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On the hydrodynamics of ‘slip–stick’ spheres

Swan, James W. and Khair, Aditya S. (2008) On the hydrodynamics of ‘slip–stick’ spheres. Journal of Fluid Mechanics, 606 . pp. 115-132. ISSN 0022-1120.

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The breakdown of the no-slip condition at fluid–solid interfaces generates a host of interesting fluid-dynamical phenomena. In this paper, we consider such a scenario by investigating the low-Reynolds-number hydrodynamics of a novel ‘slip–stick’ spherical particle whose surface is partitioned into slip and no-slip regions. In the limit where the slip length is small compared to the size of the particle, we first compute the translational velocity of such a particle due to the force density on its surface. Subsequently, we compute the rotational velocity and the response to an ambient straining field of a slip–stick particle. These three Faxén-type formulae are rich in detail about the dynamics of the particles: chiefly, we find that the translational velocity of a slip–stick sphere is coupled to all of the moments of the force density on its surface; furthermore, such a particle can migrate parallel to the velocity gradient in a shear flow. Perhaps most important is the coupling we predict between torque and translation (and force and rotation), which is uncharacteristic of spherical particles in unbounded Stokes flow and originates purely from the slip–stick asymmetry.

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Additional Information:Copyright © Cambridge University Press 2008. Reprinted with permission. (Received 10 July 2007 and in revised form 18 March 2008) Published online 12 June 2008. The authors gratefully acknowledge John F. Brady for his valuable comments and assistance. They also thank Arun Ramchandran for a stimulating question. This work was support in part by NSF grant CBET 0506701.
Funding AgencyGrant Number
National Science FoundationCBET 0506701
Subject Keywords:Boundary conditions; Surfaces; Janus particles; Faxén-type formulae
Record Number:CaltechAUTHORS:SWAjfm08
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11345
Deposited By: Archive Administrator
Deposited On:06 Aug 2008 23:55
Last Modified:03 Oct 2019 00:18

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