A note on a swirling squirmer in a shear-thinning fluid

Abstract

Micro-organisms and artificial microswimmers often move in biological fluids displaying complex rheological behaviors, including viscoelasticity and shear-thinning viscosity. A comprehensive understanding of the effectiveness of different swimming gaits in various types of complex fluids remains elusive. The squirmer model has been commonly used to represent different types of swimmers and probe the effects of different types of complex rheology on locomotion. While many studies focused only on squirmers with surface velocities in the polar direction, a recent study has revealed that a squirmer with swirling motion can swim faster in a viscoelastic fluid than in Newtonian fluids [Binagia et al., J. Fluid Mech. 900, A4, (2020)]. Here, we consider a similar setup but focus on the sole effect due to shear-thinning viscosity. We use asymptotic analysis and numerical simulations to examine how the swirling flow affects the swimming performance of a squirmer in a shear-thinning but inelastic fluid described by the Carreau constitutive equation. Our results show that the swirling flow can either increase or decrease the speed of the squirmer depending on the Carreau number. In contrast to swimming in a viscoelastic fluid, the speed of a swirling squirmer in a shear-thinning fluid does not go beyond the Newtonian value in a wide range of parameters considered. We also elucidate how the coupling of the azimuthal flow with shear-thinning viscosity can produce the rotational motion of a swirling pusher or puller.

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

“…2020; Nganguia et al. 2020; Housiadas 2021; Housiadas, Binagia & Shaqfeh 2021), among others (Pedley 2016).…”

“…Chlamydomonas) part of their body. The squirmer model has therefore become a widely used generic locomotion model for various problems in low-Reynolds-number swimming, including nutrient uptake by microorganisms (Magar, Goto & Pedley 2003;Magar & Pedley 2005;Michelin & Lauga 2011;Eastham & Shoele 2020), optimization (Michelin & Lauga 2010), hydrodynamic interactions (Ishikawa, Simmonds & Pedley 2006;Drescher et al 2009), collective motion Ishikawa, Simmonds & Pedley 2007), inertial effects (Wang & Ardekani 2012;Chisholm et al 2016) and swirling motion (Pedley, Brumley & Goldstein 2016;Binagia et al 2020;Nganguia et al 2020;Housiadas 2021;Housiadas, Binagia & Shaqfeh 2021), among others (Pedley 2016).…”

Autonomously Propelled Colloids for Penetration and Payload Delivery in Complex Extracellular Matrices

“…Toward this goal, we close this article with several suggestions for future research directions: Effect of ECM mechanics and rheology on propulsion efficiency : The motion efficiency (and thus therapeutic efficacy) of SPPs has been shown recently to depend on the topology, rheological properties, and viscoelastic properties of the medium. Recently, it was reported that shear-thinning effects cause a substantial enhancement in the propulsion of helical microswimmers [ 114 ]. On the other hand, it is also known that as ECM becomes stiffer and denser, the velocity is attenuated.…”

“…A growing body of evidence indicates that ECM viscoelasticity influences fundamental cell processes such as differentiation, spreading, migration, and ECM synthesis, and plays a key role in the procession of diseases such as fibrosis and cancer [ 49 ]. Considering the growing body of literature on microscale self-propulsion in shear-thinning [ 113 , 114 , 115 ] and viscoelastic media [ 116 , 117 ], it is reasonable to expect that ECM viscoelasticity will influence the efficiency of the self-propulsion. Accordingly, to develop SPPs that are attractive for biomedical applications in drug delivery in human tissues, it is critical that the swimming performance of SPPs be tested in environments that possess similar viscoelastic characteristics to in vivo human tissues.…”

Role of viscoelasticity on the dynamics and aggregation of chemically active sphere-dimers

“…Microswimmers encounter diverse fluidic environment during their course of motion [42][43][44][45][46][47][48][49] . The comprehensive studies on the effect of fluid reveal that the rheology of the surrounding medium can strongly affect the motility of microsswimmers 5,23,50,51 An increase in translational velocity but a decrease in the rotational diffusion in viscoelastic fluids compared to Newtonian fluids for the E.coli has been established 52 .…”