Particle mobility between two planar elastic membranes: Brownian motion and membrane deformation

TL;DR

This study investigates how a particle moves between two elastic membranes, revealing complex hydrodynamic interactions, membrane deformation effects, and subdiffusive Brownian motion, supported by analytical and simulation results.

Contribution

It provides the first analytical and numerical analysis of particle mobility and membrane deformation between two elastic membranes, highlighting the coupling effects and limitations of superposition approximations.

Findings

Hydrodynamic mobility depends on motion frequency due to membrane elasticity.

Superposition approximation is valid only for parallel motion.

Presence of the second membrane reduces membrane deformation.

Abstract

We study the motion of a solid particle immersed in a Newtonian fluid and confined between two parallel elastic membranes possessing shear and bending rigidity. The hydrodynamic mobility depends on the frequency of the particle motion due to the elastic energy stored in the membrane. Unlike the single-membrane case, a coupling between shearing and bending exists. The commonly used approximation of superposing two single-membrane contributions is found to give reasonable results only for motions in the parallel, but not in the perpendicular direction. We also compute analytically the membrane deformation resulting from the motion of the particle, showing that the presence of the second membrane reduces deformation. Using the fluctuation-dissipation theorem we compute the Brownian motion of the particle, finding a long-lasting subdiffusive regime at intermediate time scales. We finally assess the accuracy of the employed point-particle approximation via boundary-integral simulations for a truly extended particle. They are found to be in excellent agreement with the analytical predictions.