The effect of particle geometry on squirming through a shear-thinning fluid

Abstract

Biological and artificial microswimmers often encounter fluid media with non-Newtonian rheological properties. In particular, many biological fluids such as blood and mucus are shear-thinning. Recent studies have demonstrated how shear-thinning rheology can impact substantially the propulsion performance in different manners. In this work, we examine the effect of geometrical shape upon locomotion in a shear-thinning fluid using a prolate spheroidal squirmer model. We use a combination of asymptotic analysis and numerical simulations to quantify how particle geometry impacts the speed and the energetic cost of swimming. The results demonstrate the advantages of spheroidal over spherical swimmers in terms of both swimming speed and energetic efficiency when squirming through a shear-thinning fluid. More generally, the findings suggest the possibility of tuning the swimmer geometry to better exploit non-Newtonian rheological behaviours for more effective locomotion in complex fluids.

Squirmer locomotion in a yield stress fluid

“…A similar conclusion is reached for a wide range of spheroidal shape swimmers, and it is found that spheroidal swimmers compared to spherical squirmers can reach higher swimming velocity and energetic efficiency in shear-thinning fluids (van Gogh et al. 2022). In addition, it is shown that the nonlinear rheology of the fluid can modify the efficient swimming gaits in non-Newtonian fluids compared to Newtonian fluids, and allows non-motile surface actuation modes in Newtonian fluids to generate net motion in shear-thinning fluids (Pietrzyk et al.…”

“…2020; van Gogh et al. 2022). When both the swimmer and the inter-fluid boundary are spherical or ellipsoids, these models are analytically tractable and consequently can be used to produce exact results for a wide range of parameters.…”

“…Similar to many others, these studies used an idealized model of a swimmer as a squirmer (Lighthill 1952;Blake 1971;Pedley 2016). The squirmer model has been employed to study the locomotion in various complex fluids (Lauga 2009;Zhu, Lauga & Brandt 2012;Li, Karimi & Ardekani 2014;Datt et al 2017;Pietrzyk et al 2019;Binagia et al 2020;van Gogh et al 2022). When both the swimmer and the inter-fluid boundary are spherical or ellipsoids, these models are analytically tractable and consequently can be used to produce exact results for a wide range of parameters.…”

Squirmer locomotion in a yield stress fluid

“…By employing the squirmer model, it is shown that while a swimmer slows down in a shear-thinning fluid, they could have higher swimming efficiency and their maximum swimming efficiency occurs at a particular boundary actuation rate [27]. A similar conclusion is reached for a wide range of spheroidal shape swimmers and it is found that spheroidal swimmers compared to over spherical squirmers, can reach higher swimming velocity and energetic efficiency in shear-thinning fluids [17]. In addition, it is shown that the nonlinear rheology of the fluid can modify the efficient swimming gaits in non-Newtonian fluids compared to Newtonian fluids and allows non-motile surface actuation modes in Newtonian fluids to generate net motion in shear-thinning fluids [15].…”

“…Similar to many other researches, these studies used an idealized model of a swimmer as a squirmer [8][9][10]. The squirmer model has been employed to study the locomotion in various complex fluids [11][12][13][14][15][16][17]. When both the swimmer and the inter-fluid boundary are spherical or ellipsoids, these models are analytically tractable and consequently can be used to produce exact results for a wide range of parameters.…”