Two-phase flow problem coupled with mean curvature flow

TL;DR

This paper proves the existence of solutions for a complex two-phase flow model where the interface evolves with mean curvature and fluid flow, using an approximation scheme combining Galerkin and phase field methods.

Contribution

It introduces a new existence proof for two-phase non-Newtonian flow with mean curvature-driven interface evolution in 2D and 3D.

Findings

Existence of generalized solutions established.

Effective approximation scheme combining Galerkin and phase field methods.

Model captures interface motion with mean curvature and surface tension.

Abstract

We prove the existence of generalized solution for incompressible and viscous non-Newtonian two-phase fluid flow for spatial dimension 2 and 3. The phase boundary moves along with the fluid flow plus its mean curvature while exerting surface tension force to the fluid. An approximation scheme combining the Galerkin method and the phase field method is adopted.