Swimmer suspensions: fluctuations, microstructure and rheology

Abstract

The research reported in the thesis principally concerns the microstructure and rheology of a suspension of rear-actuated microswimmers. A typical pusher consists of a head (or the cell body) and a tail that may include a single flagellum, or multiple flagella combining to form a bundle, and that propels the swimmer. For bacterial pushers, the total swimmer length (head+tail) ranges from 6-20 μm, with the speeds at which they swim ranging between 20-50 μm/s (the numbers are a bit larger for algae). The typical Reynolds number (Re) based on the swimmers length is O(10−3) or smaller, and such microswimmers therefore inhabit the Stokesian regime as far as hydrodynamics goes. In propelling the swimmer, the tail exerts a rearward thrust, while the head drags the fluid along the swimming direction; the swimmer as a whole therefore remains force-free at every instant. Typical pushers, for instance peritrichously flagellated bacteria such as E. coli or B. subtilis, explore their surroundings by means of a run-and-tumble dynamics on the micro-scale, leading to a diffusive sampling of their environment on larger length scales. Here, the microorganism on average swims in a given direction for a mean run duration ∼ t (the run phase), followed by a short pause when the swimmer randomly reorients by a large amount (the tumble phase). The runs are generally not straight owing to the imperfections in the propelling flagellar bundle, resulting in an additional continuous component of orientation fluctuations that may be modelled as a rotary diffusion process. The unique ability of the micro-swimmers to inject energy into the system by virtue of their swimming activity leads to a range of novel and interesting phenomena. These include long-ranged correlated motions (as manifested in jets and whorls that arise in bacterial baths on scalesmuch larger than individual swimmers), enhanced velocity fluctuations and tracer diffusivities, shear-induced migration, reduced (even negative) shear viscosities and others. The thesis attempts to address some of these interesting phenomena.