The first part of this dissertation examines the nature of interfacial instabilities between two stratified viscous fluids, particularly for unsteady, accelerating flows. Experiments performed with a vertical interface subject to oscillations of the bounding wall are found to agree well with linear stability theory. A cyclic, three-part mechanism for wave growth is identified, which may explain instabilities occurring in transient process flows. A basic state pressure fluctuation, created by faulty pump operation or other nonidealities, is explored as a possible instability mechanism in pressure driven channel flow. The linear theory reveals th at growth rates of an interfacial disturbance can be strongly affected by a weak oscillation, provided that forcing is introduced at the correct, “natural” frequency. This selectivity with respect to frequency arises due to linear interactions between the interfacial disturbance and a secondary disturbance flow which travels upstream relative to the base flow or is contained within one of the two fluids. Finally, the stability of three experimental systems are reexamined through use of a weakly nonlinear simulation which includes all quadratic and cubic interactions between discrete Fourier modes. These calculations extend beyond the range of situations accessible by the popular Stuart-Landau theory, and resolve many discrepancies between observation and Orr-Sommerfeld predictions.

Part II of this dissertation considers experimentally two distinct problems in particulate flows. A dilute, stabilized emulsion in a simple bounded shear flow is visualized through optical techniques. The anisotropy of droplet-plane interactions causes drops to drift inward toward the centerline:​ a shear induced gradient diffusivitv due to irreversible droplet-droplet interactions acts to disperse the drops. The balance of these two competing mechanisms provides a useful measure of the diffusivity of deformable particles. The second problem studied concerns the motion of a rigid, rough sphere under shear in contact with a plane. At small but finite Reynolds number, a translating and rotating sphere experiences an inertial lift force, which can overcome other forces acting on the sphere and remove the particle from the surface. It is demonstrated that the surface roughness has a profound effect on particle motion.