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Optimal feeding is optimal swimming for all P'eclet numbers | | Sébastien Michelin
; Eric Lauga
; | | Date: |
1 Sep 2011 | | Abstract: | Cells swimming in viscous fluids create flow fields which influence the
transport of relevant nutrients, and therefore their feeding rate. We propose a
modeling approach to the problem of optimal feeding at zero Reynolds number. We
consider a simplified spherical swimmer deforming its shape tangentially in a
steady fashion (so-called squirmer). Assuming that the nutrient is a passive
scalar obeying an advection-diffusion equation, the optimal use of flow fields
by the swimmer for feeding is determined by maximizing the diffusive flux at
the organism surface for a fixed rate of energy dissipation in the fluid. The
results are obtained through the use of an adjoint-based numerical optimization
implemented by a Legendre polynomial spectral method. We show that, to within a
negligible amount, the optimal feeding mechanism consists in putting all the
energy expended by surface distortion into swimming - so-called treadmill
motion - which is also the solution maximizing the swimming efficiency.
Surprisingly, although the rate of feeding depends strongly on the value of the
P’eclet number, the optimal feeding stroke is shown to be essentially
independent of it, which is confirmed by asymptotic analysis. Within the
context of steady actuation, optimal feeding is therefore found to be
equivalent to optimal swimming for all P’eclet numbers. | | Source: | arXiv, 1109.0112 | | Services: | Forum | Review | PDF | Favorites | |
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