Physics of rheologically enhanced propulsion: Different strokes in generalized Stokes

Abstract

Shear-thinning is an important rheological property of many biological fluids, such as mucus, whereby the apparent viscosity of the fluid decreases with shear. Certain microscopic swimmers have been shown to progress more rapidly through shear-thinning fluids, but is this behavior generic to all microscopic swimmers, and what are the physics through which shear-thinning rheology affects a swimmer's propulsion? We examine swimmers employing prescribed stroke kinematics in two-dimensional, inertialess Carreau fluid: shear-thinning "Generalized Stokes" flow. Swimmers are modeled, using the method of femlets, by a set of immersed, regularized forces. The equations governing the fluid dynamics are then discretized over a bodyfitted mesh and solved with the finite element method. We analyze the locomotion of three distinct classes of microswimmer: (1) conceptual swimmers comprising sliding spheres employing both one-and two-dimensional strokes, (2) slip-velocity envelope models of ciliates commonly referred to as "squirmers" and (3) monoflagellate pushers, such as sperm. We find that morphologically identical swimmers with different strokes may swim either faster or slower in shear-thinning fluids than in Newtonian fluids. We explain this kinematic sensitivity by considering differences in the viscosity of the fluid surrounding propulsive and payload elements of the swimmer, and using this insight suggest two reciprocal sliding sphere swimmers which violate Purcell's Scallop theorem in shear-thinning fluids. We also show that an increased flow decay rate arising from shear-thinning rheology is associated with a reduction in the swimming speed of slip-velocity squirmers. For sperm-like swimmers, a gradient of thick to thin fluid along the flagellum alters the force it exerts upon the fluid, flattening trajectories and increasing instantaneous swimming speed. Montenegro-Johnson et al., Phys. Fluids 25, 081903 (2013); http://dx.

Undulatory swimming in non-Newtonian fluids

“…An experimental study by Martinez et al (2014) shows that the enhanced swimming of Escherichia coli in polymeric solutions is not related to fluid elasticity, instead it is due to the fast-rotating flagella of E. coli encountering a lower viscosity than the cell body. Swimming enhancement is also observed in simulations of a sperm cell in a shear-thinning fluid (Montenegro-Johnson et al 2012;Montenegro-Johnson, Smith & Loghin 2013). The flow field of a C. elegans is found to be affected by the fluid shear-thinning property.…”

“…These two competing effects lead to a peak in the swimming speed. For a finite-length waving sheet, this mechanism as well as the mechanism proposed by Montenegro-Johnson et al (2013) exist and may work in tandem to enhance the swimming speed.…”

Two-sphere swimmers in viscoelastic fluids

“…We see clearly, in this far field result, that the thrust is dictated purely by the elastic steady streaming flow generated by each sphere acting on the other. Now by solving equations (25) to (28) asymptotically, one can determine the flow field around an oscillating elastic sphere, then averaging to obtain the steady streaming flows v ∞ 1 and v ∞ 2 (see [55] for technical details). By prescribing an external force magnitude set by F = δωR FU the magnitude of the deformation and thus the magnitude of the steady streaming flows is equal for both swimmers.…”

Theory of Locomotion Through Complex Fluids

“…If instead the motion of the material is extensible, then there is an additional higher order non-Newtonian contribution, U − U N ∼ ± 4 N Cu 2 , with a sign which depends on the details of the waving kinematics. Recent numerical work at high amplitude and for finite swimmers by MontenegroJohnson et al confirms that the (often weak) effects of a shear-thinning fluid depend on the gait of the swimmer with examples of both faster and slower swimming given for a variety of model swimmers [48,49].…”