A diffuse interface model for two-phase ferrofluid flows

TL;DR

This paper introduces a phase field-based diffuse interface model for two-phase ferrofluid flows, along with an energy-stable numerical scheme, demonstrating stability, convergence, and the ability to replicate key ferrofluid phenomena.

Contribution

It presents a novel, energy-stable numerical scheme for a simplified ferrofluid model, with proven stability, convergence, and solution existence.

Findings

Model captures Rosensweig instability

Numerical scheme is energy-stable and convergent

Simulations demonstrate basic ferrofluid behaviors

Abstract

We develop a model describing the behavior of two-phase ferrofluid flows using phase field-techniques and present an energy-stable numerical scheme for it. For a simplified, yet physically realistic, version of this model and the corresponding numerical scheme we prove, in addition to stability, convergence and as by-product existence of solutions. With a series of numerical experiments we illustrate the potential of these simple models and their ability to capture basic phenomenological features of ferrofluids such as the Rosensweig instability.