Locomotion by tangential deformation in a polymeric fluid

Abstract

In several biologically relevant situations, cell locomotion occurs in polymeric fluids with Weissenberg number larger than one. Here we present results of three-dimensional numerical simulations for the steady locomotion of a self-propelled body in a model polymeric (Giesekus) fluid at low Reynolds number. Locomotion is driven by steady tangential deformation at the surface of the body (so-called squirming motion). In the case of a spherical squirmer, we show that the swimming velocity is systematically less than that in a Newtonian fluid, with a minimum occurring for Weissenberg numbers of order one. The rate of work done by the swimmer always goes up compared to that occurring in the Newtonian solvent alone, but is always lower than the power necessary to swim in a Newtonian fluid with the same viscosity. The swimming efficiency, defined as the ratio between the rate of work necessary to pull the body at the swimming speed in the same fluid and the rate of work done by swimming, is found to always be increased in a polymeric fluid.Further analysis reveals that polymeric stresses break the Newtonian front-back symmetry in the flow profile around the body. In particular, a strong negative elastic wake is present behind the swimmer, which correlates with strong polymer stretching, and its intensity increases with Weissenberg number and viscosity contrasts. The velocity induced by the squirmer is found to decay in space faster than in a Newtonian flow, with a strong dependence on the polymer relaxation time and viscosity. Our computational results are also extended to prolate spheroidal swimmers and smaller polymer stretching are obtained for slender shapes compared to bluff swimmers. The swimmer with an aspect ratio of two is found to be the most hydrodynamically efficient. * Electronic address: elauga@ucsd.edu † Electronic address: luca@mech.kth.se

Theory of Locomotion Through Complex Fluids

“…Indeed numerical simulations documented later in this book (Ch. 10) show that if the gait of the nematode is reversed (reflection of the wavevector), yielding an increasing amplitude head to tail, then the nematode would experience a speed enhancement similar to the results presented by Teran et al Additionally, in studies of other swimming gaits, numerical simulations of potential squirmers [40] and pushers or pullers [41] all showed a speed decrease in a Giesekus fluid versus a Newtonian one.…”

Active suspensions in thin films: nutrient uptake and swimmer motion

“…This generalization allows us to classify the swimming motion into three swimming modes (pushers, pullers and neutral swimmers), and is in good agreement with the swimming motion of several micro-organisms such as Parmecium and Opalina (Ishikawa, Locsei & Pedley 2008). The simple neutral and steady model used here has been adopted in several investigations of processes related to the physics of swimming micro-organisms, such as locomotion in stratified (Doostmohammadi, Stocker & Ardekani 2012) and viscoelastic fluids (Zhu et al 2011;Zhu, Lauga & Brandt 2012).…”

Locomotion of a microorganism in weakly viscoelastic liquids

“…In the present work we consider B n = 0 for n > 2, as commonly assumed in literature [5,20,21]. Thus, the specification of the coefficients B 1 and B 2 completely determines the type of swimming.…”

“…On the other hand, theoretical studies on the swimming of ciliated organisms in viscoelastic fluids are limited to the above-cited work of Lauga [12,19], with results valid for small-amplitude time-dependent swimming strokes, and to recent numerical simulations of steady squirmers, performed at rather high Deborah numbers [20,21].…”