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Diffusion of water vapor in binary and ternary gas mixtures at increased pressures
Respiration Physiology (1977) 30, 15-26 @ Elsevier/North-Holland Biomedical Press
DIFFUSION
Department Department
OF WATER VAPOR IN BINARY AND TERNARY MIXTURES AT INCREASED PRESSURES’~ ’
CHARLES
V. PAGANELL13
of Physiology,
School
of Physiology,
State
Abstract. Diffusion water vapor-N,
of water
system water vapor-He-O, comparison
vapor
at approximately
of binary agreement
dicted at pressures from theory 0,
University
of Hawaii,
of New York at Buffalo,
was measured
Honolulu, Buffalo.
at 25 C in the bina
Hawaii 96822, and N. Y. 14214, U.S.A.
systems
water
was also measured
vapor-He
and
in the ternary
in both 2 “/LO,-98%
He and 26% O,-74% He, and at 1 and 20 atm. At 1 atm, (a) shows that water vapor diffuses 3.3 times more readily
coefficients
at elevated pressures
with Chapman-Enskog
were reduced in proportion theory.
above 4 atm in water vapor-N,
are more pronounced
is present
Medicine,
and FRED K. KURATA
1, 4, 10, 20 and 50 atm. Diffusion
diffusion
in He than in N,. Values of9 in qualitative
of
University
GAS
in the ternary
However.
water
60”; of its rate in pure He. In contrast,
vapor-He-O,,
2% 0,
effect on gaseous
Ternary
diffusion
diffusion
The deviations
larger at higher pressures. of water
vapor
in He has little effect on diffusion
Binary diffusion Pressure
diffusion
pressure,
in 9 was less than pre-
and above 20 atm in water vapor-He.
in N, than in He, and become
system
to I/P, theabsolute
the reduction
When 267;
is reduced
to about
of water vapor.
Water vapor diffusion
in He
Water vapor diffusion
in He-O,
Water vapor diffusion
in N,
Six years ago Rahn and his colleagues published the first in a series of investigations dealing with the respiratory gas exchange of the avian egg (Wangensteen et al., 1970/71). Although it had been realized for many years that pores in the eggshell
Acceptedfor
publication
10 January 1977.
’ These studies were aided by NOAA Sea Grant 04-3-158-29 5 PO1 HL 14414 to State University 2 Presented July 1975.
at an International
3 This work was done during is: Department
of Physiology,
to University
of Hawaii,
and by NIH Grant
of New York at Buffalo.
Symposium Dr. Paganelli’s
on Man in the Sea sponsored sabbatical
State University
leave at University
of New York at Buffalo,
This paper appears in an issue dedicated to Hermann
Ruhn 15
by University of Hawaii. Buffalo,
of Hawaii
in
His present address N.Y.
14214, U.S.A.
16
C. V. PAGANELLI AND F. K. KURATA
formed the path through which such exchange took place, their work firmly established for the first time the diffusive nature of the exchange and characterized the shell by a diffusive permeability constant or conductance. Subsequent studies have explored both the importance of the eggshell as a barrier to diffusion in the respiration of the embryonic bird (Rahn and Ar, 1974; Rahn et al., 1974), and the use of the eggshell as a convenient model system to study diffusion in the gas phase (Paganelli et al., 1975). In the last-mentioned study, the authors called attention to deviations between changes observed in diffusive water vapor loss through eggshells with changing ambient pressure, and predictions based on the Chapman-Enskog theory. According to this theory, binary diffusivity is inversely proportional to ambient pressure and also varies with the molecular species of the gases in the diffusion path (Reid and Sherwood, 1966). The relation between water loss and pressure in the study of Paganelli et al. (1975) followed theory below 1 ATA but deviated significantly in the direction of larger-than-expected water losses at pressures above 1 ATA. However, the Chapman-Enskog equation assumes among other things ideal gas behavior, and yields calculated diffusion coellicients which are consistently low in binary systems containing water vapor (Reid and Sherwood, 1966). Further, there is a paucity of experimental data on the effect of pressure on diffusion coefficients in gas systems of biological interest against which to compare the predictions of the theory. Our goal in the present study was to provide such data over the range of l-50 ATA in both H,O-He and H,O-N, mixtures as a measure of the applicability of ChapmanEnskog theory. Since water vapor usually occurs in ternary or even quaternary systems in nature, we also investigated the effect on diffusion of introducing a third gas, O,, into an H,O-He system.
PRINCIPLE OF MEASUREMENT
We adapted the method of Schwertz and Brow (1951) to the study of water vapor diffusion at elevated ambient pressure. They measured the rate of evaporation of water from a capillary tube into a second gas whose water vapor pressure was kept at 0. The water vapor pressure (PHZo)at the gas-water interface in the capillary tube is the saturation vapor pressure at the temperature of the experiment (25 “C), while at the mouth of the capillary PH20 = 0, as shown in fig. 1. Thus water vapor diffuses steadily down its gradient and out of the capillary tube, and the level of liquid water in the tube falls. From the rate at which the water level falls, one may calculate 9, the binary diffusion coefficient of water vapor in the second gas. The equation governing this case of one-dimensional diffusion with a moving boundary is:
where c = concentration
of water vapor; x = distance along the axis of the capillary,
BINARY AND TERNARY GAS DIFEWSION
17
c
Dry Gas Stream
0% H,O-, Saturation
M 2mm
Fig. 1. Schematic drawing of capillary diffusion tube.
positive direction downward; v = rate of displacement of the gas-liquid interface; t = time. The solution of eq. (l), with the assumptions involved, are presented in detail by Schwertz and Brow (1951), who give the following expression for the binary diffusion coefficient derived from the solution of eq. (1): g
@‘-hi) . ._ d, . _Ps. = ___-_ 2(t-t,)
d,
P
1 ln(P/(P-Ps))
(2)
where h, h, = heights of the water vapor-gas column at times t and t,, respectively, (cm); d, = density of water at experimental temperature, (g . cmm3); d, = density of saturated water vapor at experimental temperature, (g . cm- 3); P, = saturation vapor pressure of water at experimental temperature (tori-); P = total gas pressure (torr). In practice, one measures h, the height of the water vapor-gas column at increasing times t, and plots (h2 - hi) us (t-to), where ho and t, are the initial values of h and t. $Z?is then calculated from the slope of the line, together with known values of the constants in eq. (2) and a measured value of P. Constants used were : d, = 0.9970 g cmW3, d, = 2.304x 10e5 g ’ cm - 3; P, = 23.73 torr, all at 25 “C. Materials and methods Diffusion tubes The glass capillaries used as diffusion tubes were straight-bore 200~~1 capillary pipettes, 70-80 mm in length and 2 mm inner diameter. Unifo~ity of bore was checked by mercury weighings and was found to vary by no more than 0.7 7; from point to point along the capillaries. Capillaries were cleaned in reagent-grade acetone, concentrated HNO, and distilled water, and were filled with freshly boiled distilled water immediately prior to an experiment. High pressure chamber Three capillaries were mounted parallel to each other about 1 cm apart near the
18
C. V. PAGANELLI
AND F. K. KURATA
Lu Win
Fig. 2. Diagram
of high-pressure
chamber
with a capillary
(not to scale).
front of a high-pressure chamber, shown schematically in fig. 2. The chamber was constructed of ASTM schedule 160 steel pipe, with a 2.5-cm thick plexiglass viewing port, 7.6 cm in diameter. Its maximal working pressure was 50 ATA. The chamber was equipped with a light source, an induction-motor fan to provide stirring, a tray containing indicating silica gel to keep PuZo in the chamber at 0, and a calibrated thermistor for measuring chamber temperature (YSI # 427 thermistor and model 46 TUC telethermometer, Yellow Springs Instrument Co., Yellow Springs, Ohio). Pressure within the chamber was measured with a direct-drive Bourdon-tube gauge, calibrated to an accuracy of 0.25 o/o of full scale or about 0.17 atm, according to manufacturer’s specifications (Roylyn Precision Direct Drive Gauge, 3-D Instruments, Inc., Anaheim, CA).
Cathetometer
Measurements of h, the length of the water vapor-gas column, were performed using a cathetometer readable to 0.001 cm (Precision Tool and Instrument Co., Ltd., Surrey, England). Eleven replicate determinations of distance between the top of a capillary tube and the water meniscus yielded a standard deviation of kO.0013 cm. This degree of precision is made necessary by the slow rate of water evaporation from the capillaries and hence the small differences between positions of the meniscus in time. In experiments conducted at 50 ATA of N,, for example, h changed by less than 0.03 cm in the course of 6 days.
Gases
Commercially available He and N, of high purity grade were used. Manufacturer’s specifications list high-purity He as 99.995 % He and high-purity N, as 99.99 % N,. He-O, mixtures were prepared from high-purity He and 99.6 % 0, in the laboratory and analyzed either with a Beckman OM-11 oxygen analyzer (Beckman Instruments, Inc., Fullerton, CA) or with a Quintron model R gas chromatograph (Quintron Instrument Co., Inc., Milwaukee, WI).
BINARY AND TERNARY GAS DIFFUSION
19
Temperature
The pressure chamber was placed in a constant-temperature cabinet (model 1247 LA, Hotpack Corp., Philadelphia, PA) which was capable of maintaining a set temperature to about +0.2”C. The temperature within the high-pressure chamber itself showed even smaller fluctuations, of the order of kO.02 “C, because of its large thermal mass. Temperatures were measured with YSI thermistors calibrated against precision mercury thermometers with 0.05 “C scale divisions. As Schwertz and Brow (195 1) pointed out, evaporation may cool the gas-water interface significantly below the ambient temperature in the high-pressure chamber if it proceeds too fast, and thus may lead to erroneously low values of 9. Evaporation is accelerated as the liquid level is brought closer to the open end of the capillary. In the present experiments, the liquid level was kept at least 6 cm below the open end of the capillaries for all experiments conducted at 1 ATA, where evaporation is most rapid. During an experiment in which water vapor diffused into He, the actual temperature difference between the gas-water interface and the bulk water phase was measured with a copper-constantan thermocouple made of 0.13 mm wire, a size small enough not to occupy a significant fraction of the cross-sectional area of the capillary. The voltage output of the thermocouple was measured with a Hewlett-Packard model 419A null microvoltmeter; the temperature difference recorded in this fashion was less than 0.01 “C. Sources of error
One possible source of error lies in the assumption that diffusion of water vapor out of the capillary is the rate-limiting process, i.e. that removal of water vapor from the mouth of the capillary by convection is sufficiently rapid to maintain PH20 = 0 at this point. Schwertz and Brow (195 1) checked this assumption by measuring diffusion coefficients at several volumetric flow rates in their apparatus from 50-300 cm3 . min- ’ and found no influence of flow in this range. In the present experiments, convective mixing was produced routinely within the high-pressure chamber by a small fan which caused a linear flow velocity near the tops of the capillaries of 100 cm. set-’ at 1 ATA. The binary diffusion coefficient of water vapor-helium was measured under this type of convective mixing and also with a 500 cm3 . min-’ flow of helium from a pressure cylinder directed at the tops of the capillaries. The two experiments gave values of 9 which agreed within 3.8 “/o. Possible errors in cathetometer readings caused by thermal expansion or contraction of water attendant on temperature fluctuations of the order of those which occurred during diffusion experiments were calculated and found to be negligible. Similarly, although some vapor pressure lowering is to be expected as He or N, under high pressure dissolve in water, the fractional lowering of water vapor pressure caused by dissolution of N, at 50 ATA, for example, is less than 0.1 %. Pressure per se increases water vapor pressure at a given temperature, but again, the effect is slight. For example, it may be calculated that the equilibrium vapor pressure of water is increased at 50 ATA by about 3 y0 over its 1 ATA value (Tabor, 1969).
20
C. V. PAGANELLI
AND F. K. KURATA
Another potential source of error arises from mechanical vibrations of the building and the constant-temperature cabinet in which the high pressure chamber was located. Such vibrations are capable of causing convection currents in the capillary tube, thus vitiating any attempt to measure diffusion. To prevent transmission of vibration, the high pressure chamber was placed on 2 sets of rubber isolation pads : one set between the wooden cradle which supported the chamber and the chamber itself, and the second set between the base of the cradle and the floor of the constanttemperature cabinet. The chamber weight, approximately 150 kg, was also an important factor in damping vibration. The good agreement between results obtained in our system and the literature values reported in table 1 indicate that the above factors were sufficient to prevent vibration and attendant convection currents from significantly biasing our results.
Results Diffusion measurements were made at 25 “C on the binary systems H,O-He and H,O-N, at approximately 1,4, 10, 20, and 50 ATA. (The symbol H,O is used here to mean water vapor.) A few control measurements of 9 were initially made at 34°C and 1 ATA in H,O-He to provide a direct comparison with the results of Schwertz and Brow (1951) at the same temperature and pressure. There was good agreement between the values obtained in the present experiments and those reported by both Schwertz and Brow (195 1) and Lee and Wilke (1954), as shown in table 1. Diffusion of water vapor in the ternary system H,O-He-O, was also measured in gas mixtures of 1.6 ‘4 O,-98.4 y0 He and 26 y0 O,-74 % He. Data were obtained in the form of values of h us t, and for binary systems were plotted as (h* -hi) us (t-to) for each of 3 diffusion tubes at each pressure and gas combination. Linear least-squares regression analysis was performed on the data from each capillary, and the three slopes so obtained were averaged before calculation of 9 by eq. (2). The data fall very closely on each regression line, as shown in fig. 3, a representative plot for H,O-N, at 1 ATA. Correlation coefficients were never less than 0.997 and averaged 0.999 over all experiments. A plot of (h* - hi) us (t-to) for H,O-He at pressures TABLE Comparison 3 (cm’
H,O-He H20-He H+N,
1
of results at
set- I)
1 ATA Reference
Literature
Present experiments
values
0.836 (25 C)
0.908 (25 C)
Lee and Wilke (1954)
0.860 (34 C) 0.253 (25 C)
0.902 (34 C)
Schwertz
and Brow (1951)
0.256 (34 C)
Schwertz
and Brow
( 195 I )
21
BINARY AND TERNARY GAS DIFFUSION
1 6
At, lo3 minutes Fig. 3. (h’ -hi)
in cm* vs elapsed
time dt in units of lo3 min. Water
and 25 ‘C. Each symbol
represents
a separate
vapor
diffusion
into N, at 1 ATA
capillary.
of 1,4, 10,20, and 50 ATA is shown in fig. 4. The reduction in slope with increasing pressure is immediately evident. Binary diffusion coeffkients as functions of pressure in both H,O-He and H,O-N, are given in table 2. The diffusion coefficients listed at 1 ATA in table 2 were actually obtained at prevailing atmospheric pressure (PEs), which deviated from 760 by 4-5 torr at most over several months; these diffusion coeffkients were then corrected to 1 ATA by multiplying by F’n/760. Estimates of the standard deviation in 9 in table 2 were obtained by combining standard deviations from the linear regression analysis for the 3 individual slopes in each experiment, according to rules for propagation of error (Beers, 1953).
H20-He,
0
Fig. 4. (h2pressures.
4
hg) in cm2 oselapsed The lines are drawn
12 8 At, lo3 minutes
16
25°C
_
20
time dt in units of lo3 min. Water vapor diffusion into Heat the indicated from linear least squares analysis; the points are experimental values.
22
C. V. PAGANELLI
AND F. K. KURATA
TABLE Binary diffusion Gas system
9
H,O-N,
’ f “, SD)
= ratio of binary
(“” SD values calculated
&?J&@
Deviation from theory
(ATA)
0.836
+0.2””
1.oo
1.00
0.209
kO.8:‘”
4.06
4.00
I .5 “”
9.85
_
0.0849
k
0.0444
k2.0””
20.12
18.8
+7””
9.85 44.5
+13”; _
0.0188
kO.9””
50.88
0.253
kO.4””
1.00
1.00
0.0672
rf- 1.5””
4.10
3.76
0.0297
kO.8 “”
9.84
8.52
0.0159
k1.3””
0.00749 k2.6 “,” 9,/p
at 25 C
Pressure set-
(cm’ H,O-He
2
coefftcients
diffusion
coefftcient
as described
at
+8”;, + 13””
20.05
15.9
+ 21 “”
51.01
33.8
+ 34””
1 ATA to that at experimental
pressure.
in the text)
The fourth column in table 2 gives the ratio of gO, the value of 9 at 1 ATA, to 3 at the experimental pressure. According to the Chapman-Enskog theory this ratio at moderate pressures should be equal to P/P,, or simply to P, since PO = 1 ATA. Figure 5 is a graph of go/a us P. Experimental data are plotted as points, and the line of identity is drawn. It is clear that gn,/a deviates from the Chapman-Enskog theory above 4 ATA for H,O-N,, and above 20 ATA for H,O-He; the deviations are more pronounced in N, than in He, and become larger at the higher pressures. At 50 ATA, &20,He is 13 ‘4 larger than expected (0.0188 cm2 . set-’ by actual measurement us 0.836/50.88 or 0.0164 cm’ . set-’ predicted); Sn20,NZ is 34% larger (0.00749 cm2 . set- ’ measured us 0.253/51.01 or 0.00496 cm2 . see-’ predicted).
. . 30
///
40 20 ! /
lo 0
Fig. 5. 90/p,
p 10
.
I 20
H,O-He A H,O-N,
l
I I 30 40 P, ATA
1 50
I 60
ratio of binary diffusion coefftcient at I ATA to that at experimental Points are experimental values; line of identity has been drawn.
pressure
P. 1’s P.
BINARY
AND TERNARY
23
GAS DIFFUSION
These deviations are shown in the last column of table 2. Comparison of the He and N, data at the same pressure shows that water vapor diffuses 2.5-3.3 times more readily through He than through N,, depending on the pressure. In the ternary system H,O-He-O,, flux of water vapor out of the capillary tube was used to characterize the diffusion process. For ternary systems h was plotted directly against t, as shown in fig. 6. Good straight-line fits to the experimental data were obtained by linear regression analysis, and dh/dt, the slope of the line, was determined. Correlation coefficients averaged 0.999 over all experiments. To a close approximation, dh/dt is a direct measure of the water vapor flux out of the tube per unit cross-sectional area. Because part of the liquid water which evaporates remains behind in the tube, dh/dt does not measure the flux directly. However, the amount of water vapor remaining behind is several orders of magnitude less than the quantity which evaporates, and can be neglected in the present analysis. Table 3 lists ternary fluxes computed as described above, with values of the corresponding binary fluxes in water vapor-He and ternary/binary flux ratios given for comparison. When 0, is present at a concentration of 26% by volume, water vapor flux is reduced in the ternary system to between 60 and 70 y0 of its value in pure helium, depending on the pressure. At 1.6 % 0, by volume there is very little effect on the water vapor fluxes. Standard deviations of the fluxes were calculated in the same fashion as described for the diffusion coefficients. TABLE Water vapor fluxes at 25 ‘C for the ternary
and for the binary Gas system
3
system HZOpHe-0,
Pressure
Water vapor
(ATA)
((g
set-
flux
1 cm -‘).
ternary H,O
H,O
in 74% He-26”;
m 98.4;,,
0,
He-1.67;
0,
* Binary
fluxes were derived
(“,‘,by volume),
lo6 +?“SD)
Ternary flux -__ Binary flux*
Ds (cm’
1.86k1.7”;
2.99kO.55;
0.62
0.52
0.49+2.19;
0.79 k 2.4:;
0.62
0.14
20
0.19*1.0:;
0.28 k 2.1 y0
0.68
0.031
2.99+0.5;,
0.98
0.80
0.96
0.042
1
2.94+
as described
1.2:‘,
0.27 k 1.4’6
as described
set- ‘)
binary*
1
as the corresponding
. (7; SD values calculated
compositions
4
20
at the same pressure
at indicated
system H,O-He
0.28k2.1
O0
in the text from plots of h us t for the binary ternary
system H,O-He
flux.
in the text)
Although it is not in general possible to assign a single diffusion coefficient to a system involving 3 gases (Chang et al., 1975), we used plots of (h2 -hi) us (t-to), which were linear in our ternary systems, to calculate effective diffusion coefficients (DE) (Erasmus and Rahn, 1976) for water vapor in the two He-O, mixtures at 1 ATA and at elevated pressures. Values of D, are given in the last column of table 3. Calculation of D, in this manner ignores in effect the influence of the 0, and He gradients
24
C. V. PAGANELLI
AND F. K. KURATA
on the water vapor flux. D, values may be used to calculate approximate diffusive water vapor flux in He-O, systems where diffusion geometry and water vapor pressure gradient are known, provided the composition of the system resembles those used in the present experiments. Since ternary diffusion depends explicitly on the relative composition of the three components in the system, DE’s obtained in a particular ternary mixture should not generally be used to calculate diffusive flows in another mixture of the same gases with a different fractional composition.
Discussion Deviations of binary diffusivity from l/P dependence at high pressure are not unique to systems containing water vapor. Durbin and Kobayashi (1962) have shown a similar phenomenon in the pressure dependence of 85Kr diffusion in krypton, argon, nitrogen, helium, and carbon dioxide. Their deviations are reported in the form of increasing values of the product (gas diffusivity x density) with increasing pressure and thus are in the same direction as those noted in the present study, though smaller in magnitude for comparable pressure changes. It is apparent that the simple inverse relation between $33and P for systems containing water vapor begins to break down at quite modest pressures, and at 50 ATA, a pressure already achieved in saturation diving, for example, can be seriously in error, at least for N,-containing gas mixtures. It should be pointed out that studies of water vapor diffusion at elevated pressures have implications for physiological processes such as insensible water loss and pulmonary gas exchange in human subjects living in hyperbaric environments, as in saturation diving. Hong et al. (1976), among others, have in fact reported reduction in insensible water loss in men exposed to 18 ATA helium-oxygen mixtures.
I
Water 3.75
Vapor
at 25”C,
-
3.60’
’
’
2
’
20 ATA
’
4
’ At,
’
’
lo3
mmutes
6
’
8
Fig. 6. h in cm USelapsed time dt in units of IO3 min for binary (He-O,
in a 74%‘263/,
mixture)
I
Diffusion
’
’
10
a
diffusion
(pure He) and ternary
of water vapor at 20 ATA. The lines are drawn
analysis;
the points are experimental
values.
diffusion
from linear least squares
RINARY
AND TERNARY
25
GAS DIFFUSION
Our data on reduction in guzO, N2with pressure also provide a qualitative explanation for the findings of Paganelli et al. (1975) on pressure-induced changes in water loss from eggs, which was mentioned previously. Those findings also showed the reduction in water loss rate with pressure to be less than expected on the basis of the Chapman-Enskog theory for dilute gases. The deviations from the Chapman-Enskog theory for dilute gases observed in the present experiments are not surprising in view of the assumptions on which the theory rests: that the diffusing molecules are monatomic, spherically symmetrical, and nonpolar, and undergo only binary, elastic collisions (Hirschfelder et al., 1954). In approaching problems involving diffusion of real gases at pressure, it would seem best to rely on measured values of diffusion coefficients wherever possible. Our measurements of water flux in the ternary system H,O-He-O, showed several features of interest. Introduction of 26% 0, by volume into a water vapor-He system reduced the water vapor flux by nearly 40 % at 1 and 4 ATA, and by slightly less at 20 ATA. When the 0, was reduced to 1.6 %, on the other hand, its effect on water vapor fluxes was negligible both at 1 and at 20 ATA. From our limited data, reduction of fluxes with pressure in a ternary system of given composition is seen to follow an approximate dependence on l/P. However, the reductions are substantially less than predicted at 20 ATA. We have obtained results at only two 0, concentrations; the exact nature of the dependence of water vapor flux on 0, concentration in a ternary system awaits further investigation.
Acknowledgements
The authors would like to thank Dr. Suk Ki Hong for his generous support and encouragement during this study. We also express our appreciation to Messrs. Toby Clairmont, Benjamin Respicio, and Edwin Hayashi for their excellent technical assistance.
References Beers, Y. (1953). Introduction to the Theory of Error. Reading. Chang, H.-K., R. C. Tai and L. E. Farhi (1975). Some implications Physiol. Durbin,
23
: 109-l 20.
L. and R. Kobayashi
(1962). Diffusion
of krypton-85
Erasmus, B. Dew. and H. Rahn (1976). Effects of ambient in the avian egg. Respir. Physiol. 27: 53-64. Hirschfelder,
J. O., C. F. Curtiss
New York, Hong.
MA, Addison-Wesley Press. of ternary diffusion in the lung. Respir.
in dense gases. J. Chem. Phys. 37 : 16431654.
pressures,
He and SF, on 0, and CO, transport
and R. B. Bird (1954). The Molecular
Theory
of Gases and Liquids,
John Wiley and Sons.
S. K.. J. R. Claybaugh,
C. V. Paganelli.
V. Frattali,
R. Johnson,
R. M. Smith and P. Webb
F. Kurata.
(1976). Hana
M. Matsuda.
Kai II: A l7-day
A. A. McDonough, dry saturation
dive at
18.6 ATA. 111. Body fluid balance. Undersea Biomed. Res. (accepted for publication). Lee. C. Y. and C. R. Wilke (1954). Measurements of vapor diffusion coefficient. Ind. Eny. Chem. 46: 2381-2387.
26
C. V. PAGANELLI
Paganelli,
C. V., A. Ar, H. Rahn and 0. D. Wangensteen
ambient Rahn,
AND F. K. KURATA
pressure
and gas composition.
H. and A. Ar (1974). The avian egg: incubation
Rahn, H., C. V. Paganelli
(1975). Diffusion
in the gas phase
: the effects of
Respir. Physiol. 25: 247-258. time and water loss. Condor 76: 147-152.
and A. Ar (1974). The avian egg : air-cell gas tension, metabolism.
and incubation
time. Respir. Physiol. 22: 297-309. Reid, R. C. and T. K. Sherwood Schwertz,
(1966). Properties
F. A. and J. E. Brow (1951). Diffusivity
ofGases
and Liquids,
2nd ed. New York, McGraw-Hill.
of water vapor in some common
gases. J. Chem. Phys.
19: 640446. Tabor,
D. (1969). Gases,
Wangensteen,
Liquids.
and Solids. Baltimore,
0. D., D. Wilson and H. Rahn
egg. Respir. Physiol. I1
: 1630.
(1970/71).
MD, Penguin Diffusion
Books,
Inc.
of gases across
the shell of the hen’s
DIFFUSION
Department Department
OF WATER VAPOR IN BINARY AND TERNARY MIXTURES AT INCREASED PRESSURES’~ ’
CHARLES
V. PAGANELL13
of Physiology,
School
of Physiology,
State
Abstract. Diffusion water vapor-N,
of water
system water vapor-He-O, comparison
vapor
at approximately
of binary agreement
dicted at pressures from theory 0,
University
of Hawaii,
of New York at Buffalo,
was measured
Honolulu, Buffalo.
at 25 C in the bina
Hawaii 96822, and N. Y. 14214, U.S.A.
systems
water
was also measured
vapor-He
and
in the ternary
in both 2 “/LO,-98%
He and 26% O,-74% He, and at 1 and 20 atm. At 1 atm, (a) shows that water vapor diffuses 3.3 times more readily
coefficients
at elevated pressures
with Chapman-Enskog
were reduced in proportion theory.
above 4 atm in water vapor-N,
are more pronounced
is present
Medicine,
and FRED K. KURATA
1, 4, 10, 20 and 50 atm. Diffusion
diffusion
in He than in N,. Values of9 in qualitative
of
University
GAS
in the ternary
However.
water
60”; of its rate in pure He. In contrast,
vapor-He-O,,
2% 0,
effect on gaseous
Ternary
diffusion
diffusion
The deviations
larger at higher pressures. of water
vapor
in He has little effect on diffusion
Binary diffusion Pressure
diffusion
pressure,
in 9 was less than pre-
and above 20 atm in water vapor-He.
in N, than in He, and become
system
to I/P, theabsolute
the reduction
When 267;
is reduced
to about
of water vapor.
Water vapor diffusion
in He
Water vapor diffusion
in He-O,
Water vapor diffusion
in N,
Six years ago Rahn and his colleagues published the first in a series of investigations dealing with the respiratory gas exchange of the avian egg (Wangensteen et al., 1970/71). Although it had been realized for many years that pores in the eggshell
Acceptedfor
publication
10 January 1977.
’ These studies were aided by NOAA Sea Grant 04-3-158-29 5 PO1 HL 14414 to State University 2 Presented July 1975.
at an International
3 This work was done during is: Department
of Physiology,
to University
of Hawaii,
and by NIH Grant
of New York at Buffalo.
Symposium Dr. Paganelli’s
on Man in the Sea sponsored sabbatical
State University
leave at University
of New York at Buffalo,
This paper appears in an issue dedicated to Hermann
Ruhn 15
by University of Hawaii. Buffalo,
of Hawaii
in
His present address N.Y.
14214, U.S.A.
16
C. V. PAGANELLI AND F. K. KURATA
formed the path through which such exchange took place, their work firmly established for the first time the diffusive nature of the exchange and characterized the shell by a diffusive permeability constant or conductance. Subsequent studies have explored both the importance of the eggshell as a barrier to diffusion in the respiration of the embryonic bird (Rahn and Ar, 1974; Rahn et al., 1974), and the use of the eggshell as a convenient model system to study diffusion in the gas phase (Paganelli et al., 1975). In the last-mentioned study, the authors called attention to deviations between changes observed in diffusive water vapor loss through eggshells with changing ambient pressure, and predictions based on the Chapman-Enskog theory. According to this theory, binary diffusivity is inversely proportional to ambient pressure and also varies with the molecular species of the gases in the diffusion path (Reid and Sherwood, 1966). The relation between water loss and pressure in the study of Paganelli et al. (1975) followed theory below 1 ATA but deviated significantly in the direction of larger-than-expected water losses at pressures above 1 ATA. However, the Chapman-Enskog equation assumes among other things ideal gas behavior, and yields calculated diffusion coellicients which are consistently low in binary systems containing water vapor (Reid and Sherwood, 1966). Further, there is a paucity of experimental data on the effect of pressure on diffusion coefficients in gas systems of biological interest against which to compare the predictions of the theory. Our goal in the present study was to provide such data over the range of l-50 ATA in both H,O-He and H,O-N, mixtures as a measure of the applicability of ChapmanEnskog theory. Since water vapor usually occurs in ternary or even quaternary systems in nature, we also investigated the effect on diffusion of introducing a third gas, O,, into an H,O-He system.
PRINCIPLE OF MEASUREMENT
We adapted the method of Schwertz and Brow (1951) to the study of water vapor diffusion at elevated ambient pressure. They measured the rate of evaporation of water from a capillary tube into a second gas whose water vapor pressure was kept at 0. The water vapor pressure (PHZo)at the gas-water interface in the capillary tube is the saturation vapor pressure at the temperature of the experiment (25 “C), while at the mouth of the capillary PH20 = 0, as shown in fig. 1. Thus water vapor diffuses steadily down its gradient and out of the capillary tube, and the level of liquid water in the tube falls. From the rate at which the water level falls, one may calculate 9, the binary diffusion coefficient of water vapor in the second gas. The equation governing this case of one-dimensional diffusion with a moving boundary is:
where c = concentration
of water vapor; x = distance along the axis of the capillary,
BINARY AND TERNARY GAS DIFEWSION
17
c
Dry Gas Stream
0% H,O-, Saturation
M 2mm
Fig. 1. Schematic drawing of capillary diffusion tube.
positive direction downward; v = rate of displacement of the gas-liquid interface; t = time. The solution of eq. (l), with the assumptions involved, are presented in detail by Schwertz and Brow (1951), who give the following expression for the binary diffusion coefficient derived from the solution of eq. (1): g
@‘-hi) . ._ d, . _Ps. = ___-_ 2(t-t,)
d,
P
1 ln(P/(P-Ps))
(2)
where h, h, = heights of the water vapor-gas column at times t and t,, respectively, (cm); d, = density of water at experimental temperature, (g . cmm3); d, = density of saturated water vapor at experimental temperature, (g . cm- 3); P, = saturation vapor pressure of water at experimental temperature (tori-); P = total gas pressure (torr). In practice, one measures h, the height of the water vapor-gas column at increasing times t, and plots (h2 - hi) us (t-to), where ho and t, are the initial values of h and t. $Z?is then calculated from the slope of the line, together with known values of the constants in eq. (2) and a measured value of P. Constants used were : d, = 0.9970 g cmW3, d, = 2.304x 10e5 g ’ cm - 3; P, = 23.73 torr, all at 25 “C. Materials and methods Diffusion tubes The glass capillaries used as diffusion tubes were straight-bore 200~~1 capillary pipettes, 70-80 mm in length and 2 mm inner diameter. Unifo~ity of bore was checked by mercury weighings and was found to vary by no more than 0.7 7; from point to point along the capillaries. Capillaries were cleaned in reagent-grade acetone, concentrated HNO, and distilled water, and were filled with freshly boiled distilled water immediately prior to an experiment. High pressure chamber Three capillaries were mounted parallel to each other about 1 cm apart near the
18
C. V. PAGANELLI
AND F. K. KURATA
Lu Win
Fig. 2. Diagram
of high-pressure
chamber
with a capillary
(not to scale).
front of a high-pressure chamber, shown schematically in fig. 2. The chamber was constructed of ASTM schedule 160 steel pipe, with a 2.5-cm thick plexiglass viewing port, 7.6 cm in diameter. Its maximal working pressure was 50 ATA. The chamber was equipped with a light source, an induction-motor fan to provide stirring, a tray containing indicating silica gel to keep PuZo in the chamber at 0, and a calibrated thermistor for measuring chamber temperature (YSI # 427 thermistor and model 46 TUC telethermometer, Yellow Springs Instrument Co., Yellow Springs, Ohio). Pressure within the chamber was measured with a direct-drive Bourdon-tube gauge, calibrated to an accuracy of 0.25 o/o of full scale or about 0.17 atm, according to manufacturer’s specifications (Roylyn Precision Direct Drive Gauge, 3-D Instruments, Inc., Anaheim, CA).
Cathetometer
Measurements of h, the length of the water vapor-gas column, were performed using a cathetometer readable to 0.001 cm (Precision Tool and Instrument Co., Ltd., Surrey, England). Eleven replicate determinations of distance between the top of a capillary tube and the water meniscus yielded a standard deviation of kO.0013 cm. This degree of precision is made necessary by the slow rate of water evaporation from the capillaries and hence the small differences between positions of the meniscus in time. In experiments conducted at 50 ATA of N,, for example, h changed by less than 0.03 cm in the course of 6 days.
Gases
Commercially available He and N, of high purity grade were used. Manufacturer’s specifications list high-purity He as 99.995 % He and high-purity N, as 99.99 % N,. He-O, mixtures were prepared from high-purity He and 99.6 % 0, in the laboratory and analyzed either with a Beckman OM-11 oxygen analyzer (Beckman Instruments, Inc., Fullerton, CA) or with a Quintron model R gas chromatograph (Quintron Instrument Co., Inc., Milwaukee, WI).
BINARY AND TERNARY GAS DIFFUSION
19
Temperature
The pressure chamber was placed in a constant-temperature cabinet (model 1247 LA, Hotpack Corp., Philadelphia, PA) which was capable of maintaining a set temperature to about +0.2”C. The temperature within the high-pressure chamber itself showed even smaller fluctuations, of the order of kO.02 “C, because of its large thermal mass. Temperatures were measured with YSI thermistors calibrated against precision mercury thermometers with 0.05 “C scale divisions. As Schwertz and Brow (195 1) pointed out, evaporation may cool the gas-water interface significantly below the ambient temperature in the high-pressure chamber if it proceeds too fast, and thus may lead to erroneously low values of 9. Evaporation is accelerated as the liquid level is brought closer to the open end of the capillary. In the present experiments, the liquid level was kept at least 6 cm below the open end of the capillaries for all experiments conducted at 1 ATA, where evaporation is most rapid. During an experiment in which water vapor diffused into He, the actual temperature difference between the gas-water interface and the bulk water phase was measured with a copper-constantan thermocouple made of 0.13 mm wire, a size small enough not to occupy a significant fraction of the cross-sectional area of the capillary. The voltage output of the thermocouple was measured with a Hewlett-Packard model 419A null microvoltmeter; the temperature difference recorded in this fashion was less than 0.01 “C. Sources of error
One possible source of error lies in the assumption that diffusion of water vapor out of the capillary is the rate-limiting process, i.e. that removal of water vapor from the mouth of the capillary by convection is sufficiently rapid to maintain PH20 = 0 at this point. Schwertz and Brow (195 1) checked this assumption by measuring diffusion coefficients at several volumetric flow rates in their apparatus from 50-300 cm3 . min- ’ and found no influence of flow in this range. In the present experiments, convective mixing was produced routinely within the high-pressure chamber by a small fan which caused a linear flow velocity near the tops of the capillaries of 100 cm. set-’ at 1 ATA. The binary diffusion coefficient of water vapor-helium was measured under this type of convective mixing and also with a 500 cm3 . min-’ flow of helium from a pressure cylinder directed at the tops of the capillaries. The two experiments gave values of 9 which agreed within 3.8 “/o. Possible errors in cathetometer readings caused by thermal expansion or contraction of water attendant on temperature fluctuations of the order of those which occurred during diffusion experiments were calculated and found to be negligible. Similarly, although some vapor pressure lowering is to be expected as He or N, under high pressure dissolve in water, the fractional lowering of water vapor pressure caused by dissolution of N, at 50 ATA, for example, is less than 0.1 %. Pressure per se increases water vapor pressure at a given temperature, but again, the effect is slight. For example, it may be calculated that the equilibrium vapor pressure of water is increased at 50 ATA by about 3 y0 over its 1 ATA value (Tabor, 1969).
20
C. V. PAGANELLI
AND F. K. KURATA
Another potential source of error arises from mechanical vibrations of the building and the constant-temperature cabinet in which the high pressure chamber was located. Such vibrations are capable of causing convection currents in the capillary tube, thus vitiating any attempt to measure diffusion. To prevent transmission of vibration, the high pressure chamber was placed on 2 sets of rubber isolation pads : one set between the wooden cradle which supported the chamber and the chamber itself, and the second set between the base of the cradle and the floor of the constanttemperature cabinet. The chamber weight, approximately 150 kg, was also an important factor in damping vibration. The good agreement between results obtained in our system and the literature values reported in table 1 indicate that the above factors were sufficient to prevent vibration and attendant convection currents from significantly biasing our results.
Results Diffusion measurements were made at 25 “C on the binary systems H,O-He and H,O-N, at approximately 1,4, 10, 20, and 50 ATA. (The symbol H,O is used here to mean water vapor.) A few control measurements of 9 were initially made at 34°C and 1 ATA in H,O-He to provide a direct comparison with the results of Schwertz and Brow (1951) at the same temperature and pressure. There was good agreement between the values obtained in the present experiments and those reported by both Schwertz and Brow (195 1) and Lee and Wilke (1954), as shown in table 1. Diffusion of water vapor in the ternary system H,O-He-O, was also measured in gas mixtures of 1.6 ‘4 O,-98.4 y0 He and 26 y0 O,-74 % He. Data were obtained in the form of values of h us t, and for binary systems were plotted as (h* -hi) us (t-to) for each of 3 diffusion tubes at each pressure and gas combination. Linear least-squares regression analysis was performed on the data from each capillary, and the three slopes so obtained were averaged before calculation of 9 by eq. (2). The data fall very closely on each regression line, as shown in fig. 3, a representative plot for H,O-N, at 1 ATA. Correlation coefficients were never less than 0.997 and averaged 0.999 over all experiments. A plot of (h* - hi) us (t-to) for H,O-He at pressures TABLE Comparison 3 (cm’
H,O-He H20-He H+N,
1
of results at
set- I)
1 ATA Reference
Literature
Present experiments
values
0.836 (25 C)
0.908 (25 C)
Lee and Wilke (1954)
0.860 (34 C) 0.253 (25 C)
0.902 (34 C)
Schwertz
and Brow (1951)
0.256 (34 C)
Schwertz
and Brow
( 195 I )
21
BINARY AND TERNARY GAS DIFFUSION
1 6
At, lo3 minutes Fig. 3. (h’ -hi)
in cm* vs elapsed
time dt in units of lo3 min. Water
and 25 ‘C. Each symbol
represents
a separate
vapor
diffusion
into N, at 1 ATA
capillary.
of 1,4, 10,20, and 50 ATA is shown in fig. 4. The reduction in slope with increasing pressure is immediately evident. Binary diffusion coeffkients as functions of pressure in both H,O-He and H,O-N, are given in table 2. The diffusion coefficients listed at 1 ATA in table 2 were actually obtained at prevailing atmospheric pressure (PEs), which deviated from 760 by 4-5 torr at most over several months; these diffusion coeffkients were then corrected to 1 ATA by multiplying by F’n/760. Estimates of the standard deviation in 9 in table 2 were obtained by combining standard deviations from the linear regression analysis for the 3 individual slopes in each experiment, according to rules for propagation of error (Beers, 1953).
H20-He,
0
Fig. 4. (h2pressures.
4
hg) in cm2 oselapsed The lines are drawn
12 8 At, lo3 minutes
16
25°C
_
20
time dt in units of lo3 min. Water vapor diffusion into Heat the indicated from linear least squares analysis; the points are experimental values.
22
C. V. PAGANELLI
AND F. K. KURATA
TABLE Binary diffusion Gas system
9
H,O-N,
’ f “, SD)
= ratio of binary
(“” SD values calculated
&?J&@
Deviation from theory
(ATA)
0.836
+0.2””
1.oo
1.00
0.209
kO.8:‘”
4.06
4.00
I .5 “”
9.85
_
0.0849
k
0.0444
k2.0””
20.12
18.8
+7””
9.85 44.5
+13”; _
0.0188
kO.9””
50.88
0.253
kO.4””
1.00
1.00
0.0672
rf- 1.5””
4.10
3.76
0.0297
kO.8 “”
9.84
8.52
0.0159
k1.3””
0.00749 k2.6 “,” 9,/p
at 25 C
Pressure set-
(cm’ H,O-He
2
coefftcients
diffusion
coefftcient
as described
at
+8”;, + 13””
20.05
15.9
+ 21 “”
51.01
33.8
+ 34””
1 ATA to that at experimental
pressure.
in the text)
The fourth column in table 2 gives the ratio of gO, the value of 9 at 1 ATA, to 3 at the experimental pressure. According to the Chapman-Enskog theory this ratio at moderate pressures should be equal to P/P,, or simply to P, since PO = 1 ATA. Figure 5 is a graph of go/a us P. Experimental data are plotted as points, and the line of identity is drawn. It is clear that gn,/a deviates from the Chapman-Enskog theory above 4 ATA for H,O-N,, and above 20 ATA for H,O-He; the deviations are more pronounced in N, than in He, and become larger at the higher pressures. At 50 ATA, &20,He is 13 ‘4 larger than expected (0.0188 cm2 . set-’ by actual measurement us 0.836/50.88 or 0.0164 cm’ . set-’ predicted); Sn20,NZ is 34% larger (0.00749 cm2 . set- ’ measured us 0.253/51.01 or 0.00496 cm2 . see-’ predicted).
. . 30
///
40 20 ! /
lo 0
Fig. 5. 90/p,
p 10
.
I 20
H,O-He A H,O-N,
l
I I 30 40 P, ATA
1 50
I 60
ratio of binary diffusion coefftcient at I ATA to that at experimental Points are experimental values; line of identity has been drawn.
pressure
P. 1’s P.
BINARY
AND TERNARY
23
GAS DIFFUSION
These deviations are shown in the last column of table 2. Comparison of the He and N, data at the same pressure shows that water vapor diffuses 2.5-3.3 times more readily through He than through N,, depending on the pressure. In the ternary system H,O-He-O,, flux of water vapor out of the capillary tube was used to characterize the diffusion process. For ternary systems h was plotted directly against t, as shown in fig. 6. Good straight-line fits to the experimental data were obtained by linear regression analysis, and dh/dt, the slope of the line, was determined. Correlation coefficients averaged 0.999 over all experiments. To a close approximation, dh/dt is a direct measure of the water vapor flux out of the tube per unit cross-sectional area. Because part of the liquid water which evaporates remains behind in the tube, dh/dt does not measure the flux directly. However, the amount of water vapor remaining behind is several orders of magnitude less than the quantity which evaporates, and can be neglected in the present analysis. Table 3 lists ternary fluxes computed as described above, with values of the corresponding binary fluxes in water vapor-He and ternary/binary flux ratios given for comparison. When 0, is present at a concentration of 26% by volume, water vapor flux is reduced in the ternary system to between 60 and 70 y0 of its value in pure helium, depending on the pressure. At 1.6 % 0, by volume there is very little effect on the water vapor fluxes. Standard deviations of the fluxes were calculated in the same fashion as described for the diffusion coefficients. TABLE Water vapor fluxes at 25 ‘C for the ternary
and for the binary Gas system
3
system HZOpHe-0,
Pressure
Water vapor
(ATA)
((g
set-
flux
1 cm -‘).
ternary H,O
H,O
in 74% He-26”;
m 98.4;,,
0,
He-1.67;
0,
* Binary
fluxes were derived
(“,‘,by volume),
lo6 +?“SD)
Ternary flux -__ Binary flux*
Ds (cm’
1.86k1.7”;
2.99kO.55;
0.62
0.52
0.49+2.19;
0.79 k 2.4:;
0.62
0.14
20
0.19*1.0:;
0.28 k 2.1 y0
0.68
0.031
2.99+0.5;,
0.98
0.80
0.96
0.042
1
2.94+
as described
1.2:‘,
0.27 k 1.4’6
as described
set- ‘)
binary*
1
as the corresponding
. (7; SD values calculated
compositions
4
20
at the same pressure
at indicated
system H,O-He
0.28k2.1
O0
in the text from plots of h us t for the binary ternary
system H,O-He
flux.
in the text)
Although it is not in general possible to assign a single diffusion coefficient to a system involving 3 gases (Chang et al., 1975), we used plots of (h2 -hi) us (t-to), which were linear in our ternary systems, to calculate effective diffusion coefficients (DE) (Erasmus and Rahn, 1976) for water vapor in the two He-O, mixtures at 1 ATA and at elevated pressures. Values of D, are given in the last column of table 3. Calculation of D, in this manner ignores in effect the influence of the 0, and He gradients
24
C. V. PAGANELLI
AND F. K. KURATA
on the water vapor flux. D, values may be used to calculate approximate diffusive water vapor flux in He-O, systems where diffusion geometry and water vapor pressure gradient are known, provided the composition of the system resembles those used in the present experiments. Since ternary diffusion depends explicitly on the relative composition of the three components in the system, DE’s obtained in a particular ternary mixture should not generally be used to calculate diffusive flows in another mixture of the same gases with a different fractional composition.
Discussion Deviations of binary diffusivity from l/P dependence at high pressure are not unique to systems containing water vapor. Durbin and Kobayashi (1962) have shown a similar phenomenon in the pressure dependence of 85Kr diffusion in krypton, argon, nitrogen, helium, and carbon dioxide. Their deviations are reported in the form of increasing values of the product (gas diffusivity x density) with increasing pressure and thus are in the same direction as those noted in the present study, though smaller in magnitude for comparable pressure changes. It is apparent that the simple inverse relation between $33and P for systems containing water vapor begins to break down at quite modest pressures, and at 50 ATA, a pressure already achieved in saturation diving, for example, can be seriously in error, at least for N,-containing gas mixtures. It should be pointed out that studies of water vapor diffusion at elevated pressures have implications for physiological processes such as insensible water loss and pulmonary gas exchange in human subjects living in hyperbaric environments, as in saturation diving. Hong et al. (1976), among others, have in fact reported reduction in insensible water loss in men exposed to 18 ATA helium-oxygen mixtures.
I
Water 3.75
Vapor
at 25”C,
-
3.60’
’
’
2
’
20 ATA
’
4
’ At,
’
’
lo3
mmutes
6
’
8
Fig. 6. h in cm USelapsed time dt in units of IO3 min for binary (He-O,
in a 74%‘263/,
mixture)
I
Diffusion
’
’
10
a
diffusion
(pure He) and ternary
of water vapor at 20 ATA. The lines are drawn
analysis;
the points are experimental
values.
diffusion
from linear least squares
RINARY
AND TERNARY
25
GAS DIFFUSION
Our data on reduction in guzO, N2with pressure also provide a qualitative explanation for the findings of Paganelli et al. (1975) on pressure-induced changes in water loss from eggs, which was mentioned previously. Those findings also showed the reduction in water loss rate with pressure to be less than expected on the basis of the Chapman-Enskog theory for dilute gases. The deviations from the Chapman-Enskog theory for dilute gases observed in the present experiments are not surprising in view of the assumptions on which the theory rests: that the diffusing molecules are monatomic, spherically symmetrical, and nonpolar, and undergo only binary, elastic collisions (Hirschfelder et al., 1954). In approaching problems involving diffusion of real gases at pressure, it would seem best to rely on measured values of diffusion coefficients wherever possible. Our measurements of water flux in the ternary system H,O-He-O, showed several features of interest. Introduction of 26% 0, by volume into a water vapor-He system reduced the water vapor flux by nearly 40 % at 1 and 4 ATA, and by slightly less at 20 ATA. When the 0, was reduced to 1.6 %, on the other hand, its effect on water vapor fluxes was negligible both at 1 and at 20 ATA. From our limited data, reduction of fluxes with pressure in a ternary system of given composition is seen to follow an approximate dependence on l/P. However, the reductions are substantially less than predicted at 20 ATA. We have obtained results at only two 0, concentrations; the exact nature of the dependence of water vapor flux on 0, concentration in a ternary system awaits further investigation.
Acknowledgements
The authors would like to thank Dr. Suk Ki Hong for his generous support and encouragement during this study. We also express our appreciation to Messrs. Toby Clairmont, Benjamin Respicio, and Edwin Hayashi for their excellent technical assistance.
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23
: 109-l 20.
L. and R. Kobayashi
(1962). Diffusion
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Erasmus, B. Dew. and H. Rahn (1976). Effects of ambient in the avian egg. Respir. Physiol. 27: 53-64. Hirschfelder,
J. O., C. F. Curtiss
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MA, Addison-Wesley Press. of ternary diffusion in the lung. Respir.
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pressures,
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and R. B. Bird (1954). The Molecular
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18.6 ATA. 111. Body fluid balance. Undersea Biomed. Res. (accepted for publication). Lee. C. Y. and C. R. Wilke (1954). Measurements of vapor diffusion coefficient. Ind. Eny. Chem. 46: 2381-2387.
26
C. V. PAGANELLI
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ambient Rahn,
AND F. K. KURATA
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Inc.
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the shell of the hen’s