The measurement of the second normal stress difference for some polymer solutions

Abstract

The second normal stress difference N 2 can be determined by measuring the free surface shape of fluids flowing down a semicircular channel. A photograph is taken of a graduated straight edge and its reflection in the fluid surface. The shape of the surface is then calculated from the shape of the straight edge reflection using geometrical optics. We show that the surface shape can be measured to an accuracy of ±0.01 mm by this photographic method, leading to a value of N 2 which is accurate to about ±0.1 N m −2. A study was made of a number of moderately concentrated polymer solutions. The shear stress τ and the first nomral stress difference N 1 were measured on a cone—plate rheometer while the second normal stress difference N 2 was determined from the pipe flow experiment. The normal stress ratio N 2/ N 1 was found to be negative and independent of shear rate in the range 1 < γ . < 100 s −1. The ratio N 2/ N 1 is weakly dependent on concentration and our values are consistent with those obtained by other investigators using different methods to measure N 1 and N 2.