9 - STRESS MEASUREMENTS IN UNIDIRECTIONAL SHEAR FLOW; THEORY

Abstract

For any incompressible, viscoelastic material describable by an isotropic, one-particle constitutive functional, the rheological behavior in an arbitrary unidirectional shear flow is governed by three functionals (N1, N2, and σ) of shear rate s. One of the important current tasks is to develop reliable experimental methods for determining these functional for given polymeric liquids. For this purpose, rectilinear shear flow, though apparently the simplest unidirectional shear flow, is of no use. It cannot be generated in the laboratory, and even if it could, only the traction on the shearing surfaces could be measured; this would give σ but not N1 and N2, for which two other normal components of traction should be determined. Curvilinear shear flow could be used to determine N1 and N2 from measured values of spatial distributions of the component of traction normal to shearing surfaces. The curvature of the shear surfaces and shear lines in the presence of nonzero N1 and/or N2 can give rise to a spatial variation of an additive isotropic contribution to the stress tensor field that shows up as a nonuniform spatial distribution of the normal component of traction on shearing surfaces, even when the flow history is essentially the same at all particles.