On the thermodiffusion equation for electrically charged matter

In this paper, we propose the thermodiffusion equation for electrically charged matter. It is a generalisation of the modified Fick law, which has been introduced in the paper: S. Piekarski, "On the modified Fick law and its potential applications" (J. Tech. Phys., 44, 2, 125-131, 2003). In the modified Fick law there exists a potential force acting on the diffusing matter which is described as the gradient of the potential U(x). Now we replace U(x) by U(x) - q[phi](x,t) where [phi] is the electrostatic potential, while q is the electric charge of a diffusing carrier. We write the corresponding field equations and consider the electromotive force induced by the temperature gradient. It is easy to compute this force under the assumption that the system is quasineutral. However, it seems that a more realistic model of the electromotive force induced by the temperature gradient should allow a deviation from quasineutrality. Both versions are compared and it is interesting whether the resulting expressions can be verified experimentally.