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 microorganisms, 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.Comment: 20 pages, 4 figures. Published version available at
http://rspa.royalsocietypublishing.org/content/early/2010/02/09/rspa.2009.0606.short?rss=