A comparison of Cahn-Hilliard and Navier-Stokes-Cahn-Hilliard models on manifolds

TL;DR

This paper compares the Cahn-Hilliard and Navier-Stokes-Cahn-Hilliard models for simulating phase separation on complex, evolving lipid membrane surfaces using an unfitted finite element method, highlighting the impact of lateral flow.

Contribution

It introduces a flexible numerical approach to compare phase separation models on complex surfaces, incorporating lateral flow effects with an unfitted finite element method.

Findings

Lateral flow influences phase pattern evolution.

Variable membrane properties affect phase separation.

The method effectively handles complex, evolving geometries.

Abstract

We consider phase-field models with and without lateral flow for the numerical simulation of lateral phase separation and coarsening in lipid membranes. For the numerical solution of these models, we apply an unfitted finite element method that is flexible in handling complex and possibly evolving shapes in the absence of an explicit surface parametrization. Through several numerical tests, we investigate the effect of the presence of lateral flow on the evolution of phases. In particular, we focus on understanding how variable line tension, viscosity, membrane composition, and surface shape affect the pattern formation. Keywords: Lateral phase separation, surface Cahn-Hilliard equation, lateral flow, surface Navier-Stokes-Cahn-Hilliard system, TraceFEM