Rheotaxis of spheroidal squirmers in microchannel flow: Interplay of shape, hydrodynamics, active stress, and thermal fluctuations

Abstract

Microswimmers exposed to microchannel flows exhibit an intriguing coupling between propulsion, shape, hydrodynamics, and flow which gives rise to distinct swimming behaviors. We employ a generic coarse-grained model of prolate spheroidal microswimmers, denoted as squirmers, exposed to channel flow to shed light onto their transport properties. The embedding fluid is implemented by the multiparticle collision dynamics approach (MPC), a particle-based mesoscale simulation method, which includes thermal fluctuations. Specifically, the influence of swimmer shape-spherical vs spheroidal-, active stress-pusher, ciliate, puller-, and thermal fluctuations on their rheotactic behavior is analyzed. The microswimmers accumulate at the confining walls at very low flow rates. With increasing flow strength, squirmers are depleted from the walls, and at high flow rates are also depleted from the channel center. The squirmers show pronounced cross-channel swimming between the confining walls with mixed oscillating and rotational motions due to thermal fluctuations. This strongly affects their rheotactic behavior. In particular, spherical pullers and ciliates swim upstream, whereas spherical pushers essentially swim downstream. The anisotropic shape of spheroidal squirmers enhances wall and center depletion and the alignment of the propulsion direction parallel to the flow, which leads to preferred downstream swimming for all active stresses. This emphasizes the importance of swimmer shape and hydrodynamic wall interactions on the transport properties of a microswimmer such as Volvox and Opalina, for example.

Rheotaxis and migration of an unsteady microswimmer

“…Rheotaxis of spermatozoa was first reported more than half a century ago (Bretherton & Rothschild 1961), and the underlying mechanism is understood to be the interplay among fluid shear, steric surface interactions and the chirality of the flagellar beat (Miki & Clapham 2013;Kantsler et al 2014;Omori & Ishikawa 2016). Similar wall-mediated rheotaxis has been reported for bacteria (Hill et al 2007;Ishikawa et al 2014;Mathijssen et al 2019), autophoretic Janus rods (Brosseau et al 2019), synthetic bimetallic micromotors (Ren et al 2017) and model squirmers (Ishimoto 2017;Qi et al 2020). Zott & Stark (2012) showed that rheotaxis could be induced by direct collisions with the walls or in a narrow channel.…”

Upstream rheotaxis of catalytic Janus spheres

“…Several papers have described a similar positive rheotactic response for bimetallic rods [11,12,13] . Interestingly, all of the microswimmers (both biological and artificial) discussed so far possess an anisotropy in shape, and their upstream response can be rationalized by appealing to a so-called "weather vane" mechanism [14,15] : when swimming close to the surface, the swimmer body experiences an attraction to the substrate, and can therefore function as an "anchor" or pivot point. The tail extends away from the surface, into faster fluid flow.…”

Suppression of bacterial rheotaxis in wavy channels

“…We expect hydrodynamic swimmer-wall interactions [47] to affect our results quantitatively, but not fundamentally. Possible emergent behavior due to noise effects [48,49] and chirality of flagella [4] The mobility matrix in the first line of Eqs. ( 1) of the main text mediates the hydrodynamic interaction for the translational degrees of freedom and is given by the Rotne-Prager tensor for differently sized beads [1]…”