Microswimmers near corrugated, periodic surfaces

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.

References in corpus (10)

• Self-motile colloidal particles: from directed propulsion to random walk
• Anomalous transport in the crowded world of biological cells
• Hydrodynamic attraction of swimming microorganisms by surfaces
• Fluid dynamics and noise in bacterial cell-cell and cell-surface scattering
• Hydrodynamics of self-propulsion near a boundary: predictions and accuracy of far-field approximations
• Direct measurement of the flow field around swimming microorganisms
• Bacterial hopping and trapping in porous media
• Geometric capture and escape of a microswimmer colliding with an obstacle
• Hydrodynamic Mobility Reversal of Squirmers near Flat and Curved Surfaces
• Invariance properties of bacterial random walks in complex structures