We consider the problem of determining the rate of nutrient uptake by a self-propelled spherical squirmer, a model for a microorganism that generates motion along its surface. The tangential velocity induced by the squirmer varies along the surface in such a manner that a region of fluid recirculation is formed on the rear part of the squirmer. This problem was formulated by Magar et al. [Q. J. Mech. Appl. Math. 56, 65 (2003)] who investigated it in detail numerically covering a large range of Peclet numbers, $Pe=aU/D, a$ being the radius of the squirmer, $U$ is its swimming speed, and $D$ is the diffusivity of the nutrient in the surrounding liquid. Their numerical results for large $Pe$ suggested that Sherwood number $Sh$, the nondimensional mass transfer rate, increases in proportion to $P{e}^{1/2}$ but they were unable to theoretically determine the constant of proportionality. The present study reexamines this problem in the limit of large $Pe$ and small Reynolds numbers. The concentration in the bulk of the recirculating region approaches a constant whose value is determined by requiring that the mass transfer of nutrient across the streamline dividing the open and closed streamline regions must equal the mass transfer to the squirmer from the closed streamlines. The analysis of the nutrient concentration in the vicinity of the dividing streamline is complicated by the fact that this streamline originates from the stagnation point at the squirmer surface. The boundary layers formed at the nutrient surface on the either side of this stagnation point continue along the dividing streamline resulting in a discontinuity in the nutrient flux. As a consequence, new boundary layers form within these two larger boundary layers. When the squirmer motion induces the recirculation region ahead of itself, the distribution near the dividing streamline is simpler to determine but that near the squirmer surface involves formation of new boundary layers inside the boundary layers returning from the dividing streamline. Analytical expressions for large $Pe$ are derived in both cases and shown to be in agreement with the numerical results of Magar et al.

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• Biological fluid dynamics
• Boundary layers
• Swimming