A theory for surface elevation in the weissenberg effect

Abstract

A Couette flow generated by a cylinder rotating perpendicular to the free surface of a fluid is considered and the equations of motion are solved to yield an expression for the surface shape in the vicinity of the rod. The fluid model chosen is one for which the shear stress τrθ and the normal stresses Trr and Tee obey the relations where M, n, a, b, and κ are constants characteristic of the fluid and v is the flow velocity component in the angular direction. The results are found to be in reasonable agreement with previous experimental observations of the Weissenberg effect.