Microswimmers near corrugated, periodic surfaces

TL;DR

This paper derives exact formulas for how microswimmers are affected by rough, periodic surfaces, revealing complex velocity behaviors that depend on surface wavelength and shape, with implications for biological and microfluidic systems.

Contribution

It introduces a theoretical framework using the Lorentz reciprocal theorem to quantify roughness effects on microswimmer velocities near arbitrary surfaces.

Findings

Roughness-induced velocities vary non-monotonically with surface wavelength.

Pusher microswimmers can experience repulsive forces near certain surface features.

Flow reflection at surface cavities reduces attraction to the wall.

Abstract

We explore hydrodynamic interactions between microswimmers and corrugated, or rough, surfaces, as found often in biological systems and microfluidic devices. Using the Lorentz reciprocal theorem for viscous flows we derive exact expressions for the roughness-induced velocities up to first order in the surface-height fluctuations and provide solutions for the translational and angular velocities valid for arbitrary surface shapes. We apply our theoretical predictions to elucidate the impact of a periodic, wavy surface on the velocities of microswimmers modeled in terms of a superposition of Stokes singularities. Our findings, valid in the framework of a far-field analysis, show that the roughness-induced velocities vary non-monotonically with the wavelength of the surface. For wavelengths comparable to the swimmer-surface distance a pusher can experience a repulsive contribution due to the reflection of flow fields at the edge of a surface cavity, which decreases the overall attraction to the wall.