Theory and Simulation of Shear Flow Instabilities in Complex Fluids

The physics of complex fluids is important to the understanding of many biological and industrial systems. The flow properties of these materials are dominated by their mesoscopic microstructures, which can lead to a large variety of behaviours in response to deformation. In this thesis, we study flow instabilities of two such fluids in shear flow: shear-thinning viscoelastic fluids and elastoviscoplastic yield stress fluids. Our first study examines the stability of a pressure-driven channel flow of a shear-thinning viscoelastic fluid to two-dimensional perturbations. We perform this study using three constitutive models: Rolie-Poly, Johnson-Segalman and White-Metzner. For each model, we perform linear stability analysis to determine the critical pressure drop for which the flow becomes unstable as a function of the model parameters. We find instability when the degree of shear thinning exceeds some level characterised by the logarithmic slope of the flow curve at its shallowest point. Specifically, we show that the critical pressure drop obeys a criterion expressed in terms of the degree of shear-thinning, together with the derivative of normal stress with respect to shear stress. In the Rolie-Poly and Johnson-Segalman models, the mechanism for instability appears to involve the deformation of a quasi-interface that exists in each half of the channel, across which normal stress varies rapidly. In the White-Metzner model, no such quasi-interface exists. Despite these apparent differences, the criterion for instability is of the same form in each model. We next investigate yielding during shear start-up in soft glassy materials. Employing the soft glassy rheology model (SGR), we study the effects of sample preparation and applied shear-rate on yielding. Our study performs shear start-up on samples at zero and non-zero noise temperature, which correspond to athermal and thermal materials respectively. We perform this study using three preparation protocols commonly used in the simulation of soft glassy materials. Our results demonstrate qualitative agreement with the findings of particle-based simulations at athermal soft glasses not previously simulated using SGR. For materials sheared at non-zero noise temperature, our calculations demonstrate that brittle yielding only occurs when the start-up curve has a sufficiently large overshoot. This is not the case for athermal materials, which display brittle yielding given any overshoot at small enough strain rate. In all protocols studied, we find close correspondence between material yielding and the formation of shear bands. This suggests that brittle yielding may be caused by the instability of a spatially homogeneous shear flow to heterogeneous shear rates during start-up, as opposed to a spinodal mechanism proposed by other authors. Finally we study the longevity of shear bands during shear start-up in yield stress fluids using a novel lattice implementation of the soft glassy rheology model. We characterise the longevity of heterogeneous flow by calculating the time required for a material sample to completely fluidise during start-up. Our study explores the effects of sample preparation prior to the application of shear for materials at zero and non-zero effective noise temperature. We find qualitative agreement with the findings of both experimental studies and particle-based simulations. Our study shows this model to be quite effective at capturing the physics of transient shear banding in soft glassy systems.