Descriptions of membrane mechanics from microscopic and effective two-dimensional perspectives

TL;DR

This paper develops and connects microscopic and effective two-dimensional models of membrane mechanics, providing insights into how inhomogeneous properties relate to simplified surface descriptions and their associated stresses.

Contribution

It introduces a framework linking microscopic and effective membrane mechanics, clarifying how inhomogeneous properties influence surface-level mechanical descriptions.

Findings

Established a connection between microscopic and effective membrane models.

Analyzed the dependence of free energy variations on membrane deformations.

Explored how effective stresses derive from free energy functionals.

Abstract

Mechanics of fluid membranes may be described in terms of the concepts of mechanical deformations and stresses, or in terms of mechanical free-energy functions. In this paper, each of the two descriptions is developed by viewing a membrane from two perspectives: a microscopic perspective, in which the membrane appears as a thin layer of finite thickness and with highly inhomogeneous material and force distributions in its transverse direction, and an effective, two-dimensional perspective, in which the membrane is treated as an infinitely thin surface, with effective material and mechanical properties. A connection between these two perspectives is then established. Moreover, the functional dependence of the variation in the mechanical free energy of the membrane on its mechanical deformations is first studied in the microscopic perspective. The result is then used to examine to what extent different, effective mechanical stresses and forces can be derived from a given, effective functional of the mechanical free energy.