## Diffusion of Gases

### Abstract

1 Historical Note
2 General Description of Gaseous Diffusion
3 Molecular Behavior: Kinetic Theory of Gases
3.1 Simple Kinetic Theory of Gases
3.2 Rigorous Kinetic Theory of Gases
4 Binary Diffusion
4.1 Fick's First Law: Steady Diffusion
4.2 Binary Diffusion Coefficients
4.3 Fick's Second Law: Unsteady Diffusion
4.4 Solution of Binary Diffusion Equation
5 Multicomponent Diffusion
5.1 Multicomponent Diffusion Equations
5.2 Multicomponent Diffusion Coefficients
5.3 Effective Diffusion Coefficients
6 Summary
 Figure 1. Sketch of molecular flux through plane 0 in z direction. A, B, planes; λ, distance; x, y, directions. Figure 2. Lennard‐Jones potential energy function, describing interaction of 2 spherical, nonpolar molecules, r, Distance of separation between 2 molecules; rm, separation distance where intermolecular forces change sign, i.e., repellent to attractive or vice versa; υ, maximum energy of attraction between pair of molecules; σ, collision diameter.From Bird et al. 2 Figure 3. Axisymmetric container segment of length dz with variable cross‐sectional area (A). Diffusion takes place in this container. N, molar flux with respect to stationary frame of reference. Figure 4. Diagrams illustrating principle of random‐walk method. A: from point X the “particle” in a random walk may take a step to neighboring point X1, X2, or X3 with probabilities P(1, X), P (2, X), and P(3, X), respectively. It may also terminate its walk with probability P(0, X). B: points X and X1 are surrounded by volumes V(X) and V(X1) and area of contact A(X, X1) can be assigned. Particles that move through area A(X, X1) in a unit of time are named M(X, X1).From Stibitz 42 Figure 5. Diffusion of Ar in an H2‐CH4‐Ar system. Although there is initially no gradient in Ar concentration, Ar will move transiently from CH4 side toward H2 side. Mole Fr. Diff., molar fractional difference.Data from Arnold and Toor 1 Figure 6. Fluxes of CO2 as function of the change in partial pressure of CO2 (). Nitrogen mixture passes through origin, deviating little from binary behavior; He mixture displays strong effect of multicomponent diffusion; SF6 mixture has moderate multicomponent behavior.Adapted from Chang et al. 8
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