Existence of weak solutions for a non-classical sharp interface model for a two-phase flow of viscous, incompressible fluids

TL;DR

This paper introduces a novel sharp interface model for two-phase viscous flow that incorporates diffusional effects, proving the existence of weak solutions and analyzing interface properties, advancing understanding beyond classical models.

Contribution

It presents a new coupled Navier-Stokes and Mullins-Sekerka type model with proven long-time weak solution existence, addressing an open problem in classical two-phase flow models.

Findings

Proved long-time existence of weak solutions.

Interfaces possess generalized mean curvature.

Model coincides with the asymptotic limit of diffuse interface models.

Abstract

We introduce a new sharp interface model for the flow of two immiscible, viscous, incompressible fluids. In contrast to classical models for two-phase flows we prescribe an evolution law for the interfaces that takes diffusional effects into account. This leads to a coupled system of Navier-Stokes and Mullins-Sekerka type parts that coincides with the asymptotic limit of a diffuse interface model. We prove the long-time existence of weak solutions, which is an open problem for the classical two-phase model. We show that the phase interfaces have in almost all points a generalized mean curvature.