On the use of open-channel flows to measure the second normal stress difference

Abstract

This paper deals with the measurement of the second normal stress difference in a viscoelastic flow in an open semi-circular inclined channel; associated theory is also given. The theory shows that simple correlations exist for the second normal stress difference, the shear stress, and the profile (or the deflection) of the free surface of the flow. It leads to a method for deducing the second normal stress from the measured surface profile. A treatment of surface tension, whose effect has been ignored in previous analyses is given as an integral part of the formulation. Samples of polyisobutylene/cetane and some aqueous solutions of different concentrations were used for measurements using two tubes of different materials and sizes tilted at different angles. The N.B.S. No. 1 nonlinear sample was also tested. Agreements between results for different tube sizes and angles indicate the consistency of the theory and measurements. The results presented here show that the ratio of the second to the first normal stress differences is negative and the functional form of the second normal stress difference is close to a square law in shear stress in the range investigated. Relatively speaking, we find the ratio |N2/N1| to be greater for more dilute solutions. A summary of available data onN2 is given for polyisobutylene, and reasonable consistency between various investigators is demonstrated for this material. Besides, a correlation ofN2 for various polymer solutions is also shown.