TIME-PERIODIC RECTILINEAL SIMPLE FLUID-FLOWS

Time dependent rectilineal flows with Laplace transformable relative strain histories define a common domain for the shear stress functionals of a general class of simple fluids. The elements of this domain, in equivalence classes, are in one-to-one correspondence with their transforms. On the domain of transforms the momentum balance equation for these flows may be arranged as a single functional-differential equation. The second order BKZ and Coleman-Noll theories, among others, are used to illustrate this. A formal perturbation procedure is used to analyse oscillatory flow in a parallel plate rheometer. This indicates that the classical formula for the shear rate usually adopted to analyse experiments needs correction when inertial effects are not negligible. An existence theorem for such flows is presented for a particular model.