A phase field model of capillarity

Abstract

The phenomenological derivation of a phase field model of capillarity that accounts for the structure of an interfacial layer formed by two immiscible incompressible liquids is addressed. A rheological expression for the reversible component of capillary stresses is obtained in terms of the free energy of a binary fluid, which depends on the absolute temperature, composition, and gradient of composition. This model can be applied to those flows that involve change of topology of a capillary interface, such as coalescence and breakup of drops. As an illustration, an equilibrium of a binary fluid with either a flat or spherical interfacial layer is analyzed, and a thermocapillary flow in an infinite gap is considered.

Calculation of Two-Phase Navier–Stokes Flows Using Phase-Field Modeling

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“…This smoothing allows conventional numerical approximations of interface kinematics on fixed grids. The method has been used for investigating the problems governed by Navier-Stokes equations (Antanovskii, 1995;Jacqumin, 1996).…”

Stokes–Cahn–Hilliard formulations and simulations of two-phase flows with suspended rigid particles

“…This capillary stress can be derived using a variational procedure, and yields a stress Àjrcrc plus an isotropic term which can be absorbed in the pressure [6]. Furthermore, we follow [20,21], where an isotropic term is added to the capillary stress to ensure that the capillary stresses are parallel to the interface, which yields…”