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On the modified Fick law and its potential applications

Piekarski S.

Journal of Technical Physics

2003

Vol. 44, no 2

125-131

It can be observed that the standard Einstein-Smoluchowski equation for isothermal processes can be written in the two equivalent forms which, however, become distinct when the temperature becomes spatially varying. Therefore, we have two different equations which could potentially describe the flux of diffusing particles subjected to the potential external forces and variable temperature. The first is the standard Einstein-Smoluchowski equation, while the second is its modification containing an additional term proportional to the temperature gradient. In order to fix the terminology, the above mentioned modification of standard Einstein-Smoluchowski equation shall be called '^the modified Fick law". In this paper, we shall discuss the origin of this equation and we shall try to make a preliminary discussion of its solutions and potential applications to thermodiffusion. We propose two models: one exploiting Onsager's thermodynamics and the second one independent from it. Elementary solutions of both models are identical in the limit of small concentrations.