Emergent order in rheoscopic swirls

作者：Wilkinson Michael^*; Bezuglyy Vlad; Mehlig Bernhard

来源：Journal of Fluid Mechanics, 2011, 667: 158-187.

DOI：10.1017/S0022112010004441

• general fluid mechanics
• suspensions

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 Schrodinger 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.

• 出版日期2011-1-25