Flow birefringence study at the transition from laminar to Taylor vortex flow

Abstract

We have studied the birefringence induced by the flow in a liquid containing very fine particles in the vicinity of the transition between the Couette flow and the Taylor vortex flow. We derive at first an analytical expression of the axisymmetrical hydrodynamical field and then the angular velocity of a particle in the flow. The resolution of the diffusion equation leads to the orientation distribution function F. On condition of some simplifying but realistic hypotheses, we show that the extinction angle χ and the birefringence Δn of the solution are the same as the properties of an equivalent stratified medium composed of very thin layers the orientation of which varies continuously. The results concerning the velocity profile and the critical Taylor number are in good agreement with other sources ; the theoretical computation of χ and Δn are then compared to experimental curves realized with solutions of bentonite and T.M.V. ; interesting conclusions can be drawn on the influence of the shape of the particles on the behavior of the angle of extinction and of the birefringence intensity in the region of the Taylor vortex flow.