On the Kinetic Equations for Binary Mixtures

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Abstract
We examined master equations for diffusion processes and propose that the transition probability is proportional to the number of particles of diffusing species, multiplied by the factor exp[− {E(f) − E(i)} /2kBT], which describes the ease of the transition as a function of the energy difference between the final and the initial states. In the case of a binary mixture, the resulting kinetic equation becomes where ρ is the local density of a component, ρ0 is the total density and F is the free energy functional. Due to the factor ρ (ρ0−ρ), there is a situation in which the phase separation rate slows down at later stage of a deep quenching case. On the other hand, in the neighborhood of the critical point, this factor can be replaced by a constant.

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