Diffusion With Bulk Flow And Chemical Reactions

In some practical diffusion problems involving the presence of catalysts, enzymes, or other reagents, the diffusing substance A may undergo a chemical reaction. In such a case, the general equation 8 is still valid. To solve this equation, the relationship between NA and NB, which depends on the type of chemical reaction, must be known. In the following sections it is demonstrated how equation 8 can be solved for some chemical reactions commonly observed in food systems.

In this case, if 1 mol of A is diffusing toward the reacting surface, there must be 1 mol of B diffusing away in the opposite direction (as long as Z is adequate on that surface). Substituting Na = —Nb into equation 8 and observing that

When equation 31 is used to describe diffusion of gases in solids, and because CA = PA/RT,

If the pores of the solid are very small compared to the mean free path of the gas, other types of diffusion may occur (2,3).

Diffusion in Nonideal Systems

Nonideal systems play an important role in food, biological, and life processes of humans, animals, plants, and microorganisms. In the presence of macromolecules in the system, interactions may occur between them and smaller molecules. Such phenomena cause the system to deviate from its ideal behavior, even though a true solution (e.g., colloids) might be formed. As a result, the mobility of the diffusing molecule changes unpredictably, even in dilute solutions. Diffusion in nonideal systems is complex and difficult to describe by theoretical models. Generally, it is assumed that the differential form of Fick's law applies the following equation is obtained.

Equation 35 is identical to equation 21 for equimolecular counterdiffusion. Solving equation 35 gives

If the reaction is instantaneous, no A exists on the reacting surface and XA2 = 0. Equation 36 then becomes

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