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

Abstract

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 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.

Polymer stress growth in viscoelastic fluids in oscillating extensional flows with applications to micro-organism locomotion

“…Next, we look at the flow around flexing filaments with a time-reversible oscillation of a circular arc of a given amplitude. The flow around these so-called flexors is similar to the flow around undulatory swimmers and provides a connection between the analysis of stress response at oscillatory extensional stagnation points and recent numerical studies on stress accumulation at tips of flagellated and undulatory swimmers [20,22,17,24,12].…”

“…Simulations of swimming in viscoelastic fluids involving large amplitude gaits [20,23,18] show substantially different swimming speeds than those found in low amplitude simulations and asymptotic analyses [4,5,10,6,16,3]. Concentration of polymer elastic stress at the tips of slender objects has been seen in numerical simulations of flagellated swimmers in viscoelastic fluids [20,22,23,12], and it is thought that the presence of these large stresses is related to the observed differences in behavior at low and high amplitude. We recently explained the origin of the stress concentration at the tips of steady, translating cylinders [13].…”

Filament extensibility and shear stiffening control persistence of strain and loss of coherence in cross-linked motor-filament assemblies

“…We next analyze the decay of oscillations strains in a filament. To do so, we modify the boundary condition at s = to enable imposed oscillations there, while still respecting the constraints that lead to (10). This is achieved by subjecting the free end to a small amplitude oscillatory displacement with frequency ω and amplitude U I U 0 ( ) with 1.…”

“…These conserved structures with ubiquitous functions stemming from already being present in the last eukaryote common ancestor [8][9][10], provide a great opportunity to study the integration of mechanics and control at the cell level. Cilia are comprised of almost inextensible microtubule filaments, active ATPase dynein motor proteins and passive elastic nexins which in concert deform (bend) and oscillate with well defined wavelengths and frequencies.…”

Orientation dependent elastic stress concentration at tips of slender objects translating in viscoelastic fluids

“…Numerical simulations of flagellated swimmers in viscoelastic fluids have shown the concentration of polymer elastic stress at the tips of slender objects [45,46,47,32], (see Fig. 1) but why the stress concentrates so strongly at tips, and the effect of these stresses on micro-organism locomotion is not understood.…”