  Obtaining a detailed understanding of the physical interactions between a
cell and its environment often requires information about the flow of fluid
surrounding the cell. Cells must be able to effectively absorb and discard
material in order to survive. Strategies for nutrient acquisition and toxin
disposal, which have been evolutionarily selected for their efficacy, should
reflect knowledge of the physics underlying this mass transport problem.
Motivated by these considerations, in this paper we discuss the results from an
undergraduate research project on the advection-diffusion equation at small
Reynolds number and large P\'eclet number. In particular, we consider the
problem of mass transport for a Stokesian spherical swimmer. We approach the
problem numerically and analytically through a rescaling of the concentration
boundary layer. A biophysically motivated first-passage problem for the
absorption of material by the swimming cell demonstrates quantitative agreement
between the numerical and analytical approaches. We conclude by discussing the
connections between our results and the design of smart toxin disposal systems.
