Shear Flow Instabilities in Viscoelastic Fluids

The dissertation is concerned with the stability of channel flows of viscoelastic fluids. The content is primarily theoretical. The dissertation begins with a review of instabilities observed in experiments and then attempts to elucidate possible mechanisms using linear stability theory. The first section considers a previously known interfacial instability in coextrusion flows, whose mechanism is purely elastic. This instability is investigated in different parameter régimes for an Oldroyd-B fluid. The next section generalises the study to a continuously stratified fluid, and finds that a class of models with rapid variation in their elastic properties will also show the instability. These results are confirmed both numerically and using asymptotic methods. The fundamental mechanism of this "coextrusion" instability is the same as for the interfacial instability above. The next part concerns a shear-thinning White-Metzner fluid (i.e. a viscoelastic fluid having a relaxation time that is an instantaneous function of the local shear-rate). Evidence for another instability is found where the degree of thinning in the shear viscosity is high. The mechanism for this instability is fundamentally different from that in coextrusion. In the final section of the dissertation a study of two fluids of different constitutive types but identical base-state velocity and stress profiles shows that the criterion for the "coextrusion" instability depends on properties of the model itself. The flows in question are relevant to the practical problem of extrusion of polymeric liquids. The two instabilities found may provide mechanisms for experimental observations of helical distortions of extrudates. The demonstration that the constitutive type of a model has a crucial effect on its stability may have implications for future constitutive modelling in this field