A Smoluchowski equation approach to the spinodal instability and initial decomposition kinetics in colloidal systems

Abstract The spinodal instability and the initial phase-separation kinetics in colloidal systems, consisting of spherically symmetric Brownian particles, is treated on the basis of the Smoluchowski equation, with an appropriate closure for the pair-correlation function. A microscopic expression for the wavevector dependent effective diffusion coefficient in terms of the pair-interaction potential and pair-correlation function for the colloidal particles is derived. The closure relation that is used is estimated to yield numerical results for the effective diffusion coefficient which are accurate to within 10%. For the spinodal instability at infinite wavelength, the well-known thermodynamic criterion is found. Furthermore, the Cahn-Hilliard result is recovered for pair-interaction potentials which are decaying sufficiently rapid. However, for certain slowly decaying pair-interaction potentials the square-gradient approximation fails. The approach described here opens the way to study the influence on the decomposition kinetics of hydrodynamic interactions between colloidal particles and of external fields like a shear flow.