Binary Diffusion of Gases in Capillaries in the Transition Region between Knudsen and Molecular Diffusion

Abstract

The transition region of diffusion for a binary gas mixture was experimentally investigated in an isobaric open system of fine glass capillaries in parallel. Results were obtained over a 675/1 pressure range from 0.444 to 300.2 mm of Hg absolute in the transition region between Knudsen and molecular (ordinary) diffusion and confirm the theoretical equation for the flux in true capillaries in an open system. This equation has been derived by others using a momentum balance with various assumptions, such as additivity of the momentum transfer rates for the Knudsen and molecular regions, etc. These assumptions seem to be confirmed. This appears to be the first known experimental confirmation of this equation for capillaries over a wide pressure range. Experimental flux ratios obtained in the transition region confirm the predicted inverse square root relationship with the molecular weights. Data for counterdiffusion in an open system near the Knudsen region tend to confirm the Knudsen equation and data in the molecular region also substantiate the Stefan-Maxwell relations.

Mechanism of the Initial Phenomena of Defluidization Caused by Switching Fluidizing Gases

“…He con- cluded that the molar fluxes were inversely proportional to the square roots of the molecular weights. Experimental studies obeyed this relationship for isobaric counterdiffusion (Remick and Geankoplis, 1973;Knaff and Schlünder, 1985). Conversely, pressure change was observed for isovolumetric counterdiffusion (Asaeda et al, 1981;Veldsink et al, 1994;Soukup et al, 2008).…”

Mechanism of the Initial Phenomena of Defluidization Caused by Switching Fluidizing Gases

“…He con- cluded that the molar fluxes were inversely proportional to the square roots of the molecular weights. Experimental studies obeyed this relationship for isobaric counterdiffusion (Remick and Geankoplis, 1973;Knaff and Schlünder, 1985). Conversely, pressure change was observed for isovolumetric counterdiffusion (Asaeda et al, 1981;Veldsink et al, 1994;Soukup et al, 2008).…”

Science of Water Leaks: Validated Theory for Moisture Flow in Microchannels and Nanochannels

“…For intermediate interdiffusive flow the theory has been described by Ernst and Hemond and Remick and Geankopolis . We write the water vapor conductance, C II , as where D II is the coefficient for the interdiffusive flow at intermediate Kn .…”

“…We write the water vapor conductance, C II , as where D II is the coefficient for the interdiffusive flow at intermediate Kn . Remick and Geankopolis compared this theory with experiment and found that it worked well for molecules consisting of the test gases they used, N 2 and He. Ernst and Hemond found that the equation worked well for single atoms but somewhat overestimated flow for polyatomic molecules for which internal degrees of freedom make collisions less elastic.…”

“…For intermediate interdiffusive flow the theory has been described by Ernst and Hemond 17 and Remick and Geankopolis. 18 We write the water vapor conductance, C II , as…”

Modified multi-component gas transport formulation with phoretic effects

“…By summing all the component equations, simple Navier-Stokes equation for the mixture is obtained. However, Kerkhof and Geboers (2005) showed that solving this equation for the counter-diffusion case (Remick and Geankoplis 1973) gives zero mass averaged velocity, which is inconsistent with experimental observations. Several other researchers in statistical mechanics have tried to solve the Boltzmann equation to arrive at the momentum balance equation.…”

Mechanism of the Initial Phenomena of Defluidization Caused by Switching Fluidizing Gases

“…He con- cluded that the molar fluxes were inversely proportional to the square roots of the molecular weights. Experimental studies obeyed this relationship for isobaric counterdiffusion (Remick and Geankoplis, 1973;Knaff and Schlünder, 1985). Conversely, pressure change was observed for isovolumetric counterdiffusion (Asaeda et al, 1981;Veldsink et al, 1994;Soukup et al, 2008).…”

Science of Water Leaks: Validated Theory for Moisture Flow in Microchannels and Nanochannels

“…For intermediate interdiffusive flow the theory has been described by Ernst and Hemond and Remick and Geankopolis . We write the water vapor conductance, C II , as where D II is the coefficient for the interdiffusive flow at intermediate Kn .…”

“…We write the water vapor conductance, C II , as where D II is the coefficient for the interdiffusive flow at intermediate Kn . Remick and Geankopolis compared this theory with experiment and found that it worked well for molecules consisting of the test gases they used, N 2 and He. Ernst and Hemond found that the equation worked well for single atoms but somewhat overestimated flow for polyatomic molecules for which internal degrees of freedom make collisions less elastic.…”

“…For intermediate interdiffusive flow the theory has been described by Ernst and Hemond 17 and Remick and Geankopolis. 18 We write the water vapor conductance, C II , as…”

Modified multi-component gas transport formulation with phoretic effects

“…By summing all the component equations, simple Navier-Stokes equation for the mixture is obtained. However, Kerkhof and Geboers (2005) showed that solving this equation for the counter-diffusion case (Remick and Geankoplis 1973) gives zero mass averaged velocity, which is inconsistent with experimental observations. Several other researchers in statistical mechanics have tried to solve the Boltzmann equation to arrive at the momentum balance equation.…”

Mechanism of the Initial Phenomena of Defluidization Caused by Switching Fluidizing Gases

“…He con- cluded that the molar fluxes were inversely proportional to the square roots of the molecular weights. Experimental studies obeyed this relationship for isobaric counterdiffusion (Remick and Geankoplis, 1973;Knaff and Schlünder, 1985). Conversely, pressure change was observed for isovolumetric counterdiffusion (Asaeda et al, 1981;Veldsink et al, 1994;Soukup et al, 2008).…”

Science of Water Leaks: Validated Theory for Moisture Flow in Microchannels and Nanochannels

“…For intermediate interdiffusive flow the theory has been described by Ernst and Hemond and Remick and Geankopolis . We write the water vapor conductance, C II , as where D II is the coefficient for the interdiffusive flow at intermediate Kn .…”

“…We write the water vapor conductance, C II , as where D II is the coefficient for the interdiffusive flow at intermediate Kn . Remick and Geankopolis compared this theory with experiment and found that it worked well for molecules consisting of the test gases they used, N 2 and He. Ernst and Hemond found that the equation worked well for single atoms but somewhat overestimated flow for polyatomic molecules for which internal degrees of freedom make collisions less elastic.…”

“…For intermediate interdiffusive flow the theory has been described by Ernst and Hemond 17 and Remick and Geankopolis. 18 We write the water vapor conductance, C II , as…”

Modified multi-component gas transport formulation with phoretic effects

“…By summing all the component equations, simple Navier-Stokes equation for the mixture is obtained. However, Kerkhof and Geboers (2005) showed that solving this equation for the counter-diffusion case (Remick and Geankoplis 1973) gives zero mass averaged velocity, which is inconsistent with experimental observations. Several other researchers in statistical mechanics have tried to solve the Boltzmann equation to arrive at the momentum balance equation.…”