Normal Stress Measurements on Viscoelastic Fluids Using Holographic Interferometry to Measure the Free Surface in the Weissenberg Effect

Abstract

Results obtained to date for viscometric flows of simple fluids have not provided a very detailed picture of the normal stresses for these fluids. The normal stress ratio N₂/N₁ is generally agreed to lie in the range -0.1 to -0.4 for moderately concentrated polymer solutions, but some experiments show a larger range. Most difficulty is experienced measuring N₂, due mainly to its nature (being the difference in stress between the two directions normal to the flow). The use of the shape of the free surface as a measure of the state of stress in a fluid has been explored on a limited scale over the past 30 years¹. Theoretical work by Bohme^2,3 has shown that, in restricted circumstances, it is possible to obtain expressions for the shape of the free surface of a second order fluid being sheared between two rotating solid surfaces of revolution. The experiments described here are an attempt to obtain the separate values of ψ_1,0 and ψ_2,0 from measurements of the Weissenberg effect in spherical symmetry (see eqn. 4), and compare them with the value of (ψ_1,0 + 4. ψ_2,0) from a cylindrical geometry.