Dynamics of filaments and membranes in a viscous fluid

TL;DR

This paper develops a comprehensive mathematical framework for modeling the motion of filaments and membranes in viscous fluids, emphasizing geometric and variational methods, with applications to biopolymer dynamics and membrane instabilities.

Contribution

It introduces a full nonlinear set of equations of motion for curves and surfaces in viscous fluids, incorporating geometric and hydrodynamic considerations, with specific case studies.

Findings

Analysis of twirling instability in elastic rods

Study of pearling and buckling in liposomes

Demonstration of geometric variational methods

Abstract

Motivated by the motion of biopolymers and membranes in solution, this article presents a formulation of the equations of motion for curves and surfaces in a viscous fluid. We focus on geometrical aspects and simple variational methods for calculating internal stresses and forces, and we derive the full nonlinear equations of motion. In the case of membranes, we pay particular attention to the formulation of the equations of hydrodynamics on a curved, deforming surface. The formalism is illustrated by two simple case studies: (1) the twirling instability of straight elastic rod rotating in a viscous fluid, and (2) the pearling and buckling instabilities of a tubular liposome or polymersome.