Diffusion in Three-Component Gas Mixtures in Transition Region between Knudsen and Molecular Diffusion

Cunningham, R. S.; Geankoplis, C. J.

doi:10.1021/i160027a013

Cited by 10 publications

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“…Toor (1957) derived exact analytical equations for three components in the molecular region for a closed system and obtained numerical values for fluxes showing the various types of diffusion phenomena that can occur. Cunningham and Geankoplis (1968) derived analytical equations for three components in the transition region for an open and isobaric system, but numerical values have not been obtained. A number of experimental studies for binary gases in the transition region are available (Henry et al, 1967; Rothfeld, 1963;Scott and Dullien, 1962; Wakao and Smith, 1962).…”

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confidence: 99%

“…The transition region equations derived by Cunningham and Geankoplis (1968) were theoretically investigated in detail and numerical solutions obtained by trial and error 206 Ind. Eng, Chem.…”

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confidence: 99%

“…Rothfeld (1963) and Scott and Dullien (1962) used Equation 4 and a momentum balance of molecules in a capillary in an open system in the transition region and derived the differential equations for a multicomponent system. Xa + Xb + Xc = 1.0 (9) Cunningham and Geankoplis (1968) integrated the above equations and obtained two sets of equations. For (B2 -4C) positive, the equations are of the exponential type.…”

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Numerical Study of the Three-Component Gaseous Diffusion Equations in the Transition Region between Knudsen and Molecular Diffusion

Remick¹,

Geankoplis²

1970

Ind. Eng. Chem. Fund.

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A numerical solution to the equations for steady-state diffusion in a three-component gas mixture of helium, neon, and argon was obtained by trial and error in the transition region between Knudsen and molecular diffusion in an open system. The shapes of plots of the fluxes of helium or neon having large concentration gradients vs. pressure are very similar to those of a binary mixture, increasing with pressure and approaching constant values at high pressures. Osmotic diffusion was found for argon and, unexpectedly, the shape of its curve of flux vs. pressure was somewhat similar to that of a binary mixture. Reasons were given for this behavior. Osmotic or reverse diffusion cannot occur in the Knudsen region. Under certain conditions the binary flux equations can be used to approximate the fluxes in a ternary mixture and reduce computational time. The existence of a maximum or minimum point in the plot of concentration vs. distance was indicated for argon. Such a point was shown for molecular diffusion in a closed ternary system. The flux ratios of helium to neon or helium to argon can change slightly or markedly with changes in pressure, depending on the concentration gradient of each component. This is contrary to the cases of diffusion in binary systems or multicomponent molecular diffusion in a closed system where the flux ratios are independent of pressure.

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