Emergent order in rheoscopic swirls

• 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.

Ämnesord

NATURVETENSKAP  -- Fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences (hsv//eng)

Nyckelord

general fluid mechanics; suspensions

Publikations- och innehållstyp

ref (ämneskategori)

art (ämneskategori)