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Emergent order in rheoscopic swirls

Published online by Cambridge University Press:  29 November 2010

MICHAEL WILKINSON ,
VLAD BEZUGLYY  and
BERNHARD MEHLIG
MICHAEL WILKINSON*
Affiliation:
Department of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK
VLAD BEZUGLYY
Affiliation:
Department of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK
BERNHARD MEHLIG
Affiliation:
Department of Physics, Göteborg University, 41296 Gothenburg, Sweden
*
‡Email address for correspondence: m.wilkinson@open.ac.uk
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Abstract

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.

JFM classification

Mathematical Foundations: General fluid mechanics Complex Fluids: Suspensions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 667 , 25 January 2011 , pp. 158 - 187
Copyright
Copyright © Cambridge University Press 2010

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Footnotes

†

Present address: Laboratoire d'Energétique et de Mécanique Théorique et Appliquée, Nancy- Université, CNRS, 2 avenue de la forêt de Haye, BP 160, 54504 Vandoeuvre CEDEX, France.

References

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