Physics

Prof. Ganesh Subramanian
JNCASR, Bangalore

Abstract:

I will begin by briefly summarizing our recent work on the spatial migration of microswimmers (bacteria and algae) in shearing flows, emphasizing the range of behaviour possible depending on swimmer shape and shear rate, and pointing towards the possibility of hydrodynamic focusing of swimmer populations. Thereafter, my main focus will be on the development of a novel stochastic kinetic theory framework to characterize the transition to collective motion in a dilute suspension of persistent swimmers. The fundamental equation underlying this approach is the fluctuating run-and-tumble equation - the kinetic equation for the probability density of run-and-tumble swimmers in position-orientation space driven by a noise arising from fluctuations inherent in the Poisson statistics governing the tumbles. Combining the fluctuating run-and-tumble equation with the Stokes equations that include a swim stress, allows one to examine the effects of long-wavelength velocity fluctuations, that emerge close to the onset of collective motion, on tracer diffusion. We derive an expression for the diffusivity of spherical tracers over the entire range of swimmer volume fractions, from its known plateau value in the non-interacting dilute limit to its divergence at the collective motion threshold.

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