Fluid transport by active elastic membranes

TL;DR

This paper investigates how active internal forces within elastic membranes can induce shape changes and fluid transport, expanding understanding beyond prescribed deformation models by analyzing internally driven membrane dynamics.

Contribution

It introduces models where membrane deformation results from internal active stresses, providing asymptotic calculations of shape and fluid flow for small forcing amplitudes.

Findings

Active internal stresses can generate membrane deformation and fluid transport.

Asymptotic analysis yields explicit expressions for shape and flow velocities.

Scaling analysis confirms the asymptotic results.

Abstract

A flexible membrane deforming its shape in time can self-propel in a viscous fluid. Alternatively, if the membrane is anchored, its deformation will lead to fluid transport. Past work in this area focused on situations where the deformation kinematics of the membrane were prescribed. Here we consider models where the deformation of the membrane is not prescribed, but instead the membrane is internally forced. Both the time-varying membrane shape, and the resulting fluid motion, result then from a balance between prescribed internal active stresses, internal passive resistance, and external viscous stresses. We introduce two specific models for such active internal forcing: one where a distribution of active bending moments is prescribed, and one where active inclusions exert normal stresses on the membrane by pumping fluid through it. In each case, we asymptotically calculate the membrane shape and the fluid transport velocities for small forcing amplitudes, and recover our results using scaling analysis.