Equations for the diffusive flux Ficks law

This expression for the diffusive flux can be obtained more rigorously by considering the velocities of individual species in a multi-component system. The mass average flux of component A in a mixture, 7a is defined based on the velocity of the species of interest, vX, relative to the mass average velocity of the 

For more complete definitions, the derivation of conservation of mass equations, and application of these equations in conventional chemical engineering analysis, the reader is referred to the classical textbook on transport phenomena [5]. The notation used in the present text follows the notation by Bird et al. 

Equation 3-19 defines the diffusion coefficient Da, but is inconvenient for many calculations since the flux is defined with respect to a moving coordinate system. For binary systems, JaIS simply related to the mass flux of A with respect to a stationary coordinate system, rt  

The mass flux a the sum of the diffusive flux 7a which accounts for the movement of A due to concentration gradients, and the quantity o)a( a + B) which accounts for the movement of A due to bulk motion of the fluid. Equation 3-20 is the appropriate form of the diffusive flux equation to use for most engineering problems, since quantities are usually measured with respect to some fixed frame of reference. For many of the problems considered here, A is a dilute species in water, in which case coa 0 and the bulk motion term can be neglected. 

Molecules of A can enter through any face of the volume element they can be generated or consumed within the volume by chemical reaction they can accumulate within the volume. A general balance equation (in — out -E generation = accumulation) yields  

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