Vesicle model with bending energy revisited

TL;DR

This paper revisits the equations governing mechanical equilibrium in fluid membranes with bending energy, providing systematic tools for deriving shape equations and line conditions more efficiently.

Contribution

It introduces a new method based on the principle of virtual work to simplify the derivation of shape equations and line conditions in membrane models.

Findings

Simplified derivation of shape equations and line conditions.

Applicable to all problems involving surface energies.

Provides systematic tools for membrane shape analysis.

Abstract

The equations governing the conditions of mechanical equilibrium in fluid membranes subject to bending are revisited thanks to the principle of virtual work. The note proposes systematic tools to obtain the shape equation and the line condition instead of Christoffel symbols and the complex calculations they entail. The method seems adequate to investigate all problems involving surface energies.