We find a set of conditions on a roof function to ensure topological mixing for suspension flows over a topological mixing base. In the measure theoretic case, such conditions have already been established for certain flows. Specifically, certain suspensions are topologically mixing if and only if the roof function is not cohomologous to a constant. We show that an analogous statement holds to establish topological mixing with the presence of dense periodic points. Much of the work required is to find properties specific to the equivalence class of functions cohomologous to a constant. In addition to these conditions, we show that the set of roof functions that induce a topologically mixing suspension is open and dense in the space of continuous roof functions.

Particle-laden flows occur in a variety of natural and industrial situations. As particulate suspensions flow through a medium, particles are often retained at constrictions such as pore throats, outlets or orifices. This occurs not only with oversized particles, but also with particles smaller than the constriction. For instance, jams are caused by the formation of particle bridges/arches when several particles attempt to flow through a constriction simultaneously. In many instances the success of an operation depends on our ability to either ensure or stop the flow of particles in the flow stream. Managing the flow of sand into wellbores during hydrocarbon production from poorly consolidated sandstone reservoirs, also referred to as sand control, is one such application in the oil and gas industry. This dissertation presents a multi-pronged effort at modeling the flow of granular suspensions of different concentrations, and through pore openings of different shapes, with two main objectives: (1) predicting the mass and size-distribution of the particles that are produced before jamming, and (2) investigating the underlying factors that influence the onset and stability of particle arches. Since, the dominant interactions and retention mechanisms are concentration dependent, we divided particulate suspensions into three groups based on the volumetric particle concentration ([phi]). High-concentration suspension flows ([phi]>~50%) are dominated by particle-particle interactions. We modeled polydisperse sand packs flowing through screens with rectangular and woven-square openings using 3D discrete element method (DEM). Simulations were validated against experimental data for a wide range of screen opening and sand size distributions. From the experiments and DEM simulations, a new scaling relation is identified, in which the number of different sized particles produced before retention follows a power-law correlation with the particle-to-outlet size ratio. This correlation is explained with a simple probabilistic model of bridging in polydisperse systems and a particle-size dependent jamming probability calculated from experimental data. A new method is presented to estimate the mass and size distribution of the produced solids through screens. The method uses the entire particle size distribution (PSD) of the formation sand, is validated with experimental data and numerical simulations, and provides more quantitative and accurate predictions of screen performance compared to past methods. It is also found that the stability of particle arches is compromised when adjacent outlets are less than three particle diameters away from each other. Low-concentration suspension flows ([phi]<~1%) are dominated by particle-fluid interactions. They were modeled using analytical and stochastic methods to predict sand production through screens with slot and woven-square openings. Analytical expressions were derived for screens with a constant outlet size or with a known outlet size distribution. Monte Carlo simulations showed excellent agreement with the analytical solutions. Based on experiments, we have demonstrated that the models presented here are predictive, provided that an accurate representation of the formation sand PSD and the screen pore size distribution are available. In the intermediate-concentration regime (~1%<[phi]<~50%), the particle trajectories and the flow field are both influenced by each other. The onset of particle bridging due to hydrodynamic forces was studied for monodisperse systems, in a rectangular channel with a single constriction, using coupled computational fluid dynamics (CFD) and DEM simulations. It is shown that the probability of jamming increases with [phi], and there is a critical particle concentration ([phi, superscript asterisk]) for spontaneous bridging. The outlet-to-particle size ratio is the most critical parameter affecting [phi, superscript asterisk]. The effect of inlet-to-particle size ratio, fluid velocity, particle stiffness, particle-to-fluid density ratio, and the effect of convergence in flow geometry were also studied quantitatively. Finally, the application of micro-tomography images in constructing accurate 3D representations and calculating the pore size distribution of complex filter media is demonstrated. A simulation tool is presented that allows one to evaluate the performance of different screens without running expensive and sometimes inconclusive experiments, and enhances our understanding of screen performance. This helps to improve sand screen selection to meet performance criteria under a wide variety of conditions. / text

In order to simulate cellular blood, a coarse-grained spectrin-link (SL) red blood cell (RBC) membrane model is coupled with a lattice-Boltzmann (LB) based suspension solver. The LB method resolves the hydrodynamics governed by the Navier--Stokes equations while the SL method accurately models the deformation of RBCs under numerous configurations. This method has been parallelized using Message Passing Interface (MPI) protocols for the simulation of dense suspensions of RBCs characteristic of whole blood on world-class computing resources. Simulations were performed to study rheological effects in unbounded shear using the Lees-Edwards boundary condition with good agreement with rotational viscometer results from literature. The particle-phase normal-stress tensor was analyzed and demonstrated a change in sign of the particle-phase pressure from low to high shear rates due to RBCs transitioning from a compressive state to a tensile state in the flow direction. Non-Newtonian effects such as viscosity shear thinning were observed for shear rates ranging from 14-440 inverse seconds as well as the strong dependence on hematocrit at low shear rates. An increase in membrane bending energy was shown to be an important factor for determining the average orientation of RBCs, which ultimately affects the suspension viscosity. The shear stress on platelets was observed to be higher than the average shear stress in blood, which emphasizes the importance of modeling platelets as finite particles. Hagen-Poiseuille flow simulations were performed in rigid vessels for investigating the change in cell-depleted layer thickness with shear rate, the Fåhraeus-Linqvist effect, and the process of platelet margination. The process of platelet margination was shown to be sensitive to platelet shape. Specifically, it is shown that lower aspect ratio particles migrate more rapidly than thin disks. Margination rate is shown to increase with hematocrit, due to the larger number of RBC-platelet interactions, and with the increase in suspending fluid viscosity.

Defective or diseased native valves have been replaced by bileaflet mechanical heart valves (BMHVs) for many years. However, severe complications still exist, and thus blood damage that occurs in BMHV flows must be well understood. The aim of this research is to numerically study platelet damage that occurs in BMHV flows. The numerical suspension flow method combines lattice-Boltzmann fluid modeling with the external boundary force method. This method is validated as a general suspension flow solver, and then validated against experimental BMHV flow data. Blood damage is evaluated for a physiologic adult case of BMHV flow and then for BMHVs with pediatric sizing and flow conditions. Simulations reveal intricate, small-scale BMHV flow features, and the presence of turbulence in BMHV flow. The results suggest a shift from previous evaluations of instantaneous flow to the determination of long-term flow recirculation regions when assessing thromboembolic potential. Sharp geometries that may induce these recirculation regions should be avoided in device design. Simulations for predictive assessment of pediatric sized valves show increased platelet damage values for potential pediatric valves. However, damage values do not exceed platelet activation thresholds, and highly damaged platelets are found far from the valve. Thus, the increased damage associated with resized valves is not such that pediatric valve development should be hindered. This method can also be used as a generic tool for future evaluation of novel prosthetic devices or cardiovascular flow problems.