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Fluctuations and mixing in active suspensions

Dr. Mitya Pushkin

Department of Physics, Oxford University

Suspensions of active particles, such as swimming microorganisms, turn out to be efficient stirrers of the surrounding fluid. This fact may be directly relevant to the feeding and evolutionary strategies of swimming cells. Microfluidic devices exploring swimmers-induced mixing have been proposed. The possibility of a significant biogenic contribution to the ocean circulation is currently under intense debate. However, understanding fluctuations and the effective tracer diffusion coefficient in such non-equilibrium systems remains a challenge for modern theoretical physics.

In this talk we focus on the fundamentals of these processes. We start by explaining why the theoretical approach based on the notion of the effective bacterial bath temperature and ideas of the fluctuation--dissipation theorem, such as the Stokes--Einstein relation, break down in active suspensions. Next, we discuss the impediments to stirring by force-free swimmers and give a classification of possible stirring mechanisms. We show that fluid entrainment by individual swimmers and the effects of their trajectories curvature give rise to independent mixing mechanisms. We discuss their relative strength in dilute suspensions of active swimmers and derive a simple expression for the effective tracer diffusion coefficient as a function of swimmer parameters.

During the discussion we demonstrate an interplay of topological, fluid mechanical and statistical physics concepts, such as closedness of tracer trajectories, the net fluid volume displaced by a moving body (also known as the Darwin drift) and properties of non-Gaussian random walks.