This study focuses on deposition processes from sediment laden buoyant river plumes in deltaic regions. The goal is to experimentally examine the effects of various physical phenomena influencing the rate at which sediment is removed from the plume. Previous laboratory and field measurements have suggested that, at times, sedimentation can take place at rates higher than that expected from individual particle settling (i.e., C{W}_{s}). Two potential drivers of enhanced sedimentation are flocculation and interfacial instabilities. We experimentally measured the sediment fluxes from each of these processes using two sets of laboratory experiments that investigate two different modes of instability, one driven by sediment settling and one driven by fluid shear. The settling-driven and shear-driven instability sets of experiments were carried out in a stagnant stratification tank and a stratification flume respectively. In both sets, continuous interface monitoring and concentration measurement were made to observe developments of instabilities and their effects on the removal of sediment. Floc size was measured during the experiments using a separate floc camera setup and image analysis routines. Results from the stratification tank experiments suggest that the settling-driven gravitational instabilities do occur in the presence of flocs, and that they can produce sedimentation rates higher than those predicted from floc settling. A simple cylinder based force balance approach adopting the concept of critical Grashof number was used to develop a model for the effective settling velocity under settling-driven instabilities that is a function of sediment concentration in the plume only. Results from the stratification flume experiments show that under shear instabilities, the effective settling velocity is greater than the floc settling velocity, and increases with plume velocity and interface mixing. The difference between effective and floc settling velocity was denoted as the shear-induced settling velocity. This settling rate was found to be a strong function of the Richardson number, and was attributed to mixing processes at the interface. Conceptual and empirical analysis shows that the shear-induced settling velocity is proportional to U{Ri}^{-2}. Following the experiments, analyses were made among contributions of different mechanisms on the total deposition rate, and the locations that the various mechanisms may be active in the length of a plume. This analysis leads to a conceptual discretization of a plume into three zones of sedimentation behavior and Richardson number. The first zone is the supercritical near-field plume with intense interface mixing. Zone two represents the subcritical region where interface mixing still occurs, and zone three is the high Richardson number zone where mixing at the interface is effectively nonexistent. In zones one and two, individual floc settling and shear-induced settling mechanisms play the major roles in removing sediment from the plume. While, shear-induced settling rate was found to be maximum near the river mouth, its share of the total settling rate increases in the crossshore direction, since sand and large particulates deposit near the inlet and only small particles (with relatively low settling velocity) remain as the plume propagates. The third zone, starts when the interfacial mixing diminishes and leaking commences. / Ph. D.

<div><div>This thesis analyzed three fundamental fluid dynamics problems arising from multiphase flows that may be encountered in hydraulically fractured flow passages. During hydraulic fracturing (``fracking''), complex fluids laden with proppants are pumped into tight rock formations. Flow passages in these formation are naturally heterogeneous with geometric variations, which become even more pronounced due to fracking. Upon increasing the flow area (and, thus, the conductivity of the rock), crude oil, shale gas or other hydrocarbons can then flow out of the formation more easily. In this context, we encounter the following three fluid mechanical phenomena: fluid--fluid interfacial instabilities, flow-wise variation of the hydraulic conductivity, and particle migration in the pumped fluids. </div><div><br></div><div>First, we studied the (in)stability of the interface between two immiscible liquids in angled (tapered) Hele-Shaw cells, as model of a non-uniform flow passage. We derived an expression for the growth rate of perturbations to the flat interface and for the critical capillary number, as functions of the small gap gradient (taper). On this basis, we formulated a three-regime theory to describe the interface's stability. Specifically, we found a new regime in which the growth rate changes from negative to positive (converging cells), or from positive to negative (diverging cells), thus the interface's stability can change type at some location in the cell. We conducted three-dimensional OpenFOAM simulations of the Navier--Stokes equations, using the continuous surface force method, to validate the theory.</div><div><br></div><div>Next, we investigated the flow-wise variation of the hydraulic conductivity inside a non-uniformly shaped fracture with permeable walls. Using lubrication theory for viscous flow, in conjunction with the Beavers--Joseph--Saffman boundary condition at the permeable walls, we obtained an analytical expression for the velocity profile, conductivity, and wall permeation velocity. The new expression highlights the effects of geometric variation, </div><div>the permeability of the walls, </div><div>and the effect of flow inertia.</div><div>The theory was validated against OpenFOAM simulations of the Navier--Stokes equations subject to a tensorial slip boundary condition.</div><div><br></div><div>Finally, we extended the utility of phenomenological models for particle migration in shear flow using the physics-informed neural networks (PINNs) approach. We first verified the approach for solving the inverse problem of radial particle migration in a non-Brownian suspension in an annular Couette flow. Then, we applied this approach to both non-Brownian and Brownian suspensions in Poiseuille slot flow, for which a definitive calibration of the phenomenological migration model has been lacking. Using PINNs, we identified the unknown/empirical parameters in the physical model, showing that (unlike assumptions made in the literature) they depend on the bulk volume fraction and shear P\'eclet number. </div></div>

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