Propulsion by passive filaments and active flagella near boundaries

TL;DR

This paper analytically investigates how boundaries influence the propulsion of passive filaments and active flagella, revealing complex effects depending on actuation type, flagellar properties, and boundary conditions, with implications for microorganism motility.

Contribution

It provides a detailed analytical framework to understand the boundary effects on propulsion of both passive and active filaments, highlighting nontrivial dependencies on physical and biological parameters.

Findings

Walls can increase or decrease propulsive forces depending on actuation mode.

Boundary effects on active flagella depend on frequency, wavelength, and motor organization.

Wall-induced changes can alter flagellar waveforms, affecting propulsion efficiency.

Abstract

Confinement and wall effects are known to affect the kinematics and propulsive characteristics of swimming microorganisms. When a solid body is dragged through a viscous fluid at constant velocity, the presence of a wall increases fluid drag, and thus the net force required to maintain speed has to increase. In contrast, recent optical trapping experiments have revealed that the propulsive force generated by human spermatozoa is decreased by the presence of boundaries. Here, we use a series of simple models to analytically elucidate the propulsive effects of a solid boundary on passively actuated filaments and model flagella. For passive flexible filaments actuated periodically at one end, the presence of the wall is shown to increase the propulsive forces generated by the filaments in the case of displacement-driven actuation, while it decreases the force in the case of force-driven actuation. In the case of active filaments as models for eukaryotic flagella, we demonstrate that the manner in which a solid wall affects propulsion cannot be known a priori, but is instead a nontrivial function of the flagellum frequency, wavelength, its material characteristics, the manner in which the molecular motors self-organize to produce oscillations (prescribed activity model or self-organized axonemal beating model), and the boundary conditions applied experimentally to the tethered flagellum. In particular, we show that in some cases, the increase in fluid friction induced by the wall can lead to a change in the waveform expressed by the flagella which results in a decrease in their propulsive force.