Geometry and dynamics of lipid membranes: The Scriven--Love number

TL;DR

This paper introduces the Scriven--Love number, a new dimensionless parameter that characterizes the relative importance of viscous and elastic forces in lipid membrane dynamics across different geometries.

Contribution

The study derives and analyzes the Scriven--Love number, providing a new framework for understanding force balances in lipid membranes and highlighting the significance of viscous effects.

Findings

The Scriven--Love number compares viscous and elastic forces in membranes.

Large Scriven--Love numbers indicate viscous forces dominate membrane response.

The number varies across biological processes, affecting membrane dynamics analysis.

Abstract

The equations governing lipid membrane dynamics in planar, spherical, and cylindrical geometries are presented here. Unperturbed and first-order perturbed equations are determined and non-dimensionalized. In membrane systems with a nonzero base flow, perturbed in-plane and out-of-plane quantities are found to vary over different length scales. A new dimensionless number, named the Scriven--Love number, and the well-known F\"oppl--von K\'arm\'an number result from a scaling analysis. The Scriven--Love number compares out-of-plane forces arising from the in-plane, intramembrane viscous stresses to the familiar elastic bending forces, while the F\"oppl--von K\'arm\'an number compares tension to bending forces. Both numbers are calculated in past experimental works, and span a wide range of values in various biological processes across different geometries. In situations with large Scriven--Love and F\"oppl--von K\'arm\'an numbers, the dynamical response of a perturbed membrane is dominated by out-of-plane viscous and surface tension forces---with bending forces playing a negligible role. Calculations of non-negligible Scriven--Love numbers in various biological processes and in vitro experiments show in-plane intramembrane viscous flows cannot generally be ignored when analyzing lipid membrane behavior.