Spinodal decomposition of colloids in the intermediate stage

Abstract

Spinodal decomposition in the initial and intermediate stage is described on the basis of the Smoluchowski equation, “the Liouville equation for Brownian systems”. For the intermediate stage, where a dominant length scale exists, a general scaling relation for the static structure factor is derived: the scattered intensity divided by the cubed dominant length and the second moment of the intensity should be time independent. The corresponding dynamic scaling function is found from the non-linear equations of motion for the structure factor as derived from the Smoluchowski equation. It turns out that this dynamic scaling function is universal in the sense that it is independent of the kind of colloid and the quench parameters. The scaling function in the intermediate stage is much sharper than the well known Furukawa scaling function which applies to the late stage. The time dependence of the wavevector where the scattered intensity is maximum is found to follow power law behaviour, with an exponent in (0.2,1.1), depending on the relative importance of hydrodynamic interaction, which is set by the quench parameters.