Squirming through shear-thinning fluids

Abstract

Many microorganisms find themselves immersed in fluids displaying non-Newtonian rheological properties such as viscoelasticity and shear-thinning viscosity. The effects of viscoelasticity on swimming at low Reynolds numbers have already received considerable attention, but much less is known about swimming in shear-thinning fluids. A general understanding of the fundamental question of how shear-thinning rheology influences swimming still remains elusive. To probe this question further, we study a spherical squirmer in a shear-thinning fluid using a combination of asymptotic analysis and numerical simulations. Shear-thinning rheology is found to affect a squirming swimmer in nontrivial and surprising ways; we predict and show instances of both faster and slower swimming depending on the surface actuation of the squirmer. We also illustrate that while a drag and thrust decomposition can provide insights into swimming in Newtonian fluids, extending this intuition to problems in complex media can prove problematic.

Effect of shear thinning on superhydrophobic slip: Perturbative corrections to the effective slip length

“…Similar ideas have been well explored in the context of particle motion in Stokes flows 13,14 and in understanding the dynamics of swimming microorganisms in these complex fluid environments [15][16][17] . In recent work 18 , the author has demonstrated the advantages of combining perturbation theory with integral relations derived from reciprocal theorems to study …”

“…Indeed it is precisely because of the large shear rates near the edges of the no-shear slot where the boundary condition changes type that we might expect enhanced slip in a shear-thinning fluid. Another possibility 16 to consider is an expansion in small Carreau number Cu 1, with no restriction on the viscosity difference at zero and infinite shear rates, but such an expansion is not uniformly valid across strain rates so it is not a sensible expansion to make for this superhydrophobic surface problem.…”

“…This is because it fails to give useful results as a consequence of the unbounded nature of the velocities as y → ∞, and the unboundedness of the shear rates at the edges x = ±b of the no-shear slot. The following generalized reciprocal theorem is similar in spirit to, but different from, those generalizations used in other contexts such as low-Reynolds-number locomotion [15][16][17] . To proceed we consider…”

Jeffery orbits in shear-thinning fluids

“…We note that when Cu = 0 or β = 1 the fluid is Newtonian. For weak deviations from Newtonian behaviour one may take as a small parameter Cu 2 or 1 − β [50], here we choose Cu 2 to explore the first effects of shear-thinning as this leads to a much more analytically tractable expression. Thus, flow quantities are expanded in regular perturbation series in powers of Cu 2 , u * = u * 0 +Cu 2 u * 1 +O(Cu 4 ), and τ * = τ * 0 +Cu 2 τ * 1 +O(Cu 4 ) where u * , and τ * are the dimensionless velocity field, and deviatoric stress fields respectively.…”

Active particles in geometrically confined viscoelastic fluids

“…Besides, an active particle (AP) in a viscoelastic fluid represents an example of a random walker in a nonequilibrium thermal bath, being of fundamental relevance for non-equilibrium statistical physics [21]. Despite holding such immense potential, theoretical studies involving the dynamics of self-propelled particles in complex fluids are rather scarce [22][23][24][25][26][27][28][29][30][31]. Experiments dealing with artificial microswimmers in viscoelastic fluids, demonstrate remarkable differences compared to entirely viscous environments [32,33].…”