Motion of objects embedded in lipid bilayer membranes: advection and effective viscosity

TL;DR

This paper introduces a numerical method using a regularized Stokeslet scheme to predict the motion of objects within lipid bilayer membranes and estimates their effective surface viscosity under flow conditions.

Contribution

It presents a novel numerical approach for modeling object motion in membranes and provides new predictions for effective viscosity in dilute suspensions.

Findings

The scheme accurately predicts velocities and rotations in complex flows.

Effective viscosity predictions align with some prior analytical models.

New viscosity estimates for rod-shaped membrane inclusions are provided.

Abstract

An interfacial regularized Stokeslet scheme is presented to predict the motion of solid bodies (e.g. proteins or gel-phase domains) embedded within flowing lipid bilayer membranes. The approach provides a numerical route to calculate velocities and angular velocities in complex flow fields that are not amenable to simple Fax\'en-like approximations. Additionally, when applied to shearing motions, the calculations yield predictions for the effective surface viscosity of dilute rigid body-laden membranes. In the case of cylindrical proteins, effective viscosity calculations are compared to two prior analytical predictions from the literature. Effective viscosity predictions for a dilute suspension of rod-shaped objects in the membrane are also presented.