Diffuse interface tracking of immiscible fluids: Improving phase continuity through free energy density selection

Diffuse interface (DI) tracking methods frequently adopt the double-well energy density function to describe the free energy variation across an interface, leading to phase interpenetration and spontaneous drop shrinkage when applied to immiscible two-phase systems. While the observed continuity losses can be limited by constraints placed on the interfacial width and mobility parameter, the associated increase in computational cost and mesh requirements has limited DI methods to 2D planar and axi-symmetric flow. Using the proposed temperature-variant simplified energy density function (TVSED), the effect of the metastable thermodynamic region on phase continuity is examined using a reduced temperature parameter, T(R). The solutions obtained by the proposed DI implementation and a volume-of-fluid (VOF) based solver are discussed for two common benchmark simulations (collapse of a column of water, and droplet deformation/relaxation in simple shear). While comparable solutions are obtained from the T(R) = 0 and VOF simulations; the large metastable region of the more commonly used double-well function (T(R) = 1) promoted inter-mixing in the bulk phases, diluting the inertia transferred between impacting fluids and under-predicting deformation in shear. The fundamental mechanisms responsible for spontaneous drop shrinkage are eliminated at T(R) = 0, allowing for constraints on the interfacial width and mobility to be relaxed. The comparable performance of T(R) = 0 and VOF simulations is a promising indication of the potential for application to complex 3D flows at reduced mesh resolution relative to existing DI methods. Crown Copyright (c) 2011 Published by Elsevier Ltd. All rights reserved.