A generalized diffusion equation for nonuniform fluid systems, with application to spinodal decomposition

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Abstract
Using a recent microscopic theory to describe the thermodynamics of nonuniform fluids, we develop a generalized diffusion equation which may be used to study phase separation. The linear approximation of this diffusion equation is identical in form to Cahn’s diffusion equation in his study of spinodal decomposition, but the amplification factor is quantitatively different and may be evaluated from the microscopic properties of the uniform fluid state. Predictions of the amplification factor are presented for a single component Lennard-Jones fluid at different points in the spinodal region.