On self similarity and coarsening rate of a convecting bicontinuous phase separating mixture: effect of the viscosity contrast

Abstract

We present a computational study of the hydrodynamic coarsening in 3D of a critical mixture using the Cahn-Hilliard/Navier-Stokes model. The topology of the resulting intricate bicontinuous microstructure is analyzed through the principal curvatures to prove self-similar morphological evolution. We find that the self similarity exists for both systems: iso-viscous and with variable viscosity. However the two system have distinct topological character. Our simulations confirm that the predicted viscous growth regime exists in both cases. Moreover the coarsening rate is inversely proportional to an \textit{effective viscosity} that is the geometrical average of the viscosities of the two phases.