Dynamics of phase separation of a simple fluid mixture: Comparison between molecular dynamics and numerical integration of the phenomenological equation

The dynamics of phase separation of fluid mixture is discussed. Numerical simulations in two dimensions are done both by means of the molecular dynamics at constant temperature and by the numerical integration of a phenomenological kinetic equation. Using a simplified interparticle potential, we find that final results in the molecular dynamics are seriously affected by numerical errors. The growth exponent of phase-separating domains varies from 1/3 to 2/3 due to the numerical errors for a low-viscosity fluid mixture with a critical composition. The exponent 2/3 is observed in the case where the numerical error is ineffective. On the other hand, the numerical error in the numerical integration of the phenomenological equation is not serious, and we obtain the growth exponent 2/3; as has been observed by many other similar numerical analyses. We also discuss possibilities of new growth exponents that are simultaneously associated with the inertia and the dissipation.