Dynamic model and stationary shapes of fluid vesicles

TL;DR

This paper introduces a phase-field model for fluid vesicles that accurately captures their shapes and dynamics, aligning with classical energy minimization results and enabling analysis of complex instabilities.

Contribution

A novel phase-field model for fluid vesicles derived from the Canham-Helfrich energy, capable of simulating stationary shapes and dynamic evolution.

Findings

Model reproduces known vesicle shapes

Dynamic evolution towards stationary states confirmed

Potential for studying complex vesicle instabilities

Abstract

A phase-field model that takes into account the bending energy of fluid vesicles is presented. The Canham-Helfrich model is derived in the sharp-interface limit. A dynamic equation for the phase-field has been solved numerically to find stationary shapes of vesicles with different topologies and the dynamic evolution towards them. The results are in agreement with those found by minimization of the Canham-Helfrich free energy. This fact shows that our phase-field model could be applied to more complex problems of instabilities.