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Monday 20 Apr 2015Particle displacements by swimming organisms

Jean-Luc Thiffeault - University of Wisconsin, Madison

Harrison 170 15:00-16:00

The experiments of Leptos et al. show that the displacements of small
particles affected by swimming microorganisms achieve a non-Gaussian
distribution, which nevertheless scales diffusively --- the 'diffusive
scaling.' We use a simple model where the particles undergo repeated
'kicks' due to the swimmers to explain the shape of the distribution
as a function of the volume fraction of swimmers. The net
displacement is determined by the inverse Fourier transform of a
single-swimmer characteristic function. The only adjustable parameter
is the strength of the stresslet term in our spherical squirmer model.
We give a criterion for convergence to a Gaussian distribution in
terms of moments of the drift function, and show that the
experimentally-observed diffusive scaling is a transient related to
the slow crossover of the fourth moment from a ballistic to a linear
regime with path length.

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