Statistical thermodynamics of material transport in non-isothermal binary systems

Abstract

The material transport equations derived by non-equilibrium thermodynamics are used to describe the material transport in binary non-isothermal molecular systems. The chemical potentials of the components used in the equations are calculated using statistical mechanics. As the material transport equations contain chemical potentials at constant pressure, the local pressure distribution necessary in calculations is obtained using the condition of the local thermodynamic equilibrium around the selected molecular particle. The Laplace contribution to the local pressure distribution within the layer of the liquid around the particle is accounted. The calculations yield the results equivalent to previous approaches and add new terms to the Soret coefficient, which are related to the difference in the translational and rotational thermal motion between the molecules. The kinetic contribution to thermodiffusion explains the isotope thermodiffusion effect, the role of the molecular symmetry, and the sign change in thermodiffusion observed in binary systems. The proposed theory describes thermodiffusion in binary molecular systems with a limited miscibility.

Comparative Examination of Nonequilibrium Thermodynamic Models of Thermodiffusion in Liquids

“…Finally, Equation (25) with zero off-diagonal kinetic coefficients is used to derive an expression for material flux in [16], where the pressure gradient is determined by the general Gibbs-Duhem equation [Equation 7]:…”

“…All of these arrangements begin with the same expression for entropy production, but yield different expressions for the component concentration distributions in a temperature gradient. Each of these expressions except [16] assume constant pressure and could, therefore, be improved by using the general form of the Gibbs-Duhem equation for the pressure gradient (Equation 7). Nevertheless, not all approaches can be valid, since they produce significantly different results.…”

“…The simplest example is isotope mass-and thermodiffusion, where a change in the center of mass is unavoidable even in absence of convection. Moreover, in deriving Equation (20) for entropy production, Equations (16) and (17) for the convection-free system are substituted into Equation 15, expressing the time derivative of the Gibbs equation. Such an approach is valid only for a hydrodynamically stable and closed system, where net material flux is zero.…”

“…, and k dn dt can be substituted for their respective partial derivatives from Equations(16) and(17) in closed systems without any hydrodynamic flows, because the partial and total time derivatives are identical (see the explanations above Equation (2.8) in[3]). Substituting Equations(16) and(17) into Equation(15), and using the rule of differentiation for the product of scalar (thermodynamic force) and vector (thermodynamic flux), we obtain:…”

Statistical Thermodynamics of Material Transport in Non-Isothermal Mixtures

“…In this section we present the results obtained in (Semenov, 2011). In a binary system in which the component concentrations are comparable, the material transport equations defined by Eq.…”