Swimming trajectories of a three-sphere microswimmer near a wall

Abstract

The hydrodynamic flow field generated by self-propelled active particles and swimming microorganisms is strongly altered by the presence of nearby boundaries in a viscous flow. Using a simple model three-linked sphere swimmer, we show that the swimming trajectories near a no-slip wall reveal various scenarios of motion depending on the initial orientation and the distance separating the swimmer from the wall. We find that the swimmer can either be trapped by the wall, completely escape, or perform an oscillatory gliding motion at a constant mean height above the wall. Using a far-field approximation, we find that, at leading order, the wall-induced correction has a source-dipolar or quadrupolar flow structure where the translational and angular velocities of the swimmer decay as inverse third and fourth powers with distance from the wall, respectively. The resulting equations of motion for the trajectories and the relevant order parameters fully characterize the transition between the states and allow for an accurate description of the swimming behavior near a wall. We demonstrate that the transition between the trapping and oscillatory gliding states is first order discontinuous, whereas the transition between the trapping and escaping states is continuous, characterized by non-trivial scaling exponents of the order parameters. In order to model the circular motion of flagellated bacteria near solid interfaces, we further assume that the spheres can undergo rotational motion around the swimming axis. We show that the general three-dimensional motion can be mapped onto a quasi-two-dimensional representational model by an appropriate redefinition of the order parameters governing the transition between the swimming states.

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

“…2 (l). This naturally leads in the absence of external trapping to an overall "swimming in circles", as has been previously reported for E. coli near walls 84,180 and explained via corresponding theoretical studies that include phenomenological representations of the rotating flagella 81,181 . As this component vanishes for the other singularities discussed above, we thus expect the introduction of a rotlet dipole to be the simplest possible hydrodynamic modeling of this circling behavior near surfaces.…”

A general perturbative approach for bead-based microswimmers reveals rich self-propulsion phenomena

“…Calculating the swimming velocity to leading order in the extension of the arms gives rise to a simple intuition for the swimmer's speed: the displacement of the swimmer corresponding to one swimming stroke is proportional to the area enclosed by the swimmer's trajectory in the conformation space [13]. This model has been used to investigate the hydrodynamic properties of microswimmers, including the flow fields they produce and their mutual interaction [23][24][25], as well as the interaction of a swimmer with a wall [26,27].…”

Dynamics of a simple model microswimmer in an anisotropic fluid: Implications for alignment behavior and active transport in a nematic liquid crystal

“…In Appendix B, we show some analytical calculations for the distances traveled by a microswimmer during reorientation. We then quantify in Appendix C the fluid-mediated hydrodynamic interactions between colloidal particles which could serve as a basis for future investigations of the behavior of special particle-based microswimmer models [134][135][136][137][138][139][140][141][142][143][144] .…”