AMER. ZOOL., 20:329-338 (1980)
The Physics of Gas Exchange Across the Avian Eggshell1
CHARLES V. PAGANELLI
Department of Physiology, State University of New York at Buffalo,
Buffalo, New York 14214
SYNOPSIS. The principles which govern gas exchange by diffusion across the pores of the
avian eggshell are reviewed and compared with convective gas exchange. The concept of
conductance is defined for both diffusive and convective gas exchange through pores,
and methods of calculating pore size are described. Estimates of conductances of the
elements in the gas transfer path from atmosphere to chorioallantoic capillary blood are
discussed, and recent studies on the role of ternary diffusion and a convective component
to gas fluxes are presented.
INTRODUCTION
Vertebrate respiration involves convection. Rhythmic movements of the chest
wall in mammals or of the gills in fish are
accompanied by palpable inspiratory and
expiratory flow of the fluid medium in
which the animal lives, be it air or water.
However, respiration also occurs in plants,
insects, and eggs, none of which requires
the use of ventilatory pumps and convective flow. Gas exchange in these organisms
takes place by diffusion, a process driven
by differences in concentration or chemical potential of the diffusing substances
rather than by total or hydraulic pressure
differences as is the case with convective
flow. The laws which describe convective
or diffusive flow through systems of tubes
or porous media such as the avian eggshell
have fundamental differences which must
be taken into account in any quantitative
assessment of gas exchange by the avian
embryo. It is my aim in this presentation
to review the laws which govern gas exchange by diffusion through the eggshell
and to point out how these laws have been
used to determine the functional properties of the shell and its associated membranes.
DIFFUSION THROUGH PORES AND THE
CONCEPT OF CONDUCTANCE
A simplified form of Fick's first law for
steady-state diffusion of gas x in air across
1
From the Symposium on Physiology of the Avian
Egg presented at the Annual Meeting of the American Society of Zoologists, 27-30 December 1979, at
Tampa, Florida.
a porous barrier such as the avian eggshell
is given by Equation (1):
A
where M x = net flow of gas x across the
shell (cm 3 STPD s' 1 ), D x = binary diffusion coefficient of gas x in air (cm2 s"1),
A p = total pore area of shell available for
diffusion (cm 2 ), L = length of diffusion
path or shell thickness (cm), ACX = concentration difference of gas x across the
shell (cm 3 STPD cm" 3 ).
Since diffusion of gases occurs both in
the gas phase and between gas and blood,
it is useful to replace ACX in Equation (1)
with the corresponding partial pressure
difference APX (in torr) as the driving
force:
Mv =
Dx/3gAPx
(2)
where /2g = ACX/APX, /3g is the capacitance
coefficient as defined by Piiper et al. (1971)
for any ideal gas. From the perfect gas law
j8g = 1/RT, and represents the quantity of
gas which must be added to a volume of
one liter to increase the partial pressure of
x by 1 torr. If one takes 2.785 cm3 torr
(°K)-' cm" 3 STPD as the value of the gas
constant R, /3g at 38°C is 1/866 or .00116
cm 3 STPD cm" 3 torr" 1 .
Equation (2) states that diffusive gas
flow through the shell depends on the ratio of shell pore area and thickness (Ap/L),
on the properties of the gas molecules in
the diffusion path (D x ), and on the driving
force caused by the partial pressure difference in x (APX).
330
CHARLES V. PAGANELLI
diffusion coefficient of x in air and the
pore geometry of the diffusion path in the
shell, as may be seen by comparing Equations (2) and (3):
(4)
Gv =
3
33
5
7
.2
.14
10
(I/PB)
.10 atm.
FIG. 1. The effect of pressure on G, the conductance of the hen's eggshell, for the gas pairs H2O-air
and O2-N2 at 25°C. G for each gas pair and pressure
has been divided by its corresponding value at 1 atm
to normalize the data. The line is drawn by eye. Data
replotted from Paganelli et al. (1975).
Conductance
For gases diffusing either in gas or liquid it is possible to consider Mx in general
terms as the product of a diffusive conductance (Gx) and APX, an approach used
by Wangensteen et al. (1970/71), Kutchai
and Steen (1971), and Ar et al. (1974),
among others:
M x ^ G X AP X
(3)
where Gx is the diffusive conductance or
diffusing capacity of the shell to gas x in
air (cm3 STPD s"1 torr~'). In effect, Equation (3) constitutes a definition of conductance as MX/APX.2
The term conductance is related to earlier definitions of shell porosity used by
Murray (1925), Marshall and Cruickshank
(1938), Pringle and Barott (1937), Mueller
and Scott (1940), and Tyler (1945). Its
principal advantage over earlier definitions is that it explicitly incorporates the
driving partial pressure difference. Conductance is directly related to the binary
2
More precisely, Gx should also specify the gas or
gas mixture in which diffusion takes place, e.g.,
Go..,,AIR. For simplicity of notation, if the second gas
is air, it will usually be omitted as a subscript on G
unless needed for clarity. Thus, the O2 conductance
of the shell in air is Go2. The same convention will
be followed for binary diffusivities; DO2,AIR will be
written simply as Do2.
Equation (4) permits calculation of Ap, the
pore area of the eggshell, from measured
values of G and L, and literature values of
Dx and /3g (Ar et al., 1974; Paganelli et al.,
1975). If Equation (4) is written for water
vapor and solved for Ap, one obtains:
_
An =
GH2OL _
=
DH2O/3B
0.478 GH 2 O-L
(5)
where Ap and L have units of mm2 and
mm, respectively, DH 2 O at 25°C is .25 cm2
s-\ j8g at 25° is 1.205 x 10~3 torr"1, and
1
GH 2 O is expressed in mg day~' torr" .
The direct relation between G and D has
several implications. D depends on barometric pressure and the gas species in the
diffusion path in a manner described by
the Chapman-Enskog equation (Reid and
Sherwood, 1966):
kT3/2
Dv =
PB
(- + —X
\ MX
(6)
My /
where k is a complex term depending on
the molecular interactions between the two
gases in the diffusion system, T is absolute
temperature, PB is barometric pressure in
atm, and Mx and My are the molecular
weights of gas x and the second gas in the
diffusion path, respectively.
Conductance and barometric pressure
From Equation (6) D and thus G for a
given pore geometry will vary inversely
with ambient pressure. At 0.5 atm, for example, G should be twice its value at 1 atm.
Figure 1, replotted from the data of Paganelli et al. (1975), shows the inverse relation between G and pressure for both
water vapor and O2 conductances of chicken eggs (Gallus domesticus) in air or N 2 .
Erasmus and Rahn (1976) demonstrated
similar changes in the CO2 conductance of
incubating chicken eggs exposed to ambient pressures above and below 1 atm.
The dependence of G on PB has important
331
GAS EXCHANGE ACROSS THE AVIAN EGGSHELL
consequences for species which nest at altitude. (See the contributions of Drs. Carey
and Visschedijk to this Symposium.)
Conductance, driving pressure, temperature,
and inert gas effects
Eggs exposed to gases other than air will
be affected by the relation between D and
the molecular species of gases in the diffusing path. Figure 2 (Rahn and Dick, unpublished results) shows the changes in
diffusive water vapor loss from eggs in
either air, SF6, or He. Water loss was measured as weight loss in eggs kept at a
known temperature in desiccators in which
the water vapor pressure (PH 2 O) around
the eggs was effectively 0. APH2O between
the inside of the eggs and their environment was then simply the saturation vapor
pressure at the temperature of measurement. APH 2 O was varied systematically by
equilibrating the desiccators at each of
three temperatures in turn (15°, 25°, and
35°C (Fig. 2). The slopes of the lines
(MH 2 O/APH 2 O) are measures of GH 2 O in air,
SF6, and He.
Figure 2 illustrates several important
facts. Notice that water loss varied directly
with APH 2 O, a confirmation of our assertion that diffusion controls movement of
gases through the shell. Also, the slopes of
the lines did not change measurably as
temperature changed. The relative independence of G from temperature can be
appreciated from the relation between G
and D. From Equation (6) D varies as T3'2;
from Equation (4), G = (AP/L)(D/RT).
Thus G should vary as T" 2 . As an example,
a change in temperature from 15° to 35°C
should result in an increase in G of only
(308/288)1'2 = 1.03 or 3%. In the usual
manner of calculating G by measuring daily weight loss, it is usually not possible to
detect changes of this order of magnitude.
Finally, values of G relative to air (Fig.
2) agree reasonably well with corresponding ratios of directly measured diffusivities. They can also be predicted from
Equation (6) but the agreement is better
with measured than with predicted values
(Table 1), in part because the ChapmanEnskog theory was designed to describe
diffusion in monatomic, non-polar, spher-
15
25
35 °C
1
f
VIH 2 O
mg • day'
500
400
300
.<x
/
200
/
x93 ^ ^
/**
100
1
10
20
30
1
40
ApH2O
Fie. 2. Water loss from infertile hen's eggs in He,
air, and SF(i as a function of APH2O in torr across the
shell. APH2O was varied by setting the temperature of
measurement at 15°, 25°, and 35°C, in turn. The
slopes of the lines are G values for water vapor in He,
air, and SF(i. Data from Rahn and Dick (unpublished).
ically symmetrical gas molecules. Water,
He, and SF(i molecules do not fit this description particularly well, and the Chapman-Enskog equation should be used with
caution when one deals with these gases.
The effect of He on G is particularly
striking. Other things being equal, eggs incubated in He will lose water almost three
times faster than in air. O2 and CO2 transTABLE 1. Comparison of conductance ratios in He and
SFe with corresponding diffusivity ratios, both measured and
predicted.a
GH 2 O,X
DHio,x
Predicted"
Dn,o,x
GH2O.AIR
DH 2 O,AIR
DH2O,AIR
Measured
Gas x
He
SFB
a
2.91
0.51
c
3.30
0.51"
3.95
0.43
Conductances are taken from Figure 2.
Chapman-Enskog Equation.
DH.2O, He and DH 2 O, N2 at 25°C are 0.836 and 0.253
cm- s"1, respectively (Paganelli and Kurata, 1977).
" DH2O,SFB at 25°C is 0.13 cm2 s"1 (Paganelli, unpublished results).
b
c
332
CHARLES V. PAGANELLI
Hydraulic Conductance
Diffusive Conductance
- Flow
time
shell
cm 3 O2
min.cm2.torr
cm 3 0;
,-4
=
1.9
x
10
2
min .cm «torr
-2
= 4 0
x l0
FIG. 3. Schematic diagram to illustrate the different techniques used to measure hydraulic conductance
(Ghydr) (left-hand figure) and diffusive conductance (G) (right-hand figure). Hydraulic O2 conductance was
calculated from the data of Romanoff (1943); diffusive O., conductance was taken from Wangensteen el al.
(1970/71).
port are similarly affected in He. Erasmus
and Rahn (1976) were able to reduce by a
factor of one-half both APco2 and APo2
across the air cell of incubating chicken
eggs by placing them in an He-O2 environment.
COMPARISON OF DIFFUSION AND
CONVECTION
At this point let us compare the laws
which govern convection and diffusion to
see where they differ. Equation (7) is Poiseuille's law for laminar convecdve flow of
fluid through uniform, cylindrical pores:
(7)
where N = number of pores in shell, r =
pore radius (cm), 17 = viscosity of medium
(torr-s), L = pore length (cm), and AP =
hydraulic pressure difference across pore
(torr).
If we define N7rr4/(8T;L) as G hydr , the hydraulic conductance, Equation (7) becomes:
Mx = Ghy(lrAP
(8)
Convective conductance can now be
compared with diffusive conductance if
one uses the relation Ap = Nvrr2. The ratio
of these two conductances is:
(9)
Equation (9) shows that for a given AP, the
flow of a gas by diffusion will not in general equal its flow by convection. Quite different techniques are used to measure hydraulic and diffusive conductances (Fig.
3). In the former case a difference in hydraulic pressure causes bulk flow of gas
through the shell; in the latter, a difference in partial pressure produces an O2
flux. The hydraulic conductance in Figure
3 is calculated from the measurements of
Romanoff (1943); the diffusive conductance is taken from Wangensteen et al.
(1970/71). The former is 200-fold greater
than the latter. Large differences between
hydraulic and diffusive conductances to O2
and water vapor are typically seen in values collected from the literature (Table 2).3
3
Because the measurements of shell permeability
by Hiifner (1892), Romanoff (1943), and Romijn
(1950) were performed using hydraulic rather than
purely partial pressure differences across the shell,
they obtained values of Gmdr, from which it is not
possible to estimate Gx without specific knowledge of
333
GAS EXCHANGE ACROSS THE AVIAN EGGSHELL
TABLE 2. Convective and diffusive conductances of the chicken eggshell."
1
cm'STPD •d;iy '-torr"
Ghydr
Ghydr
Ghytlr
Go,
Go,
Go,
Go,
GH 2 O
GH,O
GH.,O
GH,O
Temp.
°C
11.9
142*
3922*
1785*
20
18.8* 25
9.5* 21-24
6.2*
—
5.9*
38
17.lt
19.2t 39
15
10.6t
17.9 ?0-?5
Ref.
Small pieces of shell; membranes moist
Half shell; membranes dry
Entire shell; membranes moist
Shell and dry outer shell membrane
Shell and moist inner and outer membranes
Shell and moist inner and outer membranes
Shell and moist inner and outer membranes
Water loss from intact eggs in incubator
Water loss from intact eggs in incubator
Water loss from intact eggs in desiccator
Water loss from intact eggs in desiccator
Hiifner(1892)
Romanoff (1943)
Romijn (1950)
Wangensteen et al. (1970/71)
Kutchai and Steen (1971)
Lomholt (1976)
Tullettand Board (1976)
Murray (1925)
Pringle and Barott (1937)
Tyler (1945)
Ar etal. (1974)
a
G values are expressed as flux per torr per egg. Literature values indicated with * were originally cited
per cm- of surface area, and were multiplied by 68 cm- to give the corresponding values in the table. Values
of GH 2 O indicated with t were calculated from weight loss data and APH 2 O obtained from experimental
conditions.
and Kutchai and Steen (1971) have done
for the chicken eggshell. In Table 2 the
conductance ratio Go2/GhyciI. varies between extremes of 1.32 x 10"1 and 1.50
X 10~3; the corresponding pore radii are
0.5 and 4.4 /im, respectively.
A possibly better approach to calculation
of pore size is based on counting pores under a dissecting microscope to determine
N, the number of pores in the shell. From
the assumption that Ap = NOT 2 , and from
calculated values of Ap (determined from
values of G and L [Equation 5]) and N, r
can be calculated. If one uses Ap = .023
cm2 (Wangensteen etal., 1970/71) and N =
Calculation of pore radius
7500 (Romanoff and Romanoff, 1949), r
The differences between diffusive and is about 10 /im in the chicken egg. Figure
convective flow of substances through 4 compares pore casts from chicken eggs
pores were first given quantitative expres- (Tyler, 1962) with calculated pores about
sion in the classical papers of Pappenheim- 10 fjurn in radius drawn to the same scale.
er et al. (1951) on capillary permeability, The narrower appearance of the calculatand of Koefoed-Johnsen and Ussing ed pores is probably the result of orifice
(1953) on water and solute flow through occlusion, according to the observations of
frog skin. Equation (9), which results from Board et al. (1977). In any case, since calcombining Equations (2) and (7) according culated pore size derives from measureto principles set forth by these authors, ment of G, the total cross-sectional area
may be used to calculate pore size from represented by the calculated pores is inmeasured diffusive and hydraulic gas con- deed the effective area available for gas difductances, as Wangensteen etal. (1970/71) fusion. For N = 7500, given uniform distribution, each pore would serve a circular
domain of about 1.1 mm in diameter in an
2
pore size. Because gas exchange in eggs is diffusive, egg whose surface area is 68 cm (Fig. 5).
it is inappropriate to use Ghvdr as a measure of the This is certainly an oversimplification but
shell's resistance under physiological conditions to the serves to point out that each pore must
Qualitatively, Equation (7) shows the
strong dependence of convection on the
actual pore radius, whereas diffusion depends only on the aggregate cross-sectional area offered by all pores. It makes no
difference within quite wide limits whether
diffusion takes place through few very
large pores or many smaller ones, provided that Ap remains the same. On the other
hand, convection is profoundly altered if
one changes from large pores to small ones
of the same total cross-sectional area because of the r4 dependence in Poiseuille's
law.
flows of respiratory gases.
334
CHARLES V. PAGANELLI
0
1.1 mm
100
200
300 L
Chicken Eggshell Pores
Colculated "Effective"
Pores
Fie. 4. Pore casts redrawn from Tyler (1962) (left)
compared with an idealized, trumpet-shaped pore in
cross-section whose orifice is partly occluded (center),
and with calculated effective pores (right). See text
for details.
serve as an O2 source or CO2 or H2O vapor
sink for a segment of the underlying chorioallantoic circulation if it is to function in
Fie. 5. Sketch of the domain served by a single pore
gas exchange.
in a hen's eggshell. The left-hand portion of the circle
PARTITIONING OF CONDUCTANCES IN THE
GAS TRANSFER PATH
Let us now consider briefly the conductance elements in the gas transfer path
which are interposed in series between atmospheric air and capillary blood in the
chorioallantois.
The boundary layer
The first element which must be dealt
with is the so-called boundary layer of
slowly moving or stagnant air which lies
immediately adjacent to the outer surface
of the shell. The effective thickness, and
thus resistance to diffusion of this boundary layer, decreases with the speed of convective air flow over the egg surface. At
any given convective flow, boundary layer
resistance is greater in large than in small
eggs, as Tracy and Sotherland (1979) predicted theoretically. Weinheimer and Spotila (1978) measured progressively larger
boundary layer resistances around eggs of
increasing size from 1 to 1500 g at several
wind speeds. However, both theoretical
and experimental studies showed that
boundary layer resistances in both large
and small eggs, even under conditions of
free convection (wind speed less than 10
shows underlying blood, vessels of the chorioallantois;
dark stippling represents the capillary network. See
text for details.
cm s l), are much less than shell resistance
to water vapor diffusion. Weinheimer and
Spotila's values of r b , the boundary layer
resistance for hen's eggs, were from about
1 to 3 s cm"1, whereas their shell resistances to water vapor diffusion were between 300 and 400 s cm"1. These resistances translate into boundary layer
conductances which lie between 1900 and
5700 mg day"1 torr"1 for a 68 cm2 egg, and
into shell conductances between 14 and 19
mg day^1 torr"1. Thus the boundary layer
plays no effective role in limiting gas exchange of eggs.
Preening oil and cuticle
In some species a thin layer of preening
oil is present on the surface of the cuticle
and may reduce shell conductance by approximately a factor of two to three, depending on temperature (Tullett and
Board, 1976). These authors provide evidence that the cuticle itself has negligible
resistance to gas diffusion; that is, cuticle
conductance is very high relative to that of
the shell.
335
GAS EXCHANGE ACROSS THE AVIAN EGGSHELL
Shell, shell membranes, and chorioallantoic
membrane
Outer barrier. The next elements in the
diffusion path are the shell and outer shell
membrane, which adheres closely to the
shell over its entire inner surface. In the
chicken egg the resistance of the outer
shell membrane to diffusion of all gases is
negligible compared with the shell (Wangensteen et al., 1970/71; Kutchai and
Steen, 1971; Tullett and Board, 1976; Paganelli et al., 1978) and is compatible with
completely gas-filled interstices between its
protein fibers. For purposes of this discussion the shell and outer shell membrane
will be treated as a unit whose conductance
is set by the pore structure of the shell itself. Piiper et al. (1980) have used the term
outer barrier to describe the combined resistance of shell and outer shell membrane
(Fig. 6). The outer barrier separates the
gas in the air cell from the environment.
The shell variables (Ap/L) and gas properties (D/3g) which combine to produce the
O2 conductance of the outer barrier in the
chicken egg are given in Table 3.
In practice, experimentally determined
values of Go2 and L and literature values
of Do2 and /?g are used to calculate Ap.
Wangensteen et al. (1970/71) used this
procedure to obtain Ap = 0.023 cm2 for
the chicken egg. Piiper et al. (1980) inde-
ig (outer)
4fb2(outer)
17.7
27
; G 0 (inner)
aPn (inner)
10.0
52
FIG. 6. The elements of the O2 conductance path
between the atmosphere and the chorioallantoic capillary blood in the 16-day-old chicken embryo. Go2
(outer) is the conductance of the shell and outer shell
membrane; its value is 17.7 ml day"1 torr~'. Go2 (inner) is the conductance of the composite barrier
formed by the inner shell membrane, chorioallantoic
epithelium, interstitial space, capillary endothelium,
plasma layer, and red blood cell; its value is 10.0 ml
day"1 torr~'. The two conductances in series yield a
total conductance of 6.4 ml day"' torr"1. APo2 (outer)
is 27 torr between ambient atmosphere and air cell
gas, and APo2 (inner) is 52 torr between air cell gas
and arterialized blood in the chorioallantoic vein
(Piiper et al., 1980).
pendently found Go2 (outer) to be 12 (i\
min"1 torr" 1 (17 ml day"1 torr"1) in 16-dayold chicken eggs, which agrees closely with
the value given in Table 3.
Inner barrier. T h e inner barrier (Piiper et
TABLE 3. Components of O2 conductance of the gas-transfer path in 16-day-old chicken eggs based on the conductance
values established by Wangensteen et al. (1970/71) and Piiper et al. (1980).
(i)
ml
day torr
<O<2><3>,4,
L
cm
(2)
D
(3)
P
(4)
Time
cm2 s-
torr'-
sec day"1
I/C
% of total
Resistance
a
Go2 (outer)
17.7
.023
.030"
2.3 x 10" ' e
1.16 x 10"3g
86,400
0.057
36
Go2 (inner)
10.0
68 x .5C
1.6 x 10"4"
2.3 x lO"5'
2.4 x 10 5"
86,400
0.10
64
0.157
100
G (total)
a
6.4
Calculated by Wangensteen et al. (1970/71).
"Shell thickness from Romanoff and Romanoff (1949).
Total chorioallantoic surface area of 68 cm2 (chosen equal to shell area) of which 50% is assumed available
for capillary exchange.
" Calculated effective thickness of composite barrier between air cell and capillary blood.
e
Diffusivity of O2 in air at 38°C (Paganelli et al., 1978).
' Diffusivity of O2 in mammalian alveolar-capillary membrane at 37°C (Grote, 1967).
g
Capacitance coefficient of a perfect gas at 38°C (Piiper et al., 1971).
h
Capacitance coefficient of mammalian alveolar-capillary membrane for O2 at 37°C (Grote, 1967).
c
336
CHARLES V. PAGANELLI
al., 1980), which separates air cell gas from
chorioallantoic capillary blood, is made up
of the inner shell membrane, chorioallantoic epithelium, capillary endothelium,
plasma, red cell membrane, and the kinetics of the Hb-O2 reaction. Evidence from
several sources indicates that the conductance of the inner shell membrane measured in vitro increases substantially with
incubation, a fact which has been attributed to dehydration of the membrane as
incubation progresses (Romanoff, 1943;
Romijn, 1950; Kutchai and Steen, 1971;
Lomholt, 1976; Tullett and Board, 1976).
This increase in conductance occurs during approximately the first third of incubation in those species which have been investigated, and thereafter remains
relatively constant.
Piiper et al. (1980) and Tazawa (1980)
have discussed the conductance of the inner barrier and the elements which contribute to it in detail. Piiper et al. (1980)
attribute 50 of the 52 torr APo2 which in
the 16-day chicken embryo exists between
air cell gas and arterialized blood in the
chorioallantoic vein to an effective or physiological shunt which allows deoxygenated
blood from the arterial circulation to mix
with arterialized blood in the chorioallantoic vein, thus lowering its Po2. When this
shunt is taken into account, their experiments yield a value of 7 /xl min"1 torr"1 (10
ml day"1 torr"1) for the O2 conductance of
the inner barrier (Table 3 and Fig. 6). This
value of Go2 (inner) together with the
physical constants and assumptions given
in Table 3 enable calculation of an effective thickness of 1.6 /u,m for a "tissue" layer
which would have the same resistance to
diffusion as the inner barrier. Such a calculation of course ignores the heterogeneity of the inner barrier. Tazawa (1980)
advances reasons for suspecting that the
combined epi- and endothelial layers (the
chorioendothelium) contribute the major
part of the inner barrier's resistance to O2
diffusion but states that certain identification of the resistance elements is not yet
possible. Further information, perhaps
from quantitative electron microscopic
studies, is necessary to resolve this matter.
TERNARY DIFFUSION
Analysis of gas exchange across the avian eggshell is commonly based on the principles of binary diffusion, in which one gas
diffuses through a second. This is appropriate for diffusion of a gas in air, which
behaves as a binary system because the diffusive properties of O2 and N2 are nearly
the same. However, when the N2 in air is
replaced by a lighter gas such as He or a
heavier gas such as SF6, diffusion of a
third gas (CO2, for example) in He-O2 or
SFti-O2 must be treated as a ternary process. Chang et al. (1975) have provided a
theoretical description of ternary diffusion, and Worth and Piiper (1978) published experimental data from in vitro diffusion experiments using He, CO, and SF6
in mixtures similar to human alveolar gas.
Theory and experiments both show that in
a ternary system the flux of one gas is coupled to the fluxes of the other two components in the system. Further, the diffusivity varies with fractional concentrations
of the components of the gas mixture in
which diffusion takes place. (This situation
contrasts with binary diffusion, in which a
single diffusion coefficient which is relatively independent of the fractional concentrations of the gas species involved
characterizes the diffusion process.)
The experiments of Erasmus and Rahn
(1976) and Paganelli et al. (1979) have
demonstrated the applicability of ternary
diffusion concepts to gas exchange in
chicken eggs placed in He-O2 and SF6-O2
atmospheres. The relative ease of measurement of gas fluxes and their associated
partial pressure differences across the
shell of incubating eggs makes them a
valuable model in which to test the predictions of the laws of binary and ternary diffusion in living systems.
AIR CELL HYDROSTATIC PRESSURE
Recently Ar, Paganelli, and Rahn (unpublished results) measured a positive hydrostatic pressure of about 2 mm H2O between the air cell of incubating chicken
eggs and their surroundings, confirming
an earlier result of Romijn and Roos
GAS EXCHANGE ACROSS THE AVIAN EGGSHELL
(1938). The hydrostatic pressure varied
systematically with metabolic rate, degree
of saturation of the surrounding atmosphere with water vapor, and diffusivity of
the gas mixture in which incubation took
place. It seems probable that this hydrostatic pressure arises from coupling between diffusion and convective flow in the
pores of the eggshell. Quantitation of the
contribution of the hydrostatic pressure to
overall gas exchange of the egg awaits further experiment and analysis.
337
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ACKNOWLEDGMENTS
Data originating from this Department
were obtained in part with the support of
USPHS Grants P01-HL-14414 and R01HL-18022, and NSF Grant PCM-76-20947.
I should like to express sincere thanks to
Drs. Hermann Rahn and Amos Ar for critical discussion of many of the concepts
which appear in the manuscript.
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