SPINODAL DECOMPOSITION IN COLLOIDAL SYSTEMS, WITH AND WITHOUT SHEAR-FLOW, DESCRIBED ON THE BASIS OF THE SMOLUCHOWSKI EQUATION

The spinodal instability and the initial decomposition kinetics Of colloidal systems, with and without a simple shear flow, are described on the basis of the Smoluchowski equation, ''the Liouville equation for Brownian systems''. Without shear flow,upon formally expanding certain wave vector dependent functions, the Cahn-Hilliard form for the effective diffusion coefficient is recovered. Also the usual thermodynamic criterion for spinodal instability follows from this Smoluchowski equation approach. It is argued that, on application of a shear flow, the location of the spinodal curve no longer coincides with the cloud-point curve. Furthermore, the decomposition dynamics is highly anisotropic (already for such small shear rates for which the deformation of the pair-correlation function can be neglected), in a way that is in agreement with experiments on a binary fluid mixture.