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The dynamics and rheology of a dilute suspension of hydrodynamically Janus spheres in a linear flow

Published online by Cambridge University Press:  25 August 2009

ARUN RAMACHANDRAN  and
ADITYA S. KHAIR
ARUN RAMACHANDRAN
Affiliation:
Department of Chemical Engineering, University of California, Santa Barbara, CA 93106-5080, USA
ADITYA S. KHAIR*
Affiliation:
Department of Chemical Engineering, University of California, Santa Barbara, CA 93106-5080, USA
*
†Email address for correspondence: akhair@engineering.uscb.edu
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Abstract

The creeping motion of a hydrodynamically ‘Janus’ spherical particle, whose surface is partitioned into two distinct regions, is investigated. On one region, fluid adjacent to the particle obeys the no-slip condition, whereas on the other, fluid slips past the particle. The fore-aft asymmetry of this ‘slip–stick’ sphere (Swan & Khair, J. Fluid Mech., vol. 606, 2008, p. 115) leads to a number of interesting results when it is placed in different flows, which is illustrated by computing the particle motion to first order in the ratio of slip length to particle radius. For example, in a pure straining field the sphere attains an equilibrium orientation either along the compressional or extensional axis of the flow, depending on the ratio of slip-to-stick surface areas. In a simple shear flow, on the other hand, the slip–stick sphere undergoes a periodic rotational motion, or Jeffrey orbit. Moreover, depending on its initial orientation, the particle can either follow a periodic {translational} orbit or undergo a net displacement along the flow direction. Lastly, to first order in the volume fraction of slip–stick spheres, the suspension rheology is non-Newtonian, with non-zero first and second normal stress differences.

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Papers
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Journal of Fluid Mechanics , Volume 633 , 25 August 2009 , pp. 233 - 269
Copyright
Copyright © Cambridge University Press 2009

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