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Emergent order in rheoscopic swirls

Wilkinson, Michael; Bezuglyy, Vlad and Mehlig, Bernhard (2011). Emergent order in rheoscopic swirls. Journal of Fluid Mechanics, 667 pp. 158–187.

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We consider the ordering of particles in a rheoscopic fluid (a suspension of microscopic rod-like particles) in a steady two-dimensional flow, and discuss its consequences for the reflection of light. The ordering is described by an order parameter which is a non-oriented vector, obtained by averaging solutions of a nonlinear equation containing the strain rate of the fluid flow. Exact solutions of this equation are obtained from solutions of a linear equation which are analogous to Bloch bands for a one-dimensional Schrödinger equation with a periodic potential. On some contours of the stream function, the order parameter approaches a limit, and on others it depends increasingly sensitively upon position. However, in the long-time limit a local average of the order parameter is a smooth function of position in both cases. We analyse the topology of the order parameter and the structure of the generic zeros of the order parameter field.

Item Type: Journal Article
Copyright Holders: 2010 Cambridge University Press
ISSN: 1469-7645
Keywords: general fluid mechanics; suspensions
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 30914
Depositing User: Michael Wilkinson
Date Deposited: 06 Jan 2012 16:01
Last Modified: 30 Nov 2012 16:50
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