Asymmetric Stokes flow induced by a transverse point-force acting near a finite-sized elastic membrane

TL;DR

This paper develops a theoretical model for the flow field caused by a point-force near a finite elastic membrane, revealing how membrane properties influence hydrodynamics and particle drag, with implications for nanocarrier design.

Contribution

It introduces a new elastohydrodynamic framework for analyzing flow near elastic membranes, decoupling shear and bending effects, and explores their impact on particle mobility.

Findings

Shear and bending effects decouple linearly.

Flow solutions obtained via superposition of shear and bending contributions.

Translational speed near elastic membranes can exceed bulk fluid speeds.

Abstract

A deep understanding of the physical interactions between nanoparticles and target cell membranes is important in designing efficient nanocarrier systems for drug delivery applications. Here, we present a theoretical framework to describe the hydrodynamic flow field induced by a point-force singularity (Stokeslet) directed parallel to a finite-sized elastic membrane endowed with shear and bending rigidities. We formulate the elastohydrodynamic problem as a mixed-boundary-value problem, which we then reduce into a well-behaved system of integro-differential equations. It follows that shear and bending linearly decouple so that the solution of the overall flow problem can be obtained by linear superposition of the contributions arising from these modes of deformation. Additionally, we probe the effect of the membrane on the hydrodynamic drag acting on a nearby particle, finding that, in a certain range of parameters, translational motion near an elastic membrane with only energetic resistance toward shear can, surprisingly, be sped up compared to bulk fluid. Our results may find applications in microrheological characterizations of colloidal systems near elastic confinements.