Non-linear isotopic diffusion in dense fluids

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Abstract
A binary uncharged isotopic mixture at liquid density is described by the state variables M1 and M2, the component masses, volume V and temperature T. To these, in an extended irreversible thermodynamic treatment, is added the diffusion flow Jd. In the framework of this approach, a kinetic equation relates Jd to the driving force, - Del T( mu 1- mu 2), where the mu i are chemical potentials and T is kept constant in computing the gradient. To calculate the coefficient gamma of this force, a microscopic model is adduced which expresses gamma in terms of Pxx, the pressure tensor. Evaluation of gamma and application of reciprocity permits the calculation of Phi , the thermodynamic force associated with Jd. Once Phi is known, integrability conditions for the Helmholtz function yield the O(Jd2) terms in the pressure P and the mu i. From these results and an estimate from computer simulations of the relaxation time for Jd, the authors obtain D2 in the diffusion coefficient, D=D0+D2Jd2. Estimates for a hard-sphere model representing a mixture of 36Ar and 40Ar predict that all the Jd2 terms in D,P, mu i are negligible unless mod Jd mod >or approximately=104 kg m-2 S-1 at liquid density.