Numerical study on topological change of viscous fingering induced by a phase separation with Korteweg force

Abstract

We develop coupled evolution equations for viscous fingering (VF) and phase separation in partially miscible systems by combining a simple double-well thermodynamic free energy and Korteweg force with a classical miscible VF model for a binary system. The VF pattern transition into a droplet formation pattern by the spinodal decomposition effect is demonstrated, and the simultaneous increases in the depth of the energy minimum, in the difference in the equilibrium concentrations, and in the Korteweg force, enhance the droplet growth. The pattern's interfacial length increases with the spinodal decomposition effects. These results match the corresponding experimental results.