WEISSENBERG AND MERRINGTON EFFECTS IN NON-NEWTONIAN FLUIDS

Abstract

Weissenberg in 1946, first demonstrated an interesting phenomenon in the hydrodynamic behaviour of certain highly viscous liquids. In the experimental set-up, the liquid is sheared in a gap between two rotating cylinders both of which move at different but with steady rotational speeds, the liquid is drawn inwards against the action of centrifugal force and upwards against the force of gravity, the whole arrangement forming a sort of " Centripetal pump ".Weissenberg attributes this effect to the elasticity of the liquid. In the present investigation, the flows of general Reiner-Rivlin fluids and Rivlin-Ericksen fluids with constant coeffieients between two coaxial rotating cylinders are studied. Explicit expressions for the velocity distribution, stress components, pressure distribution, the equation to the free surface at the inner and outer cylinders have been obtained for various kinds of non-Newtonian fluids. The effect of visco-elasticity and cross viscocity are represented graphically. From the trend of the theoretical investigation, we conclude that either cross viscocity alone or viseo-elasticity alone or both will modify the shape of the free surface in the annulus prescribed by centrifugal force and the force of gravity.