A memory function equation approach to the kinetics of spinodal decomposition in the very early linear regime

The equations of Metiu, Kitahara and Ross for the kinetics of the spinodal decomposition are generalized in both time and space by using the idea of a memory function. Reinterpretation is given as to how correlations between the change in densities, at different time and spatial points will affect the kinetics of the phase separation. This new interpretation leads to an additional curvature in the spectrum of the observed rate of spinodal decomposition. Our generalized theory is in qualitative agreement with (i) the Boltzman equation approach of Nonnenmacher if a simple memory function is inserted and (ii) the result of Kawasaki and coworkers, namely that a time-dependent rate is found when a persistent range of time correlation is introduced. If persistent spatial correlation is introduced, we predict a divergent behavior of the rate constant at small k. This divergent behavior is also seen in the linearized hydrodynamics approach of Haus and Kitahara.