Respiration
Physiology (1975) 25, 247-258;
North-Holland Publishing Company, Amsterdam
DIFFUSION IN THE GAS PHASE : THE EFFECTS OF AMBIENT PRESSURE* AND GAS COMPOSITION
C. V. PAGANELLI,
A. AR2, H. RAHN and 0. D. WANGENSTEEN3
Department of Ph_vsiology, School of Medicine. State Unioersity of New York at Buffalo, Buffalo, N. Y. 14214. U.S.A.
Abstract.
Gas transport
gas phase
across
the pores
and for any particular
The egg shell is thus a convenient gas species changing water
when
its diffusion
the second
vapor
atmospheres*
and
is altered
gas in the diffusion (ata).
upon
its diffusion
model for measuring coefficient
O2 was inversely
absolute
of a hen’s egg shell occurs
gas depends
The
proportional permeability
a change
In this study to ambient
the pore
pressure
the permeability
to water
in the
geometry.
of the shell to a given
in ambient
pressures
of the shell
of diffusion
and
the diffusive permeability by either
pathway.
by a process
coefficient
over
of the
the range
vapor
in a He
or by shell
to
of .06 to 8 environment
of the shell to O2 (KHzO. ae) was 2.4 times I%,. aiT. If Ko2,NI is taken as unity. the permeabilities in He, Ar, CO, and SF, are 3.38, 0.95, 0.88, and 0.52. respectively. The results are interpreted in terms of the Chapman-Enskog given gas pairs and ambient modification
of egg
man at high ambient
equation, pressures.
from which
binary
diffusion
These results also provide
shells in altitude-adapted
chickens,
coefficients
possible
can be predicted
explanations
and for the reduced
for
for the structural
insensible
water
loss in
pressure. Egg shell permeability
Pressure
Gas composition
Water
Oxygen
vapor diffusion
diffusion
Diffusion of one gas in another is of obvious biological importance to all airbreathing animals. Processes such as gas exchange in the lungs and insensible water loss from the skin both have diffusive components and consequently will be influenced by physical and environmental factors which affect diffusion in the gas phase. Among such factors, ambient pressure and the molecular composition Accepted for publication 16 July 1975. ’ This study was aided in part by Contract Naval Research, Department of the Navy, part by NIH Grant 5 PO1 HL 14414. 2 Present
address:
3 Present address:
NOOO14-68-A-0216,
(NR
and the State University
Depqrtment
of Zoology,
Department
of Physiology,
Tel-Aviv
University,
424 Millard
Minn. 55455, U.S.A. 247
lOl-722),
between
of New York
Tel-Aviv,
Hall, University
the Office of
at Buffalo,
Ramat-Aviv, of Minnesota,
and in
Israel. Minneapolis,
248
C. V. PAGANELLI, A. AR. H. RAHN AND 0. D. WANGENSTEEN
of the gas mixture which occupies the diffusion path both play important roles. While it is difficult to study gaseous diffusion directly in the alveolar spaces of the lung, the avian egg shell provides a good system for such studies. It has been appreciated for more than 70 years that diffusion plays an essential role in gas exchange across the egg shell, and it has been over 60 years since Aggazzotti (1913) made the lirst systematic observations on the effects of barometric pressure on water loss in incubating chicken eggs. He compared weight loss in eggs on Monte Rosa at 2900 meters and in Turin, near sea level, and showed clearly the more rapid weight loss at altitude. He correctly ascribed the effect to an enhanced evaporation of water at altitude. Gas-filled pores of about 15 I_tm in diameter in the shell control the molecular traffic in 02, CO,, and water vapor. The porous nature of the shell led naturally to the early measurements of shell permeability to gases made by Romanoff (1943) and Romijn (1950). However, the techniques which they employed yielded what might be termed hydraulic conductivities, rather than diffusive permeabilities, since they used gas flow produced by a total pressure difference imposed across the shell as their .driving force. More recently, Wangensteen et al. ( 1970/7 l), and Kutchai and Steen (1971) measured the true diffusive permeability of the shell of chicken eggs to O2 an’d COZ, and estimated water permeability from their data. The diffusive loss of water as vapor through the egg shell is also a well-known and thoroughly studied phenomenon. Water loss under defined conditions as a functional measure of shell porosity or permeability has been used by Bryant and Sharp (1934), Marshall and Cruickshank (1938), and Tyler (1945), among others. The present siudy was designed to measure both penetration of O2 and loss of water vapor through the egg shell as processes representative of diffusion in the gas phase, and to demonstrate the effects of changing both ambient pressure and the second gas in the diffusion system on the fluxes of O2 and water vapor. A preliminary report of our results has been presented elsewhere (Paganelli et ul., 1971). Theory
The diffusive permeability of the egg shell to one gas in the presence of a second gas may be simply defined, in general terms, following Wangensteen et al. (1970/71), Kutchai and Steen (1971), and Ar et al. (1974), as:
(1)
J K 1.2 = A.AP
where K l,,=diffusive permeability constant of the shell (cm3 s~~.sec-‘.crn-~. torr- ‘), A = surface area of the shell (cm’), AP=partial pressure difference of gas 1 across the shell (torr), and J=flux of gas 1 across the shell (cm3 STP.S~C-I). (For simplicity, we have used the term ‘shell’ or ‘egg shell’ in the present context to denote the entire barrier to diffusion between the interior of the egg and tQe environment.) The definition of K in this manner is consistent
DIFFUSION
IN THE GAS PHASE
249
with earlier definitions of shell porosity used by Marshall and Cruickshank (1938), Mueller and Scott (1940) Romanoff (1943) and Tyler (1945) but includes additionally an explicit term for the driving partial pressure difference. The quantitative relation between K 1.2 and the binary diffusion coefficient of the gas pair may be derived by combining eq. (1) with Fick’s first law of diffusion in the steady state:
(4
J= I/,,, .Ap.$
where ‘r 1.z = binary diffusion coefficient for the gas pair (cm2.sec-‘), Ap=pore area of the shell available for diffusion (cm2), AC=concentration difference of gas 1 across the shell (cm3 srP.crn- “), and L = length of the diffusion path (equivalent to shell thickness) (cm). Thus:
AC/AP for an ide$ gas is simply the capacitance coefficient &, in a gas-gas system as defined by Piiper et al. (1971). & is equal to l/RT and at 25 “C is 1.205 x 10m3 cm3 srP.cm-3.torr-‘. Substitution of p, in eq. (3) yields:
Note that eq. (4) permits one to calculate Ap, the pore area of the egg shell, from measured values of K, A, and L, and published values of 9 I. 2 and &. From eq. (4) one can predict that the permeability constant of the shell will vary directly with Q1.2 (a property of the gas phase), and with fractional pore area and pore length (properties of the shell). Water loss data in the present experiments are also expressed in terms of conductance G, defined as mg of water lost per day and per torr of water vapor pressure difference. G is simply the product of K x A, with units properly adjusted. Both the elementary kinetic theory of gases and Chapman-Enskog theory (Reid and Sherwood, 1966) predict an inverse relation between total ambient pressure and the binary diffusion coefficient cs’, 2 of a gas pair. The Chapman-Enskog equation also relates VI .2 to the molecular species which make up the gas pair:
where T=absolute temperature (OK), PB=ambient pressure (atm), M,, M,= molecular weights of gases 1 and 2, or.2 = Lennard-Jones characteristic distance for the gas pair 1,2 (A), R,,,,=dimensionless function of temperature and of the intermolecular potential field for a single molecule of 1 interacting with a single molecule of 2.
c‘. V. PAGANELLI,
250
A. AR, H. RAHN
AND 0.
D. WANGENSTEEN
o,.~. a quantity analogous to the collision diameter in simple kinetic theory, is the distance between molecules of gas 1 and 2 at which the potential energy of interaction is 0 in a Lennard-Jones potential field (Reid and Sherwood, 1966); err ,2 is also a function
of temperature.
The quantity
Q,, , _ corrects
eq. (5) for
deviations from an idealized, rigid-sphere The dependence of ‘i, ,z on ambient explicitly in the terms P, M ,, and Mz species is also implicit in the terms gI,L between diffusion
model for the interaction of gas molecules. pressure and molecular species appears in eq. (5); its dependence on molecular and Q,, , which express the interactions the two kinds cf diffusing molecules. To calculate theoretical binary coefficients for a given gas pair from eq. (5) one uses values of
in 01.2 and Q,,., which are tabulated (1960) among other sources. From eqs. (4) and (5) it is apparent vary inversely with ambient pressure, and although the actual dependence on the complicated.
Hirschfelder
et LIZ.(1954)
and
Bird et al.
that K,,? in a binary gas system should to a first approximation, as (M; ’ + M; ‘)‘, molecular species will be somewhat more
Materials and methods PERMEABILITY
MEASUREMENTS
Infertile White Leghorn eggs were either bought at from a breeding flock maintained in our animal was measured by an oxygen electrode technique (Wangensteen et al., 1970/71). For measuring water
a local food store or obtained facilities. Oxygen permeability described in detail elsewhere vapor permeability, eggs were
placed in desiccators over either fused KOH pellets or indicating silica gel, and weighed at known time intervals, usually daily. Weight loss in infertile eggs is a good measure of water loss, and is linear with time over many weeks (Romanoff, 1940). Temperature in the desiccators fluctuated by about +2 ‘C around a mean of 24.5 C, at which the saturation water vapor pressure is 23.0 torr. Surface areas of eggs used in calculation of K for water vapor were determined individually from egg weights using the formula of Besch er al. (1968). Since surface area showed little variation from egg to egg, the average of 66.4 cm2 (+ 1.5 cm2 S.D.) was used in all water vapor calculations. AP,,,, the water vapor partial pressure difference between the interior of the egg and the environment of the desiccator ( PuLo= 0), was 23.0 torr at the temperature of the experiment. of pressure For water vapor experiments at reduced pressures, desiccators containing eggs were partially evacuated and held at known pressures with a vacuum pump. Oxygen experiments were done with the experimental assembly in a low-pressure chamber. High pressure measurements of both 0, and water vapor permeability were made in a recompression chamber. To determine the effect of ambient pressure on water vapor flux, weight loss Effect
DIFFUSION
IN THE GAS PHASE
251
in 1I or 12 eggs was measured at prevailing atmospheric pressure, usually about 740 torr. The same eggs were then subjected to either high or low pressure at the same temperature and weight loss measurements were repeated. A similar procedure was followed for O2 flux determinations, except that a single egg shell preparation was used for replicate measurements at one atmosphere; the measurements were then repeated on the same shell at either high or low pressure.
Weight loss of eggs was measured in desiccators containing either dry air or He. 0, flux was measured by electrode in the presence of each of the following second gases: N,, He, Ar, CO,, and SF6. Results Effect
of gas flow on water loss
To test the proposition that water vapor loss from eggs in desiccators is a diffusion-limited process, weight loss of the same eggs was measured in both still and flowing air. The data in table 1 are average conductances for the eggs in the two situations. There appears to be a slight tendency toward faster loss in flowing air, but the t-test for unpaired samples showed no significant difference between the average conductances (0.1
Physiology (1975) 25, 247-258;
North-Holland Publishing Company, Amsterdam
DIFFUSION IN THE GAS PHASE : THE EFFECTS OF AMBIENT PRESSURE* AND GAS COMPOSITION
C. V. PAGANELLI,
A. AR2, H. RAHN and 0. D. WANGENSTEEN3
Department of Ph_vsiology, School of Medicine. State Unioersity of New York at Buffalo, Buffalo, N. Y. 14214. U.S.A.
Abstract.
Gas transport
gas phase
across
the pores
and for any particular
The egg shell is thus a convenient gas species changing water
when
its diffusion
the second
vapor
atmospheres*
and
is altered
gas in the diffusion (ata).
upon
its diffusion
model for measuring coefficient
O2 was inversely
absolute
of a hen’s egg shell occurs
gas depends
The
proportional permeability
a change
In this study to ambient
the pore
pressure
the permeability
to water
in the
geometry.
of the shell to a given
in ambient
pressures
of the shell
of diffusion
and
the diffusive permeability by either
pathway.
by a process
coefficient
over
of the
the range
vapor
in a He
or by shell
to
of .06 to 8 environment
of the shell to O2 (KHzO. ae) was 2.4 times I%,. aiT. If Ko2,NI is taken as unity. the permeabilities in He, Ar, CO, and SF, are 3.38, 0.95, 0.88, and 0.52. respectively. The results are interpreted in terms of the Chapman-Enskog given gas pairs and ambient modification
of egg
man at high ambient
equation, pressures.
from which
binary
diffusion
These results also provide
shells in altitude-adapted
chickens,
coefficients
possible
can be predicted
explanations
and for the reduced
for
for the structural
insensible
water
loss in
pressure. Egg shell permeability
Pressure
Gas composition
Water
Oxygen
vapor diffusion
diffusion
Diffusion of one gas in another is of obvious biological importance to all airbreathing animals. Processes such as gas exchange in the lungs and insensible water loss from the skin both have diffusive components and consequently will be influenced by physical and environmental factors which affect diffusion in the gas phase. Among such factors, ambient pressure and the molecular composition Accepted for publication 16 July 1975. ’ This study was aided in part by Contract Naval Research, Department of the Navy, part by NIH Grant 5 PO1 HL 14414. 2 Present
address:
3 Present address:
NOOO14-68-A-0216,
(NR
and the State University
Depqrtment
of Zoology,
Department
of Physiology,
Tel-Aviv
University,
424 Millard
Minn. 55455, U.S.A. 247
lOl-722),
between
of New York
Tel-Aviv,
Hall, University
the Office of
at Buffalo,
Ramat-Aviv, of Minnesota,
and in
Israel. Minneapolis,
248
C. V. PAGANELLI, A. AR. H. RAHN AND 0. D. WANGENSTEEN
of the gas mixture which occupies the diffusion path both play important roles. While it is difficult to study gaseous diffusion directly in the alveolar spaces of the lung, the avian egg shell provides a good system for such studies. It has been appreciated for more than 70 years that diffusion plays an essential role in gas exchange across the egg shell, and it has been over 60 years since Aggazzotti (1913) made the lirst systematic observations on the effects of barometric pressure on water loss in incubating chicken eggs. He compared weight loss in eggs on Monte Rosa at 2900 meters and in Turin, near sea level, and showed clearly the more rapid weight loss at altitude. He correctly ascribed the effect to an enhanced evaporation of water at altitude. Gas-filled pores of about 15 I_tm in diameter in the shell control the molecular traffic in 02, CO,, and water vapor. The porous nature of the shell led naturally to the early measurements of shell permeability to gases made by Romanoff (1943) and Romijn (1950). However, the techniques which they employed yielded what might be termed hydraulic conductivities, rather than diffusive permeabilities, since they used gas flow produced by a total pressure difference imposed across the shell as their .driving force. More recently, Wangensteen et al. ( 1970/7 l), and Kutchai and Steen (1971) measured the true diffusive permeability of the shell of chicken eggs to O2 an’d COZ, and estimated water permeability from their data. The diffusive loss of water as vapor through the egg shell is also a well-known and thoroughly studied phenomenon. Water loss under defined conditions as a functional measure of shell porosity or permeability has been used by Bryant and Sharp (1934), Marshall and Cruickshank (1938), and Tyler (1945), among others. The present siudy was designed to measure both penetration of O2 and loss of water vapor through the egg shell as processes representative of diffusion in the gas phase, and to demonstrate the effects of changing both ambient pressure and the second gas in the diffusion system on the fluxes of O2 and water vapor. A preliminary report of our results has been presented elsewhere (Paganelli et ul., 1971). Theory
The diffusive permeability of the egg shell to one gas in the presence of a second gas may be simply defined, in general terms, following Wangensteen et al. (1970/71), Kutchai and Steen (1971), and Ar et al. (1974), as:
(1)
J K 1.2 = A.AP
where K l,,=diffusive permeability constant of the shell (cm3 s~~.sec-‘.crn-~. torr- ‘), A = surface area of the shell (cm’), AP=partial pressure difference of gas 1 across the shell (torr), and J=flux of gas 1 across the shell (cm3 STP.S~C-I). (For simplicity, we have used the term ‘shell’ or ‘egg shell’ in the present context to denote the entire barrier to diffusion between the interior of the egg and tQe environment.) The definition of K in this manner is consistent
DIFFUSION
IN THE GAS PHASE
249
with earlier definitions of shell porosity used by Marshall and Cruickshank (1938), Mueller and Scott (1940) Romanoff (1943) and Tyler (1945) but includes additionally an explicit term for the driving partial pressure difference. The quantitative relation between K 1.2 and the binary diffusion coefficient of the gas pair may be derived by combining eq. (1) with Fick’s first law of diffusion in the steady state:
(4
J= I/,,, .Ap.$
where ‘r 1.z = binary diffusion coefficient for the gas pair (cm2.sec-‘), Ap=pore area of the shell available for diffusion (cm2), AC=concentration difference of gas 1 across the shell (cm3 srP.crn- “), and L = length of the diffusion path (equivalent to shell thickness) (cm). Thus:
AC/AP for an ide$ gas is simply the capacitance coefficient &, in a gas-gas system as defined by Piiper et al. (1971). & is equal to l/RT and at 25 “C is 1.205 x 10m3 cm3 srP.cm-3.torr-‘. Substitution of p, in eq. (3) yields:
Note that eq. (4) permits one to calculate Ap, the pore area of the egg shell, from measured values of K, A, and L, and published values of 9 I. 2 and &. From eq. (4) one can predict that the permeability constant of the shell will vary directly with Q1.2 (a property of the gas phase), and with fractional pore area and pore length (properties of the shell). Water loss data in the present experiments are also expressed in terms of conductance G, defined as mg of water lost per day and per torr of water vapor pressure difference. G is simply the product of K x A, with units properly adjusted. Both the elementary kinetic theory of gases and Chapman-Enskog theory (Reid and Sherwood, 1966) predict an inverse relation between total ambient pressure and the binary diffusion coefficient cs’, 2 of a gas pair. The Chapman-Enskog equation also relates VI .2 to the molecular species which make up the gas pair:
where T=absolute temperature (OK), PB=ambient pressure (atm), M,, M,= molecular weights of gases 1 and 2, or.2 = Lennard-Jones characteristic distance for the gas pair 1,2 (A), R,,,,=dimensionless function of temperature and of the intermolecular potential field for a single molecule of 1 interacting with a single molecule of 2.
c‘. V. PAGANELLI,
250
A. AR, H. RAHN
AND 0.
D. WANGENSTEEN
o,.~. a quantity analogous to the collision diameter in simple kinetic theory, is the distance between molecules of gas 1 and 2 at which the potential energy of interaction is 0 in a Lennard-Jones potential field (Reid and Sherwood, 1966); err ,2 is also a function
of temperature.
The quantity
Q,, , _ corrects
eq. (5) for
deviations from an idealized, rigid-sphere The dependence of ‘i, ,z on ambient explicitly in the terms P, M ,, and Mz species is also implicit in the terms gI,L between diffusion
model for the interaction of gas molecules. pressure and molecular species appears in eq. (5); its dependence on molecular and Q,, , which express the interactions the two kinds cf diffusing molecules. To calculate theoretical binary coefficients for a given gas pair from eq. (5) one uses values of
in 01.2 and Q,,., which are tabulated (1960) among other sources. From eqs. (4) and (5) it is apparent vary inversely with ambient pressure, and although the actual dependence on the complicated.
Hirschfelder
et LIZ.(1954)
and
Bird et al.
that K,,? in a binary gas system should to a first approximation, as (M; ’ + M; ‘)‘, molecular species will be somewhat more
Materials and methods PERMEABILITY
MEASUREMENTS
Infertile White Leghorn eggs were either bought at from a breeding flock maintained in our animal was measured by an oxygen electrode technique (Wangensteen et al., 1970/71). For measuring water
a local food store or obtained facilities. Oxygen permeability described in detail elsewhere vapor permeability, eggs were
placed in desiccators over either fused KOH pellets or indicating silica gel, and weighed at known time intervals, usually daily. Weight loss in infertile eggs is a good measure of water loss, and is linear with time over many weeks (Romanoff, 1940). Temperature in the desiccators fluctuated by about +2 ‘C around a mean of 24.5 C, at which the saturation water vapor pressure is 23.0 torr. Surface areas of eggs used in calculation of K for water vapor were determined individually from egg weights using the formula of Besch er al. (1968). Since surface area showed little variation from egg to egg, the average of 66.4 cm2 (+ 1.5 cm2 S.D.) was used in all water vapor calculations. AP,,,, the water vapor partial pressure difference between the interior of the egg and the environment of the desiccator ( PuLo= 0), was 23.0 torr at the temperature of the experiment. of pressure For water vapor experiments at reduced pressures, desiccators containing eggs were partially evacuated and held at known pressures with a vacuum pump. Oxygen experiments were done with the experimental assembly in a low-pressure chamber. High pressure measurements of both 0, and water vapor permeability were made in a recompression chamber. To determine the effect of ambient pressure on water vapor flux, weight loss Effect
DIFFUSION
IN THE GAS PHASE
251
in 1I or 12 eggs was measured at prevailing atmospheric pressure, usually about 740 torr. The same eggs were then subjected to either high or low pressure at the same temperature and weight loss measurements were repeated. A similar procedure was followed for O2 flux determinations, except that a single egg shell preparation was used for replicate measurements at one atmosphere; the measurements were then repeated on the same shell at either high or low pressure.
Weight loss of eggs was measured in desiccators containing either dry air or He. 0, flux was measured by electrode in the presence of each of the following second gases: N,, He, Ar, CO,, and SF6. Results Effect
of gas flow on water loss
To test the proposition that water vapor loss from eggs in desiccators is a diffusion-limited process, weight loss of the same eggs was measured in both still and flowing air. The data in table 1 are average conductances for the eggs in the two situations. There appears to be a slight tendency toward faster loss in flowing air, but the t-test for unpaired samples showed no significant difference between the average conductances (0.1
