BGK models for diffusion in isothermal binary fluid systems

Two Bhatnagar-Gross-Krook (BGK) models for isothermal binary fluid systems- the classical single relaxation time model and a split collision term model -are discussed in detail, with emphasis on the diffusion process in perfect ly miscible ideal gases. Fluid equations, as well as the constitutive equat ion for diffusion, are derived from the Boltzmann equation using the method of moments and the values of the transport coefficients (viscosity and dif fusivity) are calculated. The Schmidt number is found to be equal to one fo r both models. The split collision term model allows the two fluid componen ts to have different Values of the viscosity, while the single relaxation t ime model does not have this characteristic. The value of the viscosity doe s not depend on the density in the split collision term model, as expected from the classical kinetic theory developed by Maxwell. Possible extension of BGK models to non-ideal gases and ideal solutions (where the Schmidt num ber is larger than 1) is also investigated. (C) 2001 Elsevier Science B.V. All rights reserved.