THERMAL EFFECTS IN THE DESCRIPTION OF A MULTICOMPONENT MIXTURE USING THE DENSITY-FUNCTIONAL METHOD

The use of a model, based on an expression for the total entropy in th e form of a functional with the temperature and density gradients of t he components, is proposed to describe a multicomponent, multiphase sy stem using continuous hydrodynamics (that is, within the framework of the approach of the continuum mechanics without discontinuities in the hydrodynamic quantities). It is proved that this model is consistent with the zeroth law of thermodynamics. Expressions for the stress tens or, the diffusion fluxes and the heat flux are found from the conditio n that the entropy production is non-negative. Compared with the class ical Newton, Fick and Four er laws, these expressions contain third-or der spatial derivatives. The problem of a mixture between two parallel and impermeable walls at different temperatures is analysed. In this case, the system of dynamic equations reduces to a system of ordinary differential equations. It is shown that the number of free parameters , on which the solution depends, corresponds to the number of boundary and general integral conditions. (C) 1998 Elsevier Science Ltd. All r ights reserved.