On the mobility of extended bodies in viscous films and membranes

TL;DR

This paper introduces methods to calculate the mobility of extended bodies in membranes and films, revealing unique local drag behaviors for certain motions and applicable to biological and viscoelastic systems.

Contribution

It presents novel computational methods for mobility in membranes, highlighting differences from bulk fluids and extending to viscoelastic systems.

Findings

Purely local drag for rotations and perpendicular motion of rods

Algebraic dependence of drag coefficient on rod dimensions

Methods applicable to biological membranes and viscoelastic materials

Abstract

We develop general methods to calculate the mobilities of extended bodies in (or associated with) membranes and films. We demonstrate a striking difference between in-plane motion of rod-like inclusions and the corresponding case of bulk (three-dimensional) fluids: for rotations and motion perpendicular to the rod axis, we find purely local drag, in which the drag coefficient is purely algebraic in the rod dimensions. These results, as well as the calculational methods are applicable to such problems as the diffusion of objects in or associated with Langmuir films and lipid membranes. The methods can also be simply extended to treat viscoelastic systems.