THE COUPLE ON A ROTATING OBLATE SPHEROID IN AN ELASTICO-VISCOUS LIQUID
N.D. Waters, D.K. Gooden · The Quarterly Journal of Mechanics and Applied Mathematics · 1980
An approximate expression is obtained for the azimuthal velocity of an elasticoviscous liquid due to the slow, steady rotation of an oblate spheroid about its axis of symmetry. The expression derived for the couple on the spheroid is found to be exact. For Newtonian liquids the expression for the azimuthal velocity is also exact and the simple expression for the couple demonstrates the effect of inertia at slow rotational speeds. The solution for the special case when the flow is due to a rotating finite disc can readily be obtained in this case. However, for non-Newtonian liquids the solution is singular near the edge of the finite disc and so expressions are given for the azimuthal velocity and the couple for a very flat discus which can be regarded as approximating a disc. It is found that good agreement exists with the available experimental evidence and that the terms associated with the shear-thinning behaviour of the liquid appear to be more important than those associated with elasticity.