Diffusion unsteady binary

Unsteady Binary Fickian Diffusion with No Convection (Optional)... 

The simplified equation (for the general equations, see Section IV, L) in the case of unsteady-state diffusion with a simultaneous chemical reaction in isothermal, incompressible dilute binary solutions with constant p and D and with coupled phenomena neglected is... 

For a binary system, under conditions of small mass transfer fluxes, the unsteady-state diffusion equations may be solved to give the fractional approach to equilibrium F defined by (see Clift et al., 1978)... 

This section contains a simple introduction to steady state and unsteady species mole (mass) diffusion in dilute binary mixtures. First, the physical interpretations of these diffusion problems are given. Secondly, the physical problem is expressed in mathematical terms relating the concentration profiles to the diffusion fluxes. Emphasis is placed on two diffusion problems that form the basis for the interfacial mass transfer modeling concepts used in reaction engineering. 

Because of the symmetry of the problem, we employ the binary, unsteady, axially symmetric convective diffusion equation with a constant diffusion coefficient ... 

To illustrate the combination of rate and equilibrium principles, we next consider a widely used separation method, which is inherently unsteady packed bed adsorption. We imagine a packed bed of finely granulated (porous) solid (e.g., charcoal) contacting a binary mixture, one component of which selectively adsorbs (physisorption) onto and within the solid material. The physical process of adsorption is so fast relative to other slow steps (diffusion within the solid particle), that in and near the solid particles, local equilibrium exists... 

A general equation can be derived for a binary mixture of A and B for diffusion and convection that also includes the terms for unsteady-state diffusion and chemical reaction. Wc shall make a mass balance on component A on an element Ax Ay Az fixed in space as shown in Pig. 7.5-1. The general mass balance on A is... 

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