Three Contributions to q in Binary Systems

For mixtures of A and B, there are two first-rank tensorial fluxes, —(q — (pp pfl and -Ja, that are coupled to two first-rank tensorial forces, (l/T jVT and (l/r)[V A + (gB — gA)] via linear transport laws. These fluxes and forces are chosen such that their products correspond to specific terms in the final expression for the rate of entropy generation per unit volume of fluid, sq. The linear laws are (see equations 25-58)  

These linear laws can be written more concisely as 

The Onsager reciprocal relation for the 2 x 2 matrix of phenomenological coupling coefficients is 

The molecular flux of thermal energy, given by equation (26-5), is rearranged as follows  

This inequality in (26-11) stems from the fact that the determinant of the 2 x 2 matrix of phenomenological transport coefficients [, y] mnst be positive to ensure a positive-definite quadratic form for sq- The contribution from thermal Soret diffusion in the final expression for Ja (see equations 25-76 and 25-77) provides a definition of P in terms of the thermal diffusion coefficient kr and the temperature dependence of cpA- 

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