusivities at low moisture
contents would have fluctuating values, if they depend upon the moisture gradient.
The available published data of liquid diffusivities were determined under the single
assumption that the diffusivity depends only u p o n the moisture. These data s h o w that
the liquid diffusivity ranges from c . 1 0 - 4 to c . 1 0 - 5 c m 2 . s " " ' (Gardner and M a y h u g h ,
1958; Volarovitch, 1964) or that they are even less than n . 1 0 - 5 c m 2 . s ^ ' (Staple and
Lehane, 1954; Doering, 1965) at low moisture contents approximating the wilting point.
Since the values of the vapour diffusivity are ranging in roughly the same limits, it is
reasonable to suppose that the m a x i m u m vapour diffusivity is at least of the same
significance as that of the liquid flow at the wilting point.
But w h e n compared with the values of the liquid diffusivities in fairly moist soil, e.g.
in the vicinity of the field capacity, the vapour diffusivity is several orders of magnitude
lower.
REFERENCES
B L A K E , G . R . and J.B. P A G E . 1948. Direct measurement of gaseous diffusion in soils. Soil Sci. Soc.
Am. Proc. 13 : 37-42.
B U D A G O V S K I J , A . I . 1964. Isspareniye Potchvennoy Vlagui (Evaporation of Soil Moisture).
Nauka, Moskva.
C H I L D S , E . C . 1956. Recent advances in the study of water movement in unsaturated soils. Trans.
Vlth Int. Congr. Soil Sci., vol. B : 265-273.
C U R R I E , J. A . 1960. Gaseous diffusion in porous media II. Brit. J. Appl. Phys. 11 : 314-324.
D O E R I N G , E.J. 1965. Diffusivity by the one step method. Soil Sci. 99 : 322-326.
G A R D N E R , W . R . and M . S . M A Y H U G H , 1958. Solutions and tests of the diffusion equation for the
movement of water in soil. Soil Sci. Soc. Am. Proc. 22 : 197-201.
359
S.A.
Wladitchensky
H A N K S , R.J. 1958. Water vapour transfer in dry soil. Soil Sci. Soc. A m . Proc. 22 : 372-374.
J A C K S O N , R . D . 1964. Water vapour diffusion in relatively dry soil. I. Theoretical considerations
and sorption experiments. II. Desorption experiments. III. Steady state experiments. Soil Sci.
Soc. A m . Proc. 28 : 174-176, 464-466, 467-470.
K L U T E , A . , 1952. A numerical method for solving the flow equation for water in unsaturated
materials. Soil Sci. 73 : 105-116.
K U R O N , H . 1930. Ztschrft. Pflanzenern., D u n g . , Bodenk. 18 : 179-203.
K U T I L E K , M . 1962. Hygroskopická pudní vláha (Hygroscopic soil water) I, II. Vodohospodársky
casopis SAV, 10: 11-29, 156-173.
— 1962. Vliv humusu na hygroskopickou pudní vláhu (The influence of h u m u s on hygroscopic
soil water). Vodohospodársky casopis SAV, 10 : 321-329.
P E N M A N , H . L . 1940. G a s and vapour movement in the soil I. The diffusion of vapours through
porous solids. / . Agrie. Sci. 30 : 437-462.
PHILIP, J . R . 1955. The concept of diffusion applied to soil water. Proc. Nat. Acad. Sci. (India).
24A : 93-104.
— and D . A . D E VRIES. 1957. Moisture movement in porous materials under temperature gradients.
Trans. A m . Geophys. Un. 38 : 222-232.
— 1958. Physics of water movement in porous solids. Highway Res. Boards Spec. Rep. 40:147-163.
S T A P L E , W . J . and J.J. L E H A N E . 1954. Movement of moisture in unsaturated soils. Can. J. Agr. Sci.
34 : 329-343.
S W A R T Z E N D R U B E R , D . 1963. Non-Darcy behavior and the flow of water in unsaturated soils.
Soil Sci. Soc. A m . Proc. 27 : 491-495.
V O L A R O V I T C H , M . P . 1964. Koll. zhurn. 26 : 139-141.
Moisture content and hydrophility as related
to the water capillary rise in soils
S.A.
Wladitchensky
A B S T R A C T : W h e n studying the capillary rise of water in soils w e characterize the latter with some
quantities (porosity, particles dimension and shape, and so on). The limits of variation of these
characteristics are rather wide so the conclusions about the regularities of capillary rise reflect the
average.
For an exhaustive description of the capillary rise (and the water movement in general as well)
one should study the water behaviour in a single utlimate pore, after this in a system of pores,
and at last in the soil as a whole.
The results of our experiments with filming support the statical nature of some capillary rise
regularities.
The uneven shape of the capillary rise curve obtained in our experiments is explained by
differences in the dimension and shape of pores through which the water moves, and by differences
in the character of pore walls.
In particular the components of the soil have different hydrophility. The different hydrophility
of pore walls material is also influenced by adsorbed water and gas.
The last assumption was examined in our experiments. The wetting angles and capillary rise
velocities were measured for glass, sand and loam with different moisture contents. It was shown
that the cosine of the wetting angle and the velocity of the capillary rise are a m i n i m u m at the
m a x i m u m hygroscopical moisture content.
360