Volume 89, Number 3, February 2010
|Number of page(s)||5|
|Section||Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics|
|Published online||22 February 2010|
Poincaré indices of rheoscopic visualisations
Department of Mathematics and Statistics, The Open University - Walton Hall, Milton Keynes, MK7 6AA, England, UK
2 Department of Physics, Göteborg University - 41296 Gothenburg, Sweden
Accepted: 18 January 2010
Suspensions of small anisotropic particles, “rheoscopic fluids”, are used for flow visualisation. By illuminating the fluid with light of three different colours, it is possible to determine Poincaré indices for vector fields formed by the longest axis of the particles. Because this vector field is non-oriented, half-integer Poincaré 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 Poincaré index appear. We describe their normal forms.
PACS: 47.57.E- – Suspensions / 47.54.-r – Pattern selection; pattern formation / 47.80.Jk – Flow visualization and imaging
© EPLA, 2010
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