Poincare Indices of Rheoscopic Visualisations

Details Poincare Indices of Rheoscopic Visualisations Poincare Indices of Rheoscopic Visualisations

2009-03-20

arxiv.org/abs/0903.3615v1

Physics

Fluid Dynamics

4 pages, 4 figures

Scientific paper

Suspensions of small anisotropic particles, termed 'rheoscopic fluids', are used for flow visualisation. By illuminating the fluid with light of three different colours, it is possible to determine Poincare indices for vector fields formed by the longest axis of the particles. Because this vector field is non-oriented, half-integer Poincare indices are possible, and are observed experimentally. An exact solution for the direction vector appears to preclude the existence of topological singularities. However, we show that upon averaging over the random initial orientations of particles, singularities with half-integer Poincare index appear. We describe their normal forms.

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