Effect of fluid elasticity on the emergence of oscillations in an active elastic filament.

Many microorganisms propel themselves through complex media by deforming their flagella. The beat is thought to emerge from interactions between forces of the surrounding fluid, the passive elastic response from deformations of the flagellum and active forces from internal molecular motors. The beat varies in response to changes in the fluid rheology, including elasticity, but there are limited data on how systematic changes in elasticity alter the beat. This work analyses a related problem with fixed-strength driving force: the emergence of beating of an elastic planar filament driven by a follower force at the tip of a viscoelastic fluid. This analysis examines how the onset of oscillations depends on the strength of the force and viscoelastic parameters. Compared to a Newtonian fluid, it takes more force to induce the instability in viscoelastic fluids, and the frequency of the oscillation is higher. The linear analysis predicts that the frequency increases with the fluid relaxation time. Using numerical simulations, the model predictions are compared with experimental data on frequency changes in the bi-flagellated alga Chlamydomonas reinhardtii. The model shows the same trends in response to changes in both fluid viscosity and Deborah number and thus provides a possible mechanistic understanding of the experimental observations.

Flagellar swimming in viscoelastic fluids: role of fluid elastic stress revealed by simulations based on experimental data.

Many important biological functions depend on microorganisms' ability to move in viscoelastic fluids such as mucus and wet soil. The effects of fluid elasticity on motility remain poorly understood, partly because the swimmer strokes depend on the properties of the fluid medium, which obfuscates the mechanisms responsible for observed behavioural changes. In this study, we use experimental data on the gaits of Chlamydomonas reinhardtii swimming in Newtonian and viscoelastic fluids as inputs to numerical simulations that decouple the swimmer gait and fluid type in order to isolate the effect of fluid elasticity on swimming. In viscoelastic fluids, cells employing the Newtonian gait swim faster but generate larger stresses and use more power, and as a result the viscoelastic gait is more efficient. Furthermore, we show that fundamental principles of swimming based on viscous fluid theory miss important flow dynamics: fluid elasticity provides an elastic memory effect that increases both the forward and backward speeds, and (unlike purely viscous fluids) larger fluid stress accumulates around flagella moving tangent to the swimming direction, compared with the normal direction.

Mechanisms of elastic enhancement and hindrance for finite-length undulatory swimmers in viscoelastic fluids.

A computational model of finite-length undulatory swimmers is used to examine the physical origin of the effect of elasticity on swimming speed. We explore two distinct target swimming strokes: one derived from the motion of Caenorhabditis elegans, with large head undulations, and a contrasting stroke with large tail undulations. We show that both favorable stroke asymmetry and swimmer elasticity contribute to a speed-up, but a substantial boost results only when these two effects work together. We reproduce conflicting results from the literature simply by changing relevant physical parameters.

Transition to mixing and oscillations in a Stokesian viscoelastic flow.

In seeking to understand experiments on low-Reynolds-number mixing and flow transitions in viscoelastic fluids, we simulate the dynamics of the Oldroyd-B model, with a simple background force driving the flow. We find that at small Weissenberg number, flows are "slaved" to the extensional geometry imposed by forcing. For large Weissenberg number, such solutions become unstable and transit to a structurally dissimilar state dominated by a single large vortex. This new state can show persistent oscillatory behavior with the production and destruction of smaller-scale vortices that drive mixing.