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Squirming motion in a Brinkman medium

Published online by Cambridge University Press:  19 September 2018

Herve Nganguia  and
On Shun Pak
Herve Nganguia
Affiliation:
Department of Mechanical Engineering, Santa Clara University, Santa Clara, CA 95053, USA
On Shun Pak*
Affiliation:
Department of Mechanical Engineering, Santa Clara University, Santa Clara, CA 95053, USA
*
†Email address for correspondence: opak@scu.edu
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Abstract

Micro-organisms encounter heterogeneous viscous environments consisting of networks of obstacles embedded in a viscous fluid medium. In this paper we analyse the characteristics of swimming in a porous medium modelled by the Brinkman equation via a spherical squirmer model. The idealized geometry allows an analytical and exact solution of the flow surrounding a squirmer. The propulsion speed obtained agrees with previous results using the Lorentz reciprocal theorem. Our analysis extends these results to calculate the power dissipation and hence the swimming efficiency of the squirmer in a Brinkman medium. The analytical solution enables a systematic analysis of the structure of the flow surrounding the squirmer, which can be represented in terms of singularities in Brinkman flows. We also discuss the spatial decay of flows due to squirming motion in a Brinkman medium in comparison with the decay in a purely viscous fluid. The results lay the foundation for subsequent studies on hydrodynamic interactions, nutrient transport and uptake by micro-organisms in heterogeneous viscous environments.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Low-Reynolds-number flows: Low-Reynolds-number flows Biological Fluid Dynamics: Micro-organism dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 855 , 25 November 2018 , pp. 554 - 573
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Copyright
© 2018 Cambridge University Press 

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