State diagram of a three-sphere microswimmer in a channel

Abstract

Geometric confinements are frequently encountered in soft matter systems and in particular significantly alter the dynamics of swimming microorganisms in viscous media. Surface-related effects on the motility of microswimmers can lead to important consequences in a large number of biological systems, such as biofilm formation, bacterial adhesion and microbial activity. On the basis of low-Reynolds-number hydrodynamics, we explore the state diagram of a three-sphere microswimmer under channel confinement in a slit geometry and fully characterize the swimming behavior and trajectories for neutral swimmers, puller- and pusher-type swimmers. While pushers always end up trapped at the channel walls, neutral swimmers and pullers may further perform a gliding motion and maintain a stable navigation along the channel. We find that the resulting dynamical system exhibits a supercritical pitchfork bifurcation in which swimming in the mid-plane becomes unstable beyond a transition channel height while two new stable limit cycles or fixed points that are symmetrically disposed with respect to the channel mid-height emerge. Additionally, we show that an accurate description of the averaged swimming velocity and rotation rate in a channel can be captured analytically using the method of hydrodynamic images, provided that the swimmer size is much smaller than the channel height.

Hydrodynamic coupling and rotational mobilities near planar elastic membranes

“…Appendix A: Green's tensor for a membrane-bounded fluid The Green's functions can conveniently be computed using a two-dimensional Fourier transform technique 55,106 and appropriately applying the no-slip boundary conditions stemming from shear and bending deformations of the membrane.…”

Oscillatory surface rheotaxis of swimming E. coli bacteria

“…Third, we introduce a term that has been identified as an important contribution for sperm rheotaxis [30,31]. The swimmer body experiences an effective anchoring to the surface when pointing towards it, because its hydrodynamic friction with the wall is larger than that of the flagellar bundle [54], an effect explained by lubrication theory [31]. Consequently, the flagella are advected with the flow, like a weathervane.…”

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

“…In the following, we derive explicit analytical expressions for the mobility functions in a uniaxial anisotropic fluid. They can, for instance, serve as a basis for future investigations of the behavior of some particlebased microswimmer models, such as the three-sphere swimmer introduced by Najafi and Golestanian and its different variations [134][135][136][137][138][139][140][141][142][143][144] . A comparison between analytical predictions and boundary integral simulations is also provided.…”

“…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] .…”