# Frequency-dependent higher-order Stokes singularities near a planar elastic boundary: implications for the hydrodynamics of an active microswimmer near an elastic interface

## TL;DR

This paper develops an analytical hydrodynamic model describing how active microswimmers interact with elastic interfaces, revealing the influence of shear and bending resistance on their velocities and transient dynamics.

## Contribution

It introduces a novel theoretical framework modeling microswimmers as higher-order Stokes singularities near elastic boundaries, highlighting the effects of elastic properties on their motion.

## Key findings

- Velocities decompose into shear and bending contributions.
- Bending resistance has a more pronounced effect on transient velocities.
- Near elastic interfaces, velocities approach those near rigid walls in steady state.

## Abstract

The emerging field of self-driven active particles in fluid environments has recently created significant interest in the biophysics and bioengineering communities owing to their promising future biomedical and technological applications. These microswimmers move autonomously through aqueous media where under realistic situations they encounter a plethora of external stimuli and confining surfaces with peculiar elastic properties. Based on a far-field hydrodynamic model, we present an analytical theory to describe the physical interaction and hydrodynamic couplings between a self-propelled active microswimmer and an elastic interface that features resistance toward shear and bending. We model the active agent as a superposition of higher-order Stokes singularities and elucidate the associated translational and rotational velocities induced by the nearby elastic boundary. Our results show that the velocities can be decomposed in shear and bending related contributions which approach the velocities of active agents close to a no-slip rigid wall in the steady limit. The transient dynamics predict that contributions to the velocities of the microswimmer due to bending resistance are generally more pronounced than to shear resistance. Our results provide insight into the control and guidance of artificial and synthetic self-propelling active microswimmers near elastic confinements.