Theoretical studies of phase-separation kinetics in a Brinkman porous medium

Abstract

Although the coarsening of binary fluid mixtures in porous media has been of great interest for some time, there are still no complete theories for describing the relevant mechanisms, and more theoretical work needs to be carried out. In this work, we have proposed a simple model for phase separation of binary fluids in a porous medium, where the Brinkman-extended-Darcy equation and Cahn-Hilliard equation are the dynamical constitutions. Using the dimensional analysis approach, our findings lead to the prediction of domain coarsening in a porous medium for several regimes, including the conventional power laws. In addition, we have found that slowed-down coarsening dynamics are caused by the hydrodynamic screening effect, which is governed by the logarithmic law for this regime. Our theoretical results are at least qualitatively consistent with previous reports using simulations or experiments. © 2010 IOP Publishing Ltd.