Variation of Flow Birefringence with Stress

Abstract

IN flowing liquids in which the same mechanism (for example, network deformation in a polymer solution) gives rise to birefringence and to stress, it is reasonable to expect these to vary together when factors such as rate of shear and concentration of solute are altered. Birefringence and stress require, for their complete description, ellipsoids, and the question arises as to how these are to be compared. According to the simplest possible relation (in which the stress tensor is equal to a constant multiple of the refractive index tensor plus an isotropic tensor), the optic and stress ellipsoids have the same orientation, and the differences of principal axes of either ellipsoid are proportional to the differences of the corresponding principal axes of the other ellipsoid. Thus for coaxial ellipsoids, which we shall consider here, it seems natural to compare differences of principal axes.