A Theory for Measurement of Normal Stress Difference by Using Circumferential Poiseuille Flow through an Annulus

Abstract

The first normal stress difference of polymer melts has often been obtained from the exit pressure by assuming that the flow at the exit of the nozzle is fully developed. This assumption, however, is not rigorously fulfilled as shown by several experiments.In this paper, one means for avoiding this assumption was presented: the circumferential Poiseuille flow through an annulus was analyzed by approximating the shear stress distribution in a simple polynomial. The equations of the flow curve and the first normal stress difference were derived. The first normal stress difference was found to be obtained from measurement of the difference in radial pressures at cylindrical surfaces. This pressure difference was roughly estimated to be smaller than the first normal stress difference by one order.