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The Quarterly Journal of Mechanics and Applied Mathematics 2003 56(1):65-91; doi:10.1093/qjmam/56.1.65
© 2003 by Oxford University Press
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Nutrient Uptake by a Self-Propelled Steady Squirmer

Vanesa Magar1, Tomonobu Goto2 and T. J. Pedley1

( 1 Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW 2 Department of Mechanical Engineering, Tottori University, Koyama, Tottori 680-8552, Japan )

In this paper we study nutrient uptake by a very simple model of a swimming microorganism, a sphere moving its surface tangentially to itself with constant concentration on the surface. The effect of its swimming motions on the concentration field and uptake is investigated. We find the relationship between the Sherwood number (Sh), a measure of the mass transfer across the surface, and the Péclet number (Pe), which indicates the relative effect of convection versus diffusion. Then we compare the results with those for a rigid sphere moving at the same speed under the action of an external force.

Analytical and computational results prove that there is little difference between the two cases when the flow field is dominated by diffusion, but substantial differences arise when convection plays an important role. In particular, for Pe large enough, Sh for a steady squirmer increases as the square root of Pe, compared with the cube root for a rigid sphere. For intermediate values of Pe, only numerical results are available, and they are obtained using a Legendre polynomial method and a separate finite volume method, allowing us to compare the two sets of results and assess the procedures used to obtain them. In Appendix A we discuss the effect of an alternative boundary condition on the Sherwood number expansions at small and large Pe.

Received 27 February 2001. Revised 25 January and 29 April 2002.


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