Particle-laden flows find relevance in numerous natural and industrial settings. Industrial coating processes, sediment transport and turbidity currents in oceanic environments, and the disk-like flow of gas and dust particles (accretion disk) in outer space; particle-laden flows are ubiquitous. A dispersed phase affects the flow dynamics via several diverse mechanisms. The underlying particulate microstructure can alter the viscosity and density of the suspension, introduce non-Newtonian rheology due to hydrodynamic interactions and for inertial particles modulate the flow via the inter-phase drag. Could these additional physics be responsible for the particulate phase destabilising a background flow? To answer this question, two problems in particle-laden flows have been investigated.

In the first problem, the stability of a gravity-driven particle-laden flow is studied. Shallow free-surface flows, devoid of particles, are susceptible to a surface mode (Yih 1963) and a shear mode (Floryan et al. 1987) instability. First, the linear regime is probed by performing a linear stability analysis to study the combined effect of shear-induced migration and buoyancy forces on the stability of the system. When the particles are neutrally buoyant and Brownian, the particles expectedly act to stabilise the system. However, when the underlying microstructure has non-equilibrium deviations, the suspension displays non-Brownian effects - shear-induced migration and normal stresses. Thus for non-Brownian particles, the viscosity stratification caused by shear-induced migration enhances both instability modes. When laden with negatively buoyant non-Brownian suspensions, shear-induced migration and buoyancy forces act together to destabilise the interfacial mode further. Next, due to the relative simplicity of equations corresponding to the neutrally buoyant colloidal particle-laden case, reduced-order nonlinear models are obtained governing the coupled evolution of the particle concentration and the film thickness beyond the onset of the linear instability. The evolution equation governing the average particle concentration is obtained using a centre manifold approach, capturing the phenomena of Taylor-Aris dispersion. A Benney-like gradient expansion approach and the integral boundary layer approach are developed for the momentum field to study the formation of ``particulate nonlinear waves".


In the second problem, the role of inter-phase drag is studied in the context of a particle-laden vortex. When devoid of particles, a vortex monopole is stable to infinitesimal disturbances. However, the inclusion of inertial particles triggers a novel instability in the system. An interesting analogy between the inter-phase drag and non-Bousinessq effects can be drawn, thus explaining the instability mechanism. This phenomenon is studied using a linear stability analysis, with the particle phase modelled using a small Stokes asymptotic expansion of the two-fluid model. Further, it is observed that the linear stability analysis results favourably compare with the predictions from the Eulerian-Lagrangian simulations of the complete nonlinear system.