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<p>Understanding the drying of droplets is of interest for processes such as spray drying, where particulate materials are produced by evaporating moisture. Even though spray-drying is a widely used method, there are still challenges, such as undesired agglomeration or controlling the morphology and size of the final dried product. This dissertation develops a physics based model that is used to examine the droplet dynamics and drying kinetics at large and small scales.  In addition, the model simulates the internal motion of insoluble particles and  is used to better understand particle formation during spray drying type processes.</p> <p><br></p> <p>The first part of this work examines the effect of droplet-droplet collisions on evaporation and the size distribution at a large scale. Droplet collision dynamics are implemented into an Eulerian-Lagrangian framework, where droplets are tracked in the Lagrangian frame, and the background gas is modeled as a continuum. The modeling framework includes fully coupled interphase heat and momentum transfer between the droplet and gas phases. Binary collision of droplets could result in coalescence, reduction in surface area, or separation of droplets, resulting in the generation of satellite droplets and an increase in total surface area. By capturing the change in size distribution due to the collision of particles, our results show a linear relationship between the Weber number and the evaporation rate at low droplet number densities. Further, it is shown that droplet number density is a critical factor influencing the evaporation rate. At high droplet number densities, the relationship between the evaporation rate and the Weber number becomes non-linear, and at extremely high droplet number densities, the evaporation rate decreases even at high Weber numbers.</p> <p><br></p> <p>In the next part of this dissertation, the drying of a single droplet containing insoluble solid particles is investigated. Using a volume-of-fluid framework coupled with the Lagrangian phase, we study the particle transport within a droplet, and how it is affected by airflow, phase properties (e.g., viscosity and density of each phase), surface tension, and evaporation. Unlike the traditional one-dimensional modeling approach, our multi-dimensional model can capture the generation of internal flow patterns due to shear flow and the accumulation of solid particles on the surface of the drying droplet. Our results show that the surface tension effect is more pronounced at larger droplet diameters and low airflow velocities. Our approach also provides a quantitative method for modeling crust growth and formation. </p> <p>Our results show that increasing solids mass fraction, and decreasing particle diameter, slow down the internal transport of solid particles, leading to a more quick accumulation near the surface of the droplet. Further, despite the droplet undergoing a constant-rate drying stage, the accumulation of solids near the surface is non-linear. In addition, the inclusion of solids within the droplet drastically reshapes the formation of internal vortices compared to the uncoupled case, which determines solids distribution.</p>

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The collisions frequency of dispersed phases (particles, droplets, bubbles) in a turbulent carrier phase is a fundamental quantity that is needed for modeling multiphase flows with applications to chemical processes, minerals flotation, food science, and many other industries. In this dissertation, numerical simulations are performed to determine collisions frequency of bi-dispersed particles (solid particles and bubbles) in homogeneous isotropic turbulence. Both direct numerical simulations (DNS) and Large Eddy simulations (LES) are conducted to determine velocity fluctuations of the carrier phase. The DNS results are used to validate existing theoretical models as well as the LES results. The dissertation also presents a CFD-based flotation model for predicting the pulp recovery rate in froth flotation machines. In the direct numerical simulations work, particles and bubbles suspended in homogeneous isotropic turbulence are tracked and their collisions frequency is determined as a function of particle Stokes number. The effects of the dispersed phases on the carrier phase are neglected. Particles and bubbles of sizes on the order of Kolmogorov length scale are treated as point masses. Equations of motion of dispersed phases are integrated simultaneously with the equations of the carrier phase using the same time stepping scheme. In addition to Stokes drag, the pressure gradient in the carrier phase and added-mass forces are also included. The collision model used here allows overlap of particles and bubbles. Collisions kernel, radial relative velocity, and radial distribution function found by DNS are compared to theoretical models over a range of particle Stokes number. In general, good agreement between DNS and recent theoretical models is obtained for radial relative velocity for both particle-particle and particle-bubble collisions. The DNS results show that around Stokes number of unity particles of the same group undergo expected preferential concentration while particles and bubbles are segregated. The segregation behavior of particles and bubbles leads to a radial distribution function that is less than one. Existing theoretical models do not account for effects of this segregation behavior of particles and bubbles on the radial distribution function. In the large-eddy simulations efforts, the dissertation addresses the importance of the subgrid fluctuations on the collisions frequency and investigates techniques for predicting those fluctuations. The cases studied are of particles-particles and particles-bubbles collisions at Reynolds number Re_λ = 96. A study is conducted first by neglecting the effects of subgrid velocity fluctuations on particles and bubbles motions. It is found that around Stokes number of unity solid particles of the same group undergo the well known preferential concentration as observed in the DNS. Effects of pressure gradient on the particles are negligible due to their small sizes. Bubbles as a low inertia particles are very sensitive to subgrid velocity and acceleration fields where the effects of pressure gradient in the carrier phase are dominant. However, particle-bubble radial distribution functions from LES are not as low as that from DNS. To account for the effects of subgrid field on the dispersion of particles and bubbles, a new multifractal methodology has been developed to construct a subgrid vorticity field from the resolved vorticity field in frame work of LES. A Poisson's solver is used to obtain the subgrid velocity field from the subgrid vorticity field. Accounting for the subgrid velocity fluctuations (but neglecting pressure gradient) produced minor changes in the radial distribution function for particle-particle and particle-bubble collisions. We conclude from this study that for accurate particle tracking in LES the subgrid velocity fluctuations must be dynamically realizable field (temporally and spatially correlated with the large scale motion). Adding random SGS velocity fluctuations is not enough to capture the correct radial distribution functions of dispersed phases especially for bubbles-particles collisions where the pressure gradient term ( or acceleration Du_f′/Dt) is responsible for particle-bubble segregation around particle Stokes number near one. A CFD-based model for minerals flotation machines has been developed in this dissertation. The objective of flotation models is to predict the recovery rate of minerals from a flotation cell. The developed model advances the state-of-the-art of pulp recovery rate prediction by incorporating validated theoretical collisions frequency models and detailed hydrodynamics from two-phase flow simulations. Spatial distributions of dissipation rate and air volume fraction are determined by the two-phase hydrodynamic simulations. Knowing these parameters throughout the machine is essential in understanding the effectiveness of different components of flotation machine (rotor, stator or disperser, jets) on the flotation efficiency. The developed model not only predicts the average pulp recovery rate but also it indicates regions of high/low recovery rates. The CFD-based flotation model presented here can be used to determine the dependence of recovery rate constant at any locality within the pulp based on particle diameter, particle specfic gravity, contact angle, and surface tension. / Ph. D.

A finite element model is developed for multiphase flow through soil involving three immiscible fluids: namely air, water, and an organic fluid. A variational method is employed for the finite element formulation corresponding to the coupled differential equations governing the flow of the three fluid phase porous medium system with constant air phase pressure. Constitutive relationships for fluid conductivities and saturations as functions of fluid pressures which may be calibrated from two-phase laboratory measurements, are employed in the finite element program. The solution procedure uses iteration by a modified Picard method to handle the nonlinear properties and the backward method for a stable time integration. Laboratory experiments involving soil columns initially saturated with water and displaced by p-cymene (benzene-derivative hydrocarbon) under constant pressure were simulated by the finite element model to validate the numerical model and formulation for constitutive properties. Transient water outflow predicted using independently measured capillary head-saturation data agreed well with observed outflow data. Two-dimensional simulations are presented for eleven hypothetical field cases involving introduction of an organic fluid near the soil surface due to leakage from an underground storage tank. The subsequent transport of the organic fluid in the variably saturated vadose and ground water zones is analysed. / Ph. D.

The presence of gas in engine liquid cooling systems can have severe consequences for engine efficiency and life. The presence of stagnant, trapped gases will result in cooling system hotspots, causing gallery wall degradation through thermal stresses, fatigue and eventual cracking. The presence of entrained, transient gases in the coolant flow will act to reduce its bulk thermal properties and the performance of the system s coolant pump; critically the liquid flow rate, which will severely affect heat transfer throughout the engine and its ancillaries. The hold-up of gas in the pump s impeller may cause the dynamic seal to run dry, without lubrication or cooling. This poses both an immediate failure threat should the seal overheat and rubber components melt and a long term failure threat from intermittent quench cooling, which causes deposit formation on sealing faces acting to abrade and reduce seal quality. Bubbles in the coolant flow will also act as nucleation sites for cavitation growth. This will reduce the Net Positive Suction Head available (NPSHA) in the coolant flow, exacerbating cavitation and its damaging effects in locations such as the cylinder cooling liners and the pump s impeller. This thesis has analysed the occurrence of trapped gas (air) during the coolant filling process, its behaviour and break-up at engine start, the two-phase character of the coolant flow these processes generate and the effects it has on coolant pump performance. Optical and parametric data has been acquired in each of these studies, providing an understanding of the physical processes occurring, key variables and a means of validating numerical (CFD) code of integral processes. From the fundamental understanding each study has provided design rules, guidelines and validated tools have been developed, helping cooling system designers minimise the occurrence of trapped air during coolant filling, promote its breakup at engine start and to minimise its negative effects in the centrifugal coolant pump. It was concluded that whilst ideally the prevention of cooling system gases should be achieved at source, they are often unavoidable. This is due to the cost implications of finding a cylinder head gasket capable of completely sealing in-cylinder combustion pressures, the regular use of nucleate boiling regimes for engine cooling and the need to design cooling channel geometries to cool engine components and not necessarily to avoid fill entrapped air. Using the provided rules and models, it may be ensured stagnant air is minimised at source and avoided whilst an engine is running. However, to abate the effects of entrained gases in the coolant pump through redesign is undesirable due to the negative effects such changes have on a pump s efficiency and cavitation characteristics. It was concluded that the best solution to entrained gases, unavoidable at source, is to remove them from the coolant flow entirely using phase separation device(s).

Tissue engineering has great potential as a method for replacing or repairing lost or damaged tissue. However, progress in the field to date has been limited, with only a few clinical successes despite active research covering a wide range of cell types and experimental approaches. Mathematical modelling can complement experiments and help improve understanding of the inherently complex tissue engineering systems, providing an alternative perspective in a more cost- and time-efficient manner. This thesis focusses on one particular experimental setup, a hollow fibre membrane bioreactor (HFMB). We develop a suite of mathematical models which consider the fluid flow, solute transport, and cell yield and distribution within a HFMB, each relevant to a different setup which could be implemented experimentally. In each case, the governing equations are obtained by taking the appropriate limit of a generalised multiphase model, based on porous flow mixture theory. These equations are then reduced as far as possible, through exploitation of the small aspect ratio of the bioreactor and by considering suitable parameter limits in the subsequent asymptotic analysis. The reduced systems are then either solved numerically or, if possible, analytically. In this way we not only aim to illustrate typical behaviours of each system in turn, but also highlight the dependence of results on key experimentally controllable parameter values in an analytically tractable and transparent manner. Due to the flexibility of the modelling approach, the models we present can readily be adapted to specific experimental conditions given appropriate data and, once validated, be used to inform and direct future experiments.

The photoactive component of a polymeric organic solar cell can be produced by drying a mixture consisting of a volatile solvent and non-volatile polymers. As the solvent evaporates, the polymers demix and self-assemble into microscale structures, the morphology of which plays a pivotal role in determining the efficiency of the resulting device. Thus, a detailed understanding of the physical mechanisms that drive and influence structure formation in evaporating solvent-polymer mixtures is of high scientific and industrial value. This thesis explores several problems that aim to produce novel insights into the dynamics of evaporating solvent-polymer mixtures. First, the role of compositional Marangoni instabilities in slowly evaporating binary mixtures is studied using the framework of linear stability theory. The analysis is non-trivial because evaporative mass loss naturally leads to a time-dependent base state. In the limit of slow evaporation compared to diffusion, a separation of time scales emerges in the linear stability problem, allowing asymptotic methods to be applied. In particular, an asymptotic solution to linear stability problems that have slowly evolving base states is derived. Using this solution, regions of parameter space where an oscillatory instability occurs are identified and used to formulate appropriate conditions for observing this phenomenon in future experiments. The second topic of this thesis is the use of multiphase fluid models to study the dynamics of evaporating solvent-polymer mixtures. A two-phase model is used to assess the role of compositional buoyancy and to examine the formation of a polymer-rich skin at the free surface. Then, a three-phase model is used to conduct a preliminary investigation of the link between evaporation and phase separation. Finally, this thesis explores the dynamics of a binary mixture that is confined between two horizontal walls using a diffusive phase-field model and its sharp-interface and thin-film approximations. We first determine the conditions under which a homogeneous mixture undergoes phase separation to form a metastable bilayer. We then present a novel mechanism for generating a repeating lateral sequence of alternating A-rich and B-rich domains from this bilayer.

Ce travail se penche sur l'étude expérimentale et la simulation numérique du GLCC, un séparateur gaz-liquide cyclonique destiné à de l'industrie pétrolière.Les expériences sont menées sur un pilote air-eau. Dans un premier temps, des observations visuelles ont permis de caractériser le fonctionnement du système en fonction des débits d'entrée. L'influence de la géométrie du système ainsi que des propriétés des fluides sont également considérées.Dans un second temps, l'hydrodynamique de l'écoulement tourbillonnaire dans le séparateur est étudiée par vélocimétrie laser Doppler.Cette étude expérimentale, en mettant l'accent sur le rôle important du fillament tourbillonnaire, a permis d'expliquer pour la première fois divers aspects des écoulements tourbillonnaires turbulents. L'analyse des résultats met également en évidence les nombreuses limites du modèle théorique utilisé pour dimensionner les GLCCs.Côté numérique, les écoulements tourbillonnaires en conduite sont étudiés par une approche CFD utilisant le code commercial Fluent 6.3. Les résultats montrent que la CFD peut reproduire correctement les écoulements tourbillonnaires monophasiques. Cependant, en diphasique, les techniques de simulation actuelles ne conviennent pas pour simuler ce type d'écoulement. / This work focuses on the experimental study and numerical simulation of the GLCC, a gas-liquid cyclone separator developed for the oil industry.The experiments are conducted on an air-water pilot. In a first step, visual observations were used to characterize the system operation according to the incoming flow rates. The influence of system's geometry and the fluid's properties are also considered.In a second step, the hydrodynamics of the vortex flow in the separator is studied by laser Doppler velocimetry.This experimental study, focusing on the important role of the vortex filament, allowed to explain for the first time various aspects of turbulent swirling flows. The analysis of the results also highlights the many limitations of the theoretical model used to design the GLCC.On the numerical side, the swirling flows in pipes are studied via the CFD commercial code Fluent 6.3. The results show that CFD can correctly reproduce the single-phase vortex flow.However, for multiphase flow simulations, it is shown that the current simulation techniques are not suitable to simulate this type of flow.

Les simulations des écoulements diphasiques à l’échelle réelle de l’application nécessitent des modèles pour les termes non fermés des équations macroscopiques. Des simulations numériques directes à particule résolue utilisant la méthode de pénalisation visqueuse ont été réalisées afin de mesurer les interactions entre des particules de différentes formes (sphérique et ellipsoïdale) et le fluide porteur à différents régimes d'écoulement (de stokes à l'inertiel). Deux méthodes ont été développées durant cette thèse afin d'extraire les forces hydrodynamiques ainsi que le transfert de chaleur sur les frontières immergées représentant les particules. Plusieurs validations ont été conduites pour différentes configurations de particules : de la simulation d’une particule isolée à un réseau aléatoire de sphères en passant par réseau cubique face centrée de sphères. Une corrélation du nombre de Nusselt est proposée pour un sphéroïde allongé plongé dans un écoulement uniforme. / The simulations of multiphase flows at real application scale need models for unclosed terms in macroscopic equations. Particle-Resolved Direct Numerical Simulations using Viscous Penalty Method have been carried out to quantify the interactions between particles of different shapes (spheres, ellipsoids) and the carrier fluid at different regimes (from Stokes to inertial). Two methods have been developed to extract hydrodynamic forcesand heat transfers on immersed boundaries representing the particles. Validations have been conducted for various configuration of particles: from an isolated sphere and spheroid to Face-Centered Cubic to a random arrangement of spheres. A correlation of the Nusselt number for an isolated prolate spheroid past by a uniform flow is proposed.