Dispersion of biased swimming micro-organisms in a fluid flowing through a tube

Martin A. Bees, Ottavio A. Croze

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Classical Taylor-Aris dispersion theory is extended to describe the transport of suspensions of self-propelled dipolar cells in a tubular flow. General expressions for the mean drift and effective diffusivity are determined exactly in terms of axial moments and compared with an approximation a la Taylor. As in the Taylor-Aris case, the skewness of a finite distribution of biased swimming cells vanishes at long times. The general expressions can be applied to particular models of swimming micro-organisms, and thus be used to predict swimming drift and diffusion in tubular bioreactors, and to elucidate competing unbounded swimming drift and diffusion descriptions. Here, specific examples are presented for gyrotactic swimming algae.

Original languageEnglish
Pages (from-to)2057-2077
Number of pages21
JournalProceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Issue number2119
Publication statusPublished - 8 Jul 2010

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