A critical re-appraisal of the jet-thrust technique for normal stresses, with particular reference to axial velocity and stress rearrangement at the exit plane

Abstract

It is shown that the thrust, T, exerted by a jet on the tube from which it flows, and the corresponding die-swell ratio, D, are closely related and dependent on the axial velocity and stress profiles at the exit plane. Velocity-profile data, calculated by Tanner using a finite element method, have been used to demonstrate that for a Newtonian liquid the reduction in measured thrust from the expected value arises from a re-arranged, non-parabolic axial velocity profile and the related re-arranged non-zero axial stress profile at the exit plane. The axial stress re-arrangement is the major effect. Using the correction-curve thus derived to determine the normal stresses, ν 1 + 1 2 ν 2 aqueous and non-aqueous polymer solutions gives values that are higher than the “correct” results by a significant, substantial amount. The difference is not due to neglect of the second normal stress difference, ν 2, nor to the neglect of the wall pressure at the exit plane, which is shown experimentally to be very small. It is suggested that the difference, which is a function only of the shear stress (or rate of shear) at the wall, may arise from a difference in the stress profile associated with the velocity re-arrangement at the exit between Newtonian liquids and elasticoviscous liquids for which the extensional viscosity may be high.