Дисертації з теми "Droplet modeling"

Black liquor is an intermediate product of pulp production. Recovery boilers process black liquor to recover the inorganic material for recycling in the mill and to generate electricity and steam for the paper mill. Black liquor droplet combustion rates and mechanisms dictate many aspects of recovery boiler performance. This investigation documents new experimental data on single droplet pyrolysis and combustion in a laboratory furnace that mimics many of the essential features of commercial boilers (temperature, composition, droplet size, etc.). These experiments monitored single droplets placed on a thermocouple wire and suspended from a mass balance. Simultaneous video images and pyrometry data provide mass loss and internal temperature data. These investigations provide an extensive data set from which to validate a model and insight into the mechanisms of combustion. Particles burning in air expelled ejecta from the particle during the entire combustion process, though ejection rates during the late stages of char combustion were observed to be higher than during other stages. In addition, char burning began almost the instant the particle entered the reactor; showing significant overlap in the combustion processes. A transient, 1-dimensional, single-droplet model describes droplet combustion. This model solves the momentum, energy, species continuity, and overall continuity equations using the control volume method. The model uses the power-law scheme for combined advection diffusion, and the fully-implicit scheme for the time step. It predicts internal velocities, gas and solid temperatures (assumed equal), pressure, and composition. Pressure and velocity equations use Darcy's Law for flow through a porous medium. Modeling results show the large effect of swelling on all particle properties. This model describes the flame region by extending the control volume into the gas phase.

MODELING AND NUMERICAL ANALYSIS OF SINGLE DROPLET DRYING DALMAZ, Nesip M.Sc., Department of Chemical Engineering Supervisor: Prof. Dr. H. Ö
nder Ö
ZBELGE Co-Supervisor: Asst. Prof. Dr. Yusuf ULUDAg August 2005, 120 pages A new single droplet drying model is developed that can be used as a part of computational modeling of a typical spray drier. It is aimed to describe the drying behavior of a single droplet both in constant and falling rate periods using receding evaporation front approach coupled with the utilization of heat and mass transfer equations. A special attention is addressed to develop two different numerical solution methods, namely the Variable Grid Network (VGN) algorithm for constant rate period and the Variable Time Step (VTS) algorithm for falling rate period, with the requirement of moving boundary analysis. For the assessment of the validity of the model, experimental weight and temperature histories of colloidal silica (SiO2), skimmed milk and sodium sulfate decahydrate (Na2SO4&
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10H2O) droplets are compared with the model predictions. Further, proper choices of the numerical parameters are sought in order to have successful iteration loops. The model successfully estimated the weight and temperature histories of colloidal silica, dried at air temperatures of 101oC and 178oC, and skimmed milk, dried at air temperatures of 50oC and 90oC, droplets. However, the model failed to predict both the weight and the temperature histories of Na2SO4&
#8901
10H2O droplets dried at air temperatures of 90oC and 110oC. Using the vapor pressure expression of pure water, which neglects the non-idealities introduced by solid-liquid interactions, in model calculations is addressed to be the main reason of the model resulting poor estimations. However, the developed model gives the flexibility to use a proper vapor pressure expression without much effort for estimation of the drying history of droplets having highly soluble solids with strong solid-liquid interactions. Initial droplet diameters, which were calculated based on the estimations of the critical droplet weights, were predicted in the range of 1.5-2.0 mm, which are in good agreement with the experimental measurements. It is concluded that the study has resulted a new reliable drying model that can be used to predict the drying histories of different materials.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2000.
Includes bibliographical references (p. 138-146).
This work describes the formulation and application of a novel two-phase integral plume model. This model describes the characteristics of a vertical plume driven by the continuous release of dissolving buoyant droplets from a fixed point in a stratified, stagnant environment. Model development is motivated by a specific application, the injection of CO 2 into the deep ocean by means of a buoyant droplet plume. This application is one method of sequestering anthropogenic C02 emissions from the atmosphere. The goal of such measures is to reduce the environmental risks associated with atmospheric emissions. Of course, sequestration of C02 in the ocean introduces other environmental concerns, as dissolved CO 2 tends to lower seawater pH. It is also necessary to ensure that the CO2 is delivered to a depth where it will not be transported to the surface over short time scales. To assess the feasibility and begin to estimate the potential for environmental impacts, a multinational group of researchers plans to conduct a pilot-scale field experiment in 2001. The aim of this work is to build a model of a buoyant droplet plume that will aid both design and interpretation of the field experiment, as well as any production-scale C02 releases. Such a model is also applicable to other two-phase plume flows. To that end, an integral model is formulated which accounts for the dynamics of the primary processes associated with a droplet plume: buoyant forces acting upon the droplets and plume water, dissolution of the droplets, turbulent entrainment of ambient water into the plume, and buoyant detrainment, or "peeling." The resulting model, at its core, is expressed as a set of nonlinear, coupled differential equations. Typical integral plume models are one-dimensional, initial-value problems which require a single integration to solve the governing equations. The particular nature of the class of plumes under investigation (droplet plumes where droplet buoyancy decreases with height due to dissolution, and dissolved C02 increases fluid density), however, is characterized by regions of upward flow, driven by the buoyant droplets, and downward flow, driven by stratification and other density effects. As these flows are coupled, solution of the governing equations for flow in each direction is iterative, increasing the complexity of the solution scheme. One implicit model assumption is that plume fluid in the vicinity of the droplets advects in the same direction as the droplets. As some coarse grid models predict that the fluid actually flows in the opposite direction, some scoping experiments were carried out to verify the nature of the velocity profile in a countercurrent droplet plume. The model is analyzed for sensitivity to both design variables, such as the flow rate of droplets at the source, and parameters which are uncertain, such as turbulent entrainment coefficients and droplet dissolution rates. In the case of C02 droplets, the dissolution rate is quite uncertain due to the formation of hydrates on the droplet surface, whose effect on mass transfer is poorly understood. Fortunately, it is clear that reduced mass transfer rates can be offset by reducing the size of the droplets. Also, while plume characteristics such as plume height are sensitive to parameter uncertainty, the dilution of C02 is strongly controlled by quantifiable factors such as the C02 mass flux and the ambient stratification. This is attributable to the density effect of dissolved C02; high concentrations of dissolved C02 creates negative buoyancy which induces mixing. This mixing aids dilution. The model is also compared to datasets describing different plume regimes in order to assess its validity. Though, when tuned to a given situation, the model agrees well with the data, there is no set of parameters which is universally applicable. Although the reasons why some parameters, such as the entrainment coefficients, change from case to case are partially understood, parameter uncertainty limits the accuracy of the model. In the case of a C02 droplet plume, the rise height predictions are estimated to be accurate to within ±30 percent.
by Brian Crounse.
S.M.

Thesis (Ph. D.)--Mechanical Engineering, Georgia Institute of Technology, 2007.
Mark Papania, MD, Committee Member ; Mark Allen, Committee Member ; Yves Berthelot, Committee Member ; Ari Glezer, Committee Member ; F. Levent Degertekin, Committee Chair ; Andrei G. Fedorov, Committee Chair.

This dissertation presents the development of a modeling scheme that is developed to model the membrane potentials and ion currents through a bilayer network system. The modeling platform builds off of work performed by Hodgkin and Huxley in modeling cell membrane potentials and ion currents with electrical circuits. This modeling platform is built specifically for cell mimics where individual aqueous volumes are separated by single bilayers like the droplet-interface-bilayer. Applied potentials in one of the aqueous volumes will propagate through the system creating membrane potentials across the bilayers of the system and ion currents through the membranes when proteins are incorporated to form pores or channels within the bilayers. The model design allows the system to be divided into individual nodes of single bilayers. The conductance properties of the proteins embedded within these bilayers are modeled and a finite element analysis scheme is used to form the system equations for all of the nodes. The system equation can be solved for the membrane potentials through the network and then solve for the ion currents through individual membranes in the system. A major part of this work is modeling the conductance of the proteins embedded within the bilayers. Some proteins embedded in bilayers open pores and channels through the bilayer in response to specific stimuli and allow ion currents to flow from one aqueous volume to an adjacent volume. Modeling examples of the conductance behavior of specific proteins are presented. The examples demonstrate aggregate conductance behavior of multiple embedded proteins in a single bilayer, and at examples where few proteins are embedded in the bilayer and the conductance comes from a single-channel or pore. The effect of ion gradients on the single channel conductance example is explored and those effects are included in the single-channel conductance model. Ultimately these conductance models are used with the system model to predict ion currents through a bilayer or through part of a bilayer network system. These modeling efforts provide a modeling tool that will assist engineers in designing bilayer network systems.
Ph. D.

Le sujet traite de l’étude et de la modélisation, à l’échelle locale, des écoulements turbulents et diphasiques vapeur-gouttes dans un cœur de réacteur nucléaire lors d’un accident de perte de réfrigérant. On considère une modélisation moyennée Euler/Euler de l’écoulement diphasique. Ce travail aborde plus précisément la modélisation des termes de transfert de quantité de mouvement entre les phases et les termes de turbulence. Ainsi, nos travaux ont d’abord permis d’évaluer les limites de certains modèles utilisés dans le code de calcul NEPTUNE-CFD pour mener des études de thermo-hydraulique accidentelle au niveau local. Des solutions ont ensuite été proposées et mises en œuvre pour améliorer plus particulièrement la modélisation de l’hydrodynamique des particules et celle de leur dispersion turbulente. Cette thèse s’inscrit dans le cadre d’une collaboration entre l’IRSN et le laboratoire PROMES à Perpignan
This thesis deals with the simulation and the modeling of a turbulent vapor-droplets two-phase flow at the local scale in the core of a PWR (Pressured Water Reactor) nuclear reactor during LOCA (Loss Of Coolant Accident). We consider a Euler / Euler two-phase flow model. This work specifically treats the modeling of the terms of transfer of momentum between the phases and the terms of turbulence. Thus, first we studied the limitations of some models used in the computer code NEPTUNE-CFD for this type of flows. Solutions were then proposed and implemented to improve the modeling of the hydrodynamics of the droplets and especially that of their turbulent dispersion. This thesis is part of a collaboration between IRSN and the laboratory PROMES in Perpignan

Recently, considerable attention has been focused on the generation of nano- and micrometer scale multicomponent polymer particles with specifically tailored mechanical, electrical and optical properties. As only a few polymer-polymer pairs are miscible, the set of multicomponent polymer systems achievable by conventional methods, such as melt blending, is severely limited in property ranges. Therefore, researchers have been evaluating synthesis methods that can arbitrarily blend immiscible solvent pairs, thus expanding the range of properties that are practical. The generation of blended microparticles by evaporating a co-solvent from aerosol droplets containing two dissolved immiscible polymers in solution seems likely to exhibit a high degree of phase uniformity. A second important advantage of this technique is the formation of nano- and microscale particulates with very low impurities, which are not attainable through conventional solution techniques. When the timescale of solvent evaporation is lower than that of polymer diffusion and self-organization, phase separation is inhibited within the atto- to femto-liter volume of the droplet, and homogeneous blends of immiscible polymers can be produced. We have studied multicomponent polymer particles generated from highly monodisperse micrordroplets that were produced using a Vibrating Orifice Aerosol Generator (VOAG). The particles are characterized for both external and internal morphology along with homogeneity of the blends. Ultra-thin slices of polymer particles were characterized by a Scanning Electron Microscope (SEM), and the degree of uniformity was examined using an Electron Dispersive X-ray Analysis (EDAX). To further establish the homogeneity of the polymer blend microparticles, differential scanning calorimeter was used to measure the glass transition temperature of the microparticles obtained. A single glass transition temperature was obtained for these microparticles and hence the homogeneity of the blend was concluded. These results have its significance in the field of particulate encapsulation. Also, better control of the phase morphologies can be obtained by simply changing the solvent/solvents in the dilute solutions. Evaporation and drying of a binary droplet containing a solute and a solvent is a complicated phenomenon. Most of the present models do not consider convection in the droplet phase as solvent is usually water which is not very volatile. In considering highly volatile solvents the evaporation is very rapid. The surface of the droplet recedes inwards very fast and there is an inherent convective flow that is established inside the solution droplet. In this dissertation work, a model is developed that incorporates convection inside the droplet. The results obtained are compared to the size obtained from experimental results. The same model when used with an aqueous solution droplet predicted concentration profiles that are comparable to results obtained when convection was not taken into account. These results have significance for more rigorous modeling of binary and multicomponent droplet drying.

Les gouttes liquides se sont avérées l’un des principaux vecteurs pour la génération de particules solides à propriétés contrôlées. Ce type de vecteur est utilisé dans plusieurs domaines industriels, y compris le séchage par atomisation. Le développement de ces particules structurées est poussé par la demande pour des particules à propriétés contrôlées, comme la cinétique de dissolution, le relargage contrôlé ou la réactivité. Le principal verrou scientifique est la description détaillée de la distribution des constituants au sein de la goutte pendant le séchage, en plus de la prédiction de la morphologie de la particule finale. L'objectif de cette thèse est de comprendre, par une approche couplée modélisation/expérimentation, comment les conditions de séchage et les formulations liquides impactent la structure de la poudre. L'étude expérimentale a d'abord été réalisée dans un sécheur par atomisation à l'échelle laboratoire pour la création d'une cartographie représentant les morphologies obtenues pour les deux systèmes de séchage. Un dispositif expérimental a été conçu de manière à étudier la formation d'une particule solide à partir d'une goutte suspendue par un filament, ce qui permet d'appréhender des éléments fondamentaux relatifs au séchage de la goutte ainsi que des aspects sur la modification de la structure solide. Une nouveauté explorée à l'échelle de la goutte avec un lévitateur acoustique consistait à appliquer la spectroscopie Raman in situ afin d'évaluer l'évolution de la distribution spatiale de deux composants lors du séchage de la goutte. Enfin, un modèle de séchage de goutte en 2-D avec la Dynamique des Fluides Numérique est conçu, ce qui permet de quantifier la distribution spatiale des composants de la goutte sous un séchage convectif, jusqu’à la formation de la croûte. Une analyse de sensibilité est réalisée de manière à montrer l'influence des conditions expérimentales sur la cinétique de séchage et la distribution spatiale des solutés
Liquid droplets are one of the major means of generation of solid particles with controlled. These templates are encountered with a variety of industrial processes, among them, spray drying. These tailored structures would meet the demand for particles with controlled properties, like improved kinetics, sustained release or controlled reactivity. The major scientific obstacle is the detailed description of the components distribution inside the droplet during drying, besides prediction of the final particle morphology. An experimental/modeling approach is undertaken in this thesis to understand how the drying conditions and the liquid formulation impact the final structure of the powders. The drying systems studied were sucrose-dextran and lactose-whey protein isolate aqueous solutions. The experimental work was firstly carried out at the lab-scale spray-dryer giving a reference picture of the possible particle morphologies for the drying systems. An experimental set-up was designed and developed to suspend a liquid droplet by a filament, from which the droplet mass variation over time could be accurately measured, giving fundamental insight into the drying process and allowing the analysis of the modification of the solid structures. A novelty explored at the droplet scale with an acoustic levitator was to apply an in situ Raman spectroscopy to assess the evolution of the spatial distribution of two components in drying droplets. Finally, a 2-D droplet drying model using Computational Fluid Dynamics was developed for allowing the assessment of the spatial distribution of the droplet components under a convective drying, until the formation of a crust. A sensitivity analysis was performed in order to show the influence of the experimental conditions on the drying kinetics and the component spatial distribution

Fuel cells are promising alternatives to conventional energy conversion devices. Cells fueled with hydrogen are environmentally friendly and their effciency is up to 3 times higher than that of high-temperature combustion devices. However, they are still expensive and their durability is limited. One of the key factors in fuel cell performance is the so-called water management. Water produced within the fuel cell is evacuated through the gas channels, but at high current densities water can block the channel, limiting the current density generated in the fuel cell and thus reducing its effciency. Novel numerical analysis methods with feasible computational cost and high accuracy could help characterizing droplet transport in gas microchannels. In this work we focus on modeling and simulation of droplet emergence, deformation and detachment in fuel cell gas channels as this defines the most common mode of liquid transport in the problem at hand. However, methods presented could be applied to other problems involving a gas-liquid system, where liquid is found as small droplets or films. A semi-analytical model of a water droplet emerging from a pore of the gas diffusion layer surface in a Polymer Electrolyte fuel cell channel is developed. The geometry of the static and deformed shape is characterized and the main geometric variables (i.e. radius, height, perimeter) are assumed to depend on the contact angles only. The forces acting on the droplet are the drag force of the air and the surface tension force, which acts as adhesion force. The analytical study solves the problem of a growing droplet in a gas ow channel to see the effects of: i) air velocity and liquid mass ow in droplet deformation and oscillation; and, ii) droplet height in frequency of oscillation. The predicted values for both drag and surface tension force are higher than the results found in literature. Higher air velocity values lead to more deformation of the droplet and oscillation with lower frequency but higher amplitude. Similar effects have been identified when the liquid mass ow is increased, leading to faster detachment of the droplet. A continuum Lagrangian formulation for the simulation of droplet dynamics is proposed next. This model is developed in two and three dimensions. Using the Lagrangian framework, liquid surface can be accurately identified. The surface tension force is computed using the curvature defined by the boundary of the Lagrangian mesh. Special emphasis is given to the treatment of the surface tension term in the linearized version of governing equations. The corresponding tangent matrix allows for alleviating the severe time step size restrictions associated to the capillary wave scale. A dynamic contact angle condition is developed in order to include effects of rough surfaces in contact line evolution. Numerical examples of sessile drop in a horizontal surface and sessile drop in an inclined plane are compared to experimental results. Results show excellent agreement with experimental data. Numerical results are also compared the semi-analytical model previously developed by the authors in order to discuss the limitations of the semi-analytical approach. An embedded formulation for the simulation of immiscible coupled gas-liquid problems is then presented. Previous model considered only the liquid domain, and air ow effects were not included at the continuum level. The embedded method is particularly designed for handling gas-liquid systems where liquid represents a small fraction of the total domain. Gas and liquid are modeled using the Eulerian and the Lagrangian formulation, respectively. The Lagrangian domain (liquid) moves on top of the fixed Eulerian mesh. The location of the material interface is accurately defined by the position of the boundary mesh of the Lagrangian domain. The individual fluid problems are solved in a partitioned fashion and are coupled using a Dirichlet-Neumann algorithm. Neumann part of the coupling includes the entire stress tensor (normal and tangential components). Representation of the pressure discontinuity across the interface does not require any additional techniques being an intrinsic feature of the method. The proposed formulation is validated with several numerical examples and a convergence analysis is included as well. Finally, the embedded formulation is used to model the problem of interest, which is the dynamics of a droplet in a PEFC electrode channel. Numerical examples include a time detachment analysis, where the droplet pins and detachment occurs when a threshold value of contact angle hysteresis is reached. Results show good agreement with experimental data available, and results using the semi-analytical method again show the limitations of this model. An extension to the previous example includes water injection into the gas channel in order to compare results with previous studies in literature.
Las pilas de combustible son una alternativa prometedora a los dispositivos de conversión de energía convencionales. Las pilas alimentadas con hidrogeno son respetuosas con el medio ambiente y su eficiencia es hasta 3 veces mayor que la de los dispositivos de combustión de alta temperatura. Sin embargo, su precio todavía es elevado y su durabilidad es limitada. Uno de los factores clave en el rendimiento de las pilas de combustible es la denominada gestión del agua. El agua producida dentro de la pila es evacuada a través de los canales de gas, pero en condiciones de alta densidad de corriente, el agua puede bloquear el canal, limitando la densidad de corriente generada en la pila de combustible y reduciendo así su eficiencia. Nuevos métodos de análisis numérico con un coste computacional factible y una mayor precisión podrán ayudar a caracterizar el transporte de gotas en microcanales de gas. En este trabajo nos centramos en la formación de la gota, su deformación y posterior desprendimiento en los canales de gas de las pilas de combustible, ya que esto define el modo de transporte de la fase líquida más común en el problema analizado. Sin embargo, los métodos presentados podrán ser aplicados a otros problemas relacionados con un sistema gas-líquido, donde el líquido se encuentra como pequeñas gotas o películas. En la presente tesis, se ha desarrollado un modelo semi-analítico de una gota de agua que emerge de un poro de la superficie de la capa de difusión en un canal de una pila de combustible tipo PEFC (Polymer Electrolyte fuel cell). La geómetra de la gota estática y deformada se ha caracterizado y se ha supuesto que las principales variables geométricas (radio, altura, perímetro) sólo dependen de los ángulos de contacto. Las fuerzas que actúan sobre la gota son la fuerza de arrastre del aire y la fuerza de tensión superficial, que actúa como fuerza de adherencia. El estudio analítico resuelve el problema de una gota que crece en un canal de gas para ver los efectos de: i) la velocidad del aire y del caudal de líquido en la deformación de las gotas y su oscilación; y, ii) la altura de la gota en la frecuencia de oscilación. Los valores predichos tanto para la fuerza de arrastre como para la tensión superficial son más altos que los resultados encontrados en la literatura. A mayor velocidad del aire, mayor es la deformación de la gota y sus oscilaciones tienen menor frecuencia pero mayor amplitud. Se han identificado efectos similares cuando se incrementa el caudal de líquido, dando lugar a un desprendimiento más rápido de la gota. Los valores de oscilación de frecuencia predichos son significativamente menores que los valores de la literatura, pero estos resultados han sido obtenidos en condiciones distintas de inyección de agua. Como alternativa al modelo semi-analítico, se propone una formulación continua Lagrangiana para la simulación de la dinámica de gotas. El modelo se ha desarrollado en dos y tres dimensiones. Utilizando el enfoque Lagrangiano, la superficie del líquido se puede identificar con precisión. La fuerza de tensión superficial se calcula utilizando la curvatura definida por el borde de la malla Lagrangiana. Se hace especial hincapié en el tratamiento del término de tensión superficial en la versión linealizada de las ecuaciones de gobierno. La matriz tangente correspondiente permite suavizar las restricciones de paso de tiempo asociadas a la escala de la onda capilar. Se ha incluido una condición de ángulo de contacto dinámico con el fin de incluir los efectos de las superficies rugosas en la evolución de la línea de contacto. Los resultados obtenidos en los ejemplos numéricos de una gota estática en una superficie horizontal y en un plano inclinado se han comparado con resultados experimentales. Los resultados muestran una excelente concordancia con los datos experimentales. También se han comparado los resultados numéricos con el modelo semi-analítico desarrollado previamente por los autores con el _n de discutir las limitaciones del enfoque semi-analítico. Con el _n de incluir los efectos del aire sobre la gota, se presenta una formulación incrustada (embedded de su terminología en inglés) para la simulación de problemas de varios fluidos inmiscibles. El modelo anterior sólo considera el dominio de líquido, y los efectos del flujo de aire no se incluyen. El método está diseñado especialmente para la simulación de sistemas gas-líquido donde el líquido representa una pequeña fracción del dominio. El gas y el líquido se modelan mediante las formulaciones Euleriana y Lagrangiana, respectivamente. El dominio Lagrangiano (líquido) se mueve por encima de la malla Euleriana fija. La ubicación de la interfaz material se define exactamente por la posición del borde de la malla del dominio Lagrangiano. Los problemas de cada fluido se resuelven de una manera particionada y se acoplan mediante un algoritmo de Dirichlet-Neumann. La representación de la discontinuidad de la presión a través de la interfaz no requiere técnicas adicionales, ya que es una característica intrínseca del método. La formulación propuesta se valida con varios ejemplos numéricos y también se ha incluido un análisis de convergencia. Finalmente, la formulación embedded se utiliza para modelar el problema objetivo, que es la dinámica de una gota en un canal de una pila PEFC. Los ejemplos numéricos incluyen un análisis del tiempo de desprendimiento, donde la línea de contacto de la gota se fija y el desprendimiento se produce cuando se alcanza un valor de umbral de la histéresis del ángulo de contacto. Los resultados concuerdan satisfactoriamente con los datos experimentales disponibles, y los resultados utilizando el modelo semi-analítico muestran de nuevo las limitaciones de este modelo. Finalmente el ejemplo anterior se extiende incluyendo la inyección de agua en el canal de gas con el fin de comparar los resultados con estudios previos encontrados en la literatura.

A numerical simulation of electrowetting on a dielectric was performed in COMSOL to grant insight on various parameters that play a critical role in system performance. The specific system being simulated was the Open Drop experiment and the parameters being investigated were the applied voltage, contact angle at the advancing triple point, and droplet overlap onto neighboring actuated electrodes. These parameters were investigated with respect to their effect on droplet locomotion performance. This performance was quantified by the droplets velocity and the dielectrophortic (DEP) force’s magnitude; the DEP force was calculated from integration of the Maxwell Stress Tensor, however, the force was not integrated into the simulation to assist with droplet movement. It was found that as the droplet overlap onto the neighboring electrode, or droplet radius to electrode size ratio, decreased, the droplet velocity increased. As the applied potential increased, and induced contact angle at the advancing triple point decreased, droplet velocity also increased. Both the decreasing overlap and increasing voltage had a linear effect on droplet velocity. As the droplet overlap increased, the rate of change of droplet velocity decreased as increasing voltages were considered. A 2D DEP calculation illustrated that an increase in voltage induced a tenfold increase in the corresponding DEP force; a linear relationship was found between droplet overlap and DEP force for the Open Drop size regime.

Thesis (Ph. D.)--Ohio State University, 2005.
Title from first page of PDF file. Document formatted into pages; contains xxi, 225 p.; also includes graphics (some col.). Includes bibliographical references (p. 218-225). Available online via OhioLINK's ETD Center

Aqueous droplets submerged in an oil-lipid mixture become enclosed by a lipid monolayer. The droplets can be connected to form robust networks of droplet interface bilayers (DIBs) with functions such as a biobattery and a light sensor. The discovery and characterization of an engineered nanopore with diode-like properties is enabling the construction of DIB networks capable of biochemical computing. Moreover, DIB networks might be used as model systems for the study of membrane-based biological phenomena. We develop and experimentally validate an electrical modeling approach for DIB networks. Electrical circuit simulations will be important in guiding the development of increasingly complex DIB networks. In cell membranes, the lipid compositions of the inner and outer leaflets differ. Therefore, a robust model system that enables single-channel electrical recording with asymmetric bilayers would be very useful. Towards this end, we incorporate lipid vesicles of different compositions into aqueous droplets and immerse them in an oil bath to form asymmetric DIBs (a-DIBs). Both α-helical and β-barrel membrane proteins insert readily into a-DIBs, and their activity can be measured by single-channel electrical recording. We show that the gating behavior of outer membrane protein G (OmpG) from Escherichia coli differs depending on the side of insertion in an asymmetric DIB with a positively charged leaflet opposing a negatively charged leaflet. The a-DIB system provides a general platform for studying the effects of bilayer leaflet composition on the behavior of ion channels and pores. Even with the small volumes (~100 nL) that can be used to form DIBs, the separation between two adjacent bilayers in a DIB network is typically still hundreds of microns. In contrast, dual-membrane spanning proteins require the bilayer separation to be much smaller; for example, the bilayer separation for gap junctions must be less than 5 nm. We designed a double bilayer system that consists of two monolayer-coated aqueous spheres brought into contact with each side of a water film submerged in an oil-lipid solution. The spheres could be brought close enough together such that they physically deflected without rupturing the double bilayer. Future work on quantifying the bilayer separation and studying dual-membrane spanning proteins with the double bilayer platform is planned.

The ultimate goal of this project has been to develop a computational model for quantifying the interactions between of a body of fluid and a fibrous surface. To achieve this goal, one has to develop a model to create virtual structures that resemble the morphology of a fibrous surface (Objective-1) as well as a model that can simulate the flow of a fluid over these virtual surfaces (Objective-2). To achieve the first objective, we treated fibers as an array of beads interconnected through viscoelastic elements (springs and dampers). The uniqueness of our algorithm lies in its ability to simulate the curvature of the fibers in terms of their rigidity, fiber diameter, and fiber orientation. Moving on to Objective-2, we considered woven screens for their geometric periodicity, as a starting point. We studied how fiber diameter, fiber spacing, and contact angle can affect the skin-friction drag of a submerged hydrophobic woven screen, and how such surfaces resist against water intrusion under elevated hydro-static pressures (a requirement for providing drag reduction benefits). We also studied the impact of surface geometry and wetting properties on droplet mobility over these surfaces. Laboratory experiment was conducted at various stages throughout this investigation, and good agreement was observed between the experimental data and the results from our numerical simulation.

The focus of this dissertation is the development of a fundamental understanding of the acoustics and piezoelectric transducer governing the operation of piezoelectric inkjets and horn-based ultrasonic atomizers when utilizing high viscosity working fluids. This work creates coupled, electro-mechanical analytical models of the acoustic behavior of these devices by extending models from the literature which make minimal simplifications in the handling terms that account for viscous losses. Models are created for each component of the considered fluid ejectors: piezoelectric transducers, acoustic pipes, and acoustic horns. The acoustic pipe models consider the two limited cases when either the acoustic boundary layer or attenuation losses dominate the acoustic field and are adapted to account for changes in cross-sectional area present in acoustic horns. A full electro-mechanical analytical model of the fluid ejectors is formed by coupling the component models using appropriate boundary conditions. The developed electro-mechanical model is applied to understand the acoustic response of the fluid cavity alone and when combined with the transducer in horn-based ultrasonic atomizers. An understanding of the individual and combined acoustic response of the fluid cavity and piezoelectric transducer allow for an optimal geometry to be selected for the ejection of high viscosity working fluids. The maximum pressure gradient magnitude produced by the atomizer is compared to the pressure gradient threshold required for fluid ejection predicted by a hydrodynamic scaling analysis. The maximum working fluid viscosity of the standard horn-based ultrasonic atomizer and those with dual working fluid combinations, a low viscosity and a high viscosity working fluid to minimize viscous dissipation, is established to be on the order of 100mPas. The developed electro-mechanical model is also applied to understand the acoustic response of the fluid cavity and annular piezoelectric transducer in squeeze type ejectors with high viscosity working fluids. The maximum pressure gradient generated by the ejector is examined as a function of the principle geometric properties. The maximum pressure gradient magnitude produced by the ejector is again compared to the pressure gradient threshold derived from hydrodynamic scaling. The upper limit on working fluid viscosity is established as 100 mPas.

I dispositivi microfluidici costituiscono una rivoluzione nella manipolazione di piccole quantità di fluidi, anche inferiori al picolitro. Le gocce in questi dispositivi fungono da microreattori, poiché sono utilizzate per incapsulare campioni e reagenti. Esse vengono manipolate all'interno del dispositivo per eseguire, su un chip con area nell'ordine dei centimetri, esperimenti normalmente realizzabili solo in laboratorio. L'obiettivo di questa tesi è estendere le funzionalità attuali dei dispositivi microfluidici passivi che manipolano gocce. Questi dispositivi non richiedono l'integrazione di componenti elettronici sul chip microfluidico né strumentazione di controllo per manipolare le gocce in maniera attiva. Essi, piuttosto, sfruttano soltanto effetti idrodinamici e, quindi, non richiedono un processo di fabbricazione complesso e costoso essendo totalmente passivi. I dispositivi microfluidici passivi che manipolano gocce sono usati principalmente per esperimenti e analisi chimiche e biologiche ma non sono in grado di eseguire protocolli di analisi complessi. Infatti, ogni dispositivo è progettato unicamente per una specifica applicazione ed è in grado di compiere solo operazioni semplici sulle gocce. Queste limitazioni possono essere superate introducendo una tecnologia di networking flessibile e modulare, che doti questi sistemi di una rete di comunicazione in modo da consentire sia lo scambio di informazione che di specie chimiche, trasportate entrambe dalle gocce. La rete microfluidica risultante sarà in grado di combinare le funzionalità specifiche di ciascun dispositivo microfluidico connesso ad essa, formando una potente e versatile piattaforma microfluidica in grado di implementare protocolli biochimici diversi su un unico chip.

I dispositivi microfluidici costituiscono una rivoluzione nella manipolazione di piccole quantità di fluidi, anche inferiori al picolitro. Le gocce in questi dispositivi fungono da microreattori, poiché sono utilizzate per incapsulare campioni e reagenti. Esse vengono manipolate all'interno del dispositivo per eseguire, su un chip con area nell'ordine dei centimetri, esperimenti normalmente realizzabili solo in laboratorio. L'obiettivo di questa tesi è estendere le funzionalità attuali dei dispositivi microfluidici passivi che manipolano gocce. Questi dispositivi non richiedono l'integrazione di componenti elettronici sul chip microfluidico né strumentazione di controllo per manipolare le gocce in maniera attiva. Essi, piuttosto, sfruttano soltanto effetti idrodinamici e, quindi, non richiedono un processo di fabbricazione complesso e costoso essendo totalmente passivi. I dispositivi microfluidici passivi che manipolano gocce sono usati principalmente per esperimenti e analisi chimiche e biologiche ma non sono in grado di eseguire protocolli di analisi complessi. Infatti, ogni dispositivo è progettato unicamente per una specifica applicazione ed è in grado di compiere solo operazioni semplici sulle gocce. Queste limitazioni possono essere superate introducendo una tecnologia di networking flessibile e modulare, che doti questi sistemi di una rete di comunicazione in modo da consentire sia lo scambio di informazione che di specie chimiche, trasportate entrambe dalle gocce. La rete microfluidica risultante sarà in grado di combinare le funzionalità specifiche di ciascun dispositivo microfluidico connesso ad essa, formando una potente e versatile piattaforma microfluidica in grado di implementare protocolli biochimici diversi su un unico chip.
Microfluidic devices represent a revolution in handling small volumes of fluids down to less than pico-liters. Droplets in these devices are used as microreactors to encapsulate samples and reagents. They are manipulated to perform laboratory functions on a single chip of only a few square centimeters in size. The aim of this thesis is the extension of the current capabilities of microfluidic passive droplet-based devices. These devices do not rely on in-chip electronics and macro-scale control supplies to actively manipulate droplets. They exploit, instead, hydrodynamic effects without requiring complex and costly production processes. Microfluidic passive droplet-based devices are mainly used for chemical and biological experiments and analyses, but lack of capabilities to perform complex and programmable laboratory workflows (i.e. they are single-purpose). These limitations can be overcome by introducing a flexible and modular microfluidic networking technology to provide to such systems a communication network for the exchange of both information and chemical/biological samples carried by droplets. The resulting microfluidic communication network will combine the specific functionalities of each connected microfluidic device, in a programmable and versatile microfluidic platform for diverse assay protocols on a single chip.

Thesis (M.S.)--University of Toledo, 2010.
Typescript. "Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Master of Science Degree in Mechanical Engineering." "A thesis entitled"--at head of title. Title from title page of PDF document. Bibliography: p. 90-94.

Ce travail consiste en une étude des phénomènes de coalescence dans un nuage de gouttes, par la simulation numérique directe d'un écoulement turbulent gazeux, couplée avec une approche de suivi Lagrangien pour la phase dispersée. La première étape consiste à développer et valider une méthode de détection des collisions pour une phase polydispersée. Elle est ensuite implémentée dans un code couplé de simulation directe et de suivi Lagrangien existant. Des simulations sont menées pour une turbulence homogène isotrope de la phase continue et pour des phases dispersées en équilibre avec le fluide. L'influence de l'inertie des gouttes et de la turbulence sur le taux de coalescence des gouttes est discutée dans un régime de coalescence permanente. Un aperçu est donné de la prise en compte d'autres régimes de collision et de coalescence entre gouttes. Ces simulations sont la base de développement et de validation des approches utilisées dans les calculs à l'échelle industrielle. En particulier, les résultats des simulations sont comparés avec les prédictions d'une approche Lagrangienne de type Monte-Carlo et de l'approche Eulerienne 'Direct Quadrature Method of Moments' (DQMOM). Différents types de fermeture des termes de coalescence sont validés. Les uns sont basés sur l'hypothèse de chaos-moléculaire, les autres sont capables de prendre en compte des corrélations de vitesses des gouttes avant la collision. Il est montré que cette derniere approche prédit beaucoup mieux le taux de coalescence par comparaison avec les résultats des simulations déterministes
Coalescence in a droplet cloud is studied in this work by means of direct numerical simulation of the turbulent gas flow, which is coupled with a Lagrangian tracking of the disperse phase. In a first step, a collision detection algorithm is developed and validated, which can account for a polydisperse phase. This algorithm is then implemented into an existing code for direct numerical simulations coupled with a Lagrangian tracking scheme. Second, simulations are performed for the configuration of homogeneous isotropic turbulence of the fluid phase and a disperse phase in local equilibrium with the fluid. The influence of both droplet inertia and turbulence intensity on the coalescence rate of droplets is discussed in a pure permanent coalescence regime. First results are given, if other droplet collision outcomes than permanent coalescence (i.e. stretching and reflexive separation) are considered. These results show a strong dependence on the droplet inertia via the relative velocity of the colliding droplets at the moment of collision. The performed simulations serve also as reference data base for the development and validation of statistical modeling approaches, which can be used for simulations of industrial problems. In particular, the simulation results are compared to predictions from a Lagrangian Monte-Carlo type approach and the Eulerian 'Direct Quadrature Method of Moments' (DQMOM) approach. Different closures are validated for the coalescence terms in these approaches, which are based either on the assumption of molecular-chaos, or based on a formulation, which allows to account for the correlation of droplet velocities before collision by the fluid turbulence. It is shown that the latter predicts much better the coalescence rates in comparison with results obtained by the performed deterministic simulations

Understanding the interactions between a body of liquid and a curvy surface is important for many applications such as underwater drag force reduction, droplet filtration, self-cleaning, and fog harvesting, among many others. This study investigates ways to predict the performance of granular and fibrous surfaces for some of the above applications. More specifically, our study is focused on 1) modeling the mechanical stability of the air-water interface over submerged superhydrophobic (SHP) surfaces and their expected drag reduction benefits, and 2) predicting the mechanical stability of a droplet on a fiber in the presence of an external body force. For the first application, we modeled the air–water interface over submerged superhydrophobic coatings comprised of particles/fibers of different diameters or Young–Laplace contact angles. We developed mathematical expressions and modeling methodologies to determine the maximum depth to which such coatings can be used for underwater drag reduction as well as the magnitude of the depth-dependent drag reduction effect of the surface. For the second application, we studied the force required to detach a droplet from a single fiber or from two crossing fibers. The results of our numerical simulations were compared to those obtained from experiment with ferrofluid droplets under a magnetic field, and excellent agreement was observed. Such information is of crucial importance in design and manufacture of droplet–air and droplet–fluid separation media, fog harvesting media, protective clothing, fiber-reinforced composite materials, and countless other applications.

The role of aerosols and clouds is one of the largest sources of uncertainty in understanding climate change. The primary scientific goal of this thesis is to improve the understanding of cloud-aerosol interactions by applying inverse modeling using Markov Chain Monte Carlo (MCMC) simulation. Through a set of synthetic tests using a pseudo-adiabatic cloud parcel model, it is shown that a self adaptive MCMC algorithm can efficiently find the correct optimal values of meteorological and aerosol physiochemical parameters for a specified droplet size distribution and determine the global sensitivity of these parameters. For an updraft velocity of 0.3 m s-1, a shift towards an increase in the relative importance of chemistry compared to the accumulation mode number concentration is shown to exist somewhere between marine (~75 cm-3) and rural continental (~450 cm-3) aerosol regimes. Examination of in-situ measurements from the Marine Stratus/Stratocumulus Experiment (MASE II) shows that for air masses with higher number concentrations of accumulation mode (Dp = 60-120 nm) particles (~450 cm-3), an accurate simulation of the measured droplet size distribution requires an accurate representation of the particle chemistry. The chemistry is relatively more important than the accumulation mode particle number concentration, and similar in importance to the particle mean radius. This result is somewhat at odds with current theory that suggests chemistry can be ignored in all except for the most polluted environments. Under anthropogenic influence, we must consider particle chemistry also in marine environments that may be deemed relatively clean. The MCMC algorithm can successfully reproduce the observed marine stratocumulus droplet size distributions. However, optimising towards the broadness of the measured droplet size distribution resulted in a discrepancy between the updraft velocity, and mean radius/geometric standard deviation of the accumulation mode. This suggests that we are missing a dynamical process in the pseudo-adiabatic cloud parcel model.
At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 3: Submitted. Paper 4: Manuscript.

The current dissertation is motivated by the need for an improved understanding of aerosol water interactions both in subsaturated and supersaturated atmospheric conditions with a strong emphasis on air pollution and climate change modeling. A cloud droplet formation parameterization was developed to i) predict droplet formation from a lognormal representation of aerosol size distribution and composition, and, ii) include a size-dependant mass transfer coefficient for the growth of water droplets which explicitly accounts for the impact of organics on droplet growth kinetics. The parameterization unravels most of the physics of droplet formation and is in remarkable agreement with detailed numerical parcel model simulations, even for low values of the accommodation coefficient. The parameterization offers a much needed rigorous and computationally inexpensive framework for directly linking complex chemical effects on aerosol activation in global climate models. The new aerosol activation parameterization was also tested against observations from highly polluted clouds (within the vicinity of power plant plumes). Remarkable closure was achieved (much less than the 20% measurement uncertainty). The error in predicted cloud droplet concentration was mostly sensitive to updraft velocity. Optimal closure is obtained if the water vapor uptake coefficient is equal to 0.06. These findings can serve as much needed constraints in modeling of aerosol-cloud interactions in the North America. Aerosol water interactions in ambient relative humidities less than 100% were studied using a thermodynamic equilibrium model for inorganic aerosol and a three dimensional air quality model. We developed a new thermodynamic equilibrium model, ISORROPIA-II, which predicts the partitioning of semi-volatiles and the phase state of K+/Ca2+/Mg2+/NH4+/Na+/SO42-/NO3-/Cl-/H2O aerosols. A comprehensive evaluation of its performance was conducted against the thermodynamic module SCAPE2 over a wide range of atmospherically relevant conditions. Based on its computational rigor and performance, ISORROPIA-II appears to be a highly attractive alternative for use in large scale air quality and atmospheric transport models. The new equilibrium model was also used to thermodynamically characterize aerosols measured at a highly polluted area. In the ammonia-rich environment of Mexico City, nitrate and chloride primarily partition in the aerosol phase with a 20-min equilibrium timescale; PM2.5 is insensitive to changes in ammonia but is to acidic semivolatile species. When RH is below 50%, predictions improve substantially if the aerosol follows a deliquescent behavior. The impact of including crustal species (Ca2+, K+, M2+) in equilibrium calculations within a three dimensional air quality model was also studied. A significant change in aerosol water (-19.8%) and ammonium (-27.5%) concentrations was predicted when crustals are explicitly included in the calculations even though they contributed, on average, only a few percent of the total PM2.5 mass, highlighting the need for comprehensive thermodynamic calculations in the presence of dust.

Thesis (Ph. D.)--West Virginia University, 2007.
Title from document title page. Document formatted into pages; contains xv, 141 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 132-135).

Cette thèse introduit un modèle hydrodynamique minimal de polarisation, migration et déformation d'une cellule vivante confinée entre deux surfaces parallèles. Le cytoplasme cellulaire, décrit comme une goutte visqueuse, est entraîné par une force active contrôlée par un soluté diffusif. Une analyse de stabilité linéaire révèle que l'activité du soluté déstabilise d'abord un mode global de polarisation et de translation, induisant une motilité cellulaire par rupture spontanée de symétrie. Pour une activité plus grande, le système traverse une série de bifurcations de Hopf conduisant à des oscillations couplées de la forme de la goutte et de la concentration de soluté. Nous trouvons également des solutions non linéaires de type onde progressive associées à des formes polarisées ressemblant à des observations expérimentales. De plus, nous avons développé des simulations numériques de ce problème basées sur la méthode des éléments finis. L'étude numérique a mis en évidence la stabilité des solutions de type onde progressive, l’existence d’attracteurs oscillants et l’apparition d’une singularité du bord à temps fini. En intégrant des interactions mécaniques avec l'environnement extérieur, nous avons exploré la diffusion cellulaire en présence de parois et d'obstacles stationnaires, la migration à travers des micro-géométries imposées et les collisions cellule-cellule. Ces simulations ont capturé une gamme de motifs non triviaux résultant de la mémoire intrinsèque et de la déformabilité de la cellule. Globalement, notre étude fournit un paradigme mathématique de systèmes actifs déformables qui couplent l'hydrodynamique de Stokes à des transducteurs de force diffusifs
This thesis introduces a minimal hydrodynamic model of polarization, migration, and deformation of a biological cell confined between two parallel surfaces. Our model describes the cell cytoplasm as a viscous droplet that is driven by an active cytoskeleton force, itself controlled by a diffusive cytoplasmic solute. A linear stability analysis of this two-dimensional system reveals that solute activity first destabilizes a global polarization-translation mode, prompting cell motility through spontaneous-symmetry-breaking. At higher activity, the system crosses a series of Hopf bifurcations leading to coupled oscillations of droplet shape and solute concentration profiles. At the nonlinear level, we find traveling-wave solutions associated with unique polarized shapes that resemble experimental observations. In addition, we developed a numerical simulation of our moving-boundary problem based on the finite element method. The numerical study demonstrated the stability of our traveling-wave solutions, the existence of sustained oscillatory attractors, and the emergence of a finite-time pinch-off singularity. By incorporating mechanical interactions with the external environment, we explored cell scattering from stationary walls and obstacles, migration through imposed micro-geometries, and cell-cell collisions. These exercises capture a range of nontrivial patterns resulting from the intrinsic memory and deformability of the cell. Altogether, our work offers a mathematical paradigm of active deformable systems in which Stokes hydrodynamics are coupled to diffusive force-transducers

Dans les moteurs à combustion interne, l'injection de carburant est une phase essentielle pour la préparation du mélange et la combustion. En effet, la structure du jet liquide joue un rôle essentiel pour la qualité du mélange du combustible avec le gaz. Le présent travail porte sur les phénomènes d'atomisation de jet liquides dans les conditions opératoires des moteurs diesel. Dans ces conditions, la morphologie du jet liquide comprend une phase liquide séparée (c'est à dire un noyau liquide) et une phase liquide dispersée (c'est à dire un spray). Ce manuscrit décrit les étapes de développement d'un nouveau modèle d'atomisation, pour un jet liquide à grande vitesse, basée sur une approche eulérienne diphasique. Le phénomène d'atomisation est modélisée par des équations définissant une densité de surface pour le noyau liquide en plus de celle des gouttelettes du spray. Ce nouveau modèle a été couplé avec un système d'équations diphasique et turbulent de type Baer-Nunziato. Le processus de rupture des ligaments et son éclatement subséquent en gouttelettes sont modélisés en utilisant des connaissances rassemblées à partir des expériences disponibles et des simulations numériques précises. Dans la région dense du jet de liquide, l'atomisation primaire est modélisée comme un processus de dispersion en raison de l'étirement turbulent de l'interface, à partir du côté du liquide en plus du côté du gaz. Différents cas tests académiques ont été effectués afin de vérifier la mise en œuvre numérique du modèle dans le code IFP-C3D. Enfin, le modèle est validé avec les résultats DNS récemment publiés dans des conditions typiques de moteurs Diesel à injection directe
In internal combustion engines, the liquid fuel injection is an essential step for the air/fuel mixture preparation and the combustion process. Indeed, the structure of the liquid jet coming out from the injector plays a key role in the proper mixing of the fuel with the gas in the combustion chamber. The present work focuses on the liquid jet atomization phenomena under Diesel engine conditions. Under these conditions, liquid jet morphology includes a separate liquid phase (i.e. a liquid core) and a dispersed liquid phase (i.e. a spray). This manuscript describes the development stages of a new atomization model, for a high speed liquid jet, based on an eulerian two-phase approach. The atomization phenomenon is modeled by defining different surface density equations, for the liquid core and the spray droplets. This new model has been coupled with a turbulent two-phase system of equations of Baer-Nunziato type. The process of ligament breakup and its subsequent breakup into droplets are handled with respect to available experiments and high fidelity numerical simulations. In the dense region of the liquid jet, the atomization is modeled as a dispersion process due to the turbulent stretching of the interface, from the side of liquid in addition to the gas side. Different academic test cases have been performed in order to verify the numerical implementation of the model in the IFP-C3D software. Finally, the model is validated with the recently published DNS results under typical conditions of direct injection Diesel engines

Trace gases and aerosols, or suspended liquid and solid material in the atmosphere, have significant climatological and societal impacts; consequently, accurate representation of their contribution to atmospheric composition is vital to predicting climate change and informing policy actions. Sensitivity analysis allows scientists and environmental decision makers alike to ascertain the role a specific component of the very complex system that is the atmosphere of the Earth. Anthropogenic and natural emissions of gases and aerosol are transported by winds and interact with sunlight, allowing significant transformation before these species reach the end of their atmospheric life on land or in water. The adjoint-based sensitivity method assesses the relative importance of each emissions source to selected results of interest, including aerosol and cloud droplet concentration. In this work, the adjoint of a comprehensive inorganic aerosol thermodynamic equilibrium model was produced to improve the representativeness of regional and global chemical transport modeling. Furthermore, a global chemical transport model adjoint equipped with the adjoint of a cloud droplet activation parameterization was used to explore the footprint of emissions contributing to current and potential future cloud droplet concentrations, which impact the radiative balance of the earth. In future work, these sensitivity relationships can be exploited in optimization frameworks for assimilation of observations of the system, such as satellite-based or in situ measurements of aerosol or precursor trace gas concentrations.

Droplet behaviour influences significantly the quality of emulsions and the performance of microfluidics applications. Despite the numerous studies on droplet behaviour, the interactions between the suspended droplet and its surrounding walls, especially for non-Newtonian fluids, are not yet fully understood. Here, we investigate the behaviour of isolated droplets subjected to a simple shear in a wide range of capillary numbers, confinement ratios and viscosity relations between the droplet and the carrier fluid. Simulations are performed using the colour-gradient lattice Boltzmann method (LBM), which is also adapted to handle power-law fluids. Findings on the Newtonian droplets in a Newtonian carrier fluid show that droplet deformation and orientation to the flow, i.e. tumbling, are enhanced with increasing confinement. Even more, with a larger viscosity ratio the rate of the deformation increases more significantly while the rate of tumbling becomes smaller. Noteworthy, the largest deformation is presented by droplets of the same viscosity as the matrix fluid. We also find that in a shear-thickening carrier fluid droplet deformation and tumbling are enhanced while they are reduced in a shear-thinning fluid. Additionally, with increasing confinement, the lowest capillary number a droplet breaks increases in the low viscosity ratio cases, contrary to the high viscosity ratio ones. At unity viscosity ratio this critical capillary number is slightly affected while droplets are found to break at a lower capillary number in a power-law carrier fluid. Simulations are performed to examine the behaviour of power-law droplets sheared in a Newtonian carrier fluid. The results are correlated well with the ones of the Newtonian droplets when the droplets obtain ellipsoidal shapes. However, upon slight deviation from the ellipsoidal shape the behaviour of power-law droplets differs substantially from their Newtonian counterparts.

The central aim for the research undertaken in this PhD thesis is the development of a model for simulating water droplet movement on a leaf surface and to compare the model behavior with experimental observations. A series of five papers has been presented to explain systematically the way in which this droplet modelling work has been realised. Knowing the path of the droplet on the leaf surface is important for understanding how a droplet of water, pesticide, or nutrient will be absorbed through the leaf surface. An important aspect of the research is the generation of a leaf surface representation that acts as the foundation of the droplet model. Initially a laser scanner is used to capture the surface characteristics for two types of leaves in the form of a large scattered data set. After the identification of the leaf surface boundary, a set of internal points is chosen over which a triangulation of the surface is constructed. We present a novel hybrid approach for leaf surface fitting on this triangulation that combines Clough-Tocher (CT) and radial basis function (RBF) methods to achieve a surface with a continuously turning normal. The accuracy of the hybrid technique is assessed using numerical experimentation. The hybrid CT-RBF method is shown to give good representations of Frangipani and Anthurium leaves. Such leaf models facilitate an understanding of plant development and permit the modelling of the interaction of plants with their environment. The motion of a droplet traversing this virtual leaf surface is affected by various forces including gravity, friction and resistance between the surface and the droplet. The innovation of our model is the use of thin-film theory in the context of droplet movement to determine the thickness of the droplet as it moves on the surface. Experimental verification shows that the droplet model captures reality quite well and produces realistic droplet motion on the leaf surface. Most importantly, we observed that the simulated droplet motion follows the contours of the surface and spreads as a thin film. In the future, the model may be applied to determine the path of a droplet of pesticide along a leaf surface before it falls from or comes to a standstill on the surface. It will also be used to study the paths of many droplets of water or pesticide moving and colliding on the surface.

The central aim for the research undertaken in this PhD thesis is the development of a model for simulating water droplet movement on a leaf surface and to compare the model behavior with experimental observations. A series of five papers has been presented to explain systematically the way in which this droplet modelling work has been realised. Knowing the path of the droplet on the leaf surface is important for understanding how a droplet of water, pesticide, or nutrient will be absorbed through the leaf surface. An important aspect of the research is the generation of a leaf surface representation that acts as the foundation of the droplet model. Initially a laser scanner is used to capture the surface characteristics for two types of leaves in the form of a large scattered data set. After the identification of the leaf surface boundary, a set of internal points is chosen over which a triangulation of the surface is constructed. We present a novel hybrid approach for leaf surface fitting on this triangulation that combines Clough-Tocher (CT) and radial basis function (RBF) methods to achieve a surface with a continuously turning normal. The accuracy of the hybrid technique is assessed using numerical experimentation. The hybrid CT-RBF method is shown to give good representations of Frangipani and Anthurium leaves. Such leaf models facilitate an understanding of plant development and permit the modelling of the interaction of plants with their environment. The motion of a droplet traversing this virtual leaf surface is affected by various forces including gravity, friction and resistance between the surface and the droplet. The innovation of our model is the use of thin-film theory in the context of droplet movement to determine the thickness of the droplet as it moves on the surface. Experimental verification shows that the droplet model captures reality quite well and produces realistic droplet motion on the leaf surface. Most importantly, we observed that the simulated droplet motion follows the contours of the surface and spreads as a thin film. In the future, the model may be applied to determine the path of a droplet of pesticide along a leaf surface before it falls from or comes to a standstill on the surface. It will also be used to study the paths of many droplets of water or pesticide moving and colliding on the surface.

We investigate the behavior of moving droplets and rivulets, driven by a combination of gravity and surface shear (wind). The problem is motivated by a desire to model the behavior of raindrops on aircraft wings. We begin with the Stokes equations and use the approximations of lubrication theory to derive the specific thin film equation relevant to our situation. This fourth-order partial differential equation describing the height of the fluid is then solved numerically from varying initial conditions, using a fully implicit discretization for time stepping, and a precursor film to avoid singularities at the drop contact line. Results describing general features of droplet deformation, limited parameter studies, and the applicability of our implementation to the long-term goal of modeling wings in rain are discussed.

The results of numerical study of heating and evaporation of monodisperse fuel droplets in an ambient air of fixed temperature and atmospheric pressure are reported and compared to experimental data from the literature. The numerical model is based on the Effective Thermal Conductivity (ETC) model and the analytical solution to the heat conduction equation inside droplets. It is pointed out that the interactions between droplets lead to noticeable reduction of their heating in the case of ethanol, 3-pentanone, n-heptane, n-decane and n-dodecane droplets, and reduction of their cooling in the case of acetone. A simplified model for bi- component droplet heating and evaporation is developed. The predicted time evolution of the average temperatures is shown to be reasonably close to the measured one (ethanol/acetone mixture). The above-mentioned simplified model is generalised to take into account the coupling between droplets and the ambient gas. The model is applied to the analysis of the experimentally observed heating and evaporation of a monodispersed n-decane/3-pentanone mixture of droplets at atmospheric pressure. It is pointed out that the number of terms in the series in the expressions for droplet temperature and species mass fractions can be reduced to as few as three, with possible errors less than about 0.5%. In this case, the model can be recommended for implementation into CFD codes. The simplified model for bi- component droplet heating and evaporation, based on the analytical solutions to the heat transfer and species diffusion equations, is generalised to take into account the effect of the moving boundary and its predictions are compared with those of the model based on the numerical solutions to the heat transfer and species diffusion equations for both moving and stationary boundary conditions. A new model for heating and evaporation of complex multi-component hydrocarbons fuel droplets is developed and applied to Diesel and gasoline fuels. In contrast to all previous models for multi-component fuel droplets with large number of components, the new model takes into account the effects of thermal diffusion and diffusion of components within the droplets.

This thesis concerns the development of mathematical models to describe the interactions that occur between spray droplets and leaves. Models are presented that not only provide a contribution to mathematical knowledge in the field of fluid dynamics, but are also of utility within the agrichemical industry. The thesis is presented in two parts. First, thin film models are implemented with efficient numerical schemes in order to simulate droplets on virtual leaf surfaces. Then the interception event is considered, whereby energy balance techniques are employed to instantaneously predict whether an impacting droplet will bounce, splash, or adhere to a leaf.

Cette thèse de doctorat est dédiée au développement de modèles physiques pour l’étude des systèmes d’aspersion de gouttelettes d’eau en milieu réactif d’hydrogène-air pré-mélangée dans les centrales nucléaires. Des modèles d’ordre réduit sont développés pour décrire l’évaporation des gouttelettes d’eau dans la flamme, la dispersion des nuages de particules après le passage des ondes de choc et l’évolution de l’échelle caractéristiques de turbulence avec la présence d’un jet d’eau. Une nouvelle méthodologie est proposée pour évaluer les effets de l’évaporation par l’aspersion sur la propagation de la flamme d’hydrogène turbulente à l’intérieur d’un volume fermé et un modèle simple est développé pour la quantification de la décélération de la vitesse laminaire avec l’évaporation des gouttelettes à l’intérieur de la flamme. Également, un modèle analytique est proposé pour la prédiction de la dispersion de nuage de particule après le passage d’une onde de choc en s’appuyant sur le one-way formalisme avec une extension afin de prédire l’apparition d’un pic de densité du nombre de particules en utilisant le two-way formalisme. En ce qui concerne la modulation de la turbulence induite par les particules, un modèle simple est utilisé pour l’estimation des échelles intégrales de la turbulence induites par l’injection de nuage des particules. Ces modèles numériques développés peuvent être couplés pour être mis en œuvre dans les simulations numériques à grande échelle de l’effet du système d’aspersion sur les explosions accidentelles d’hydrogène dans les centrales nucléaires
This PhD dissertation is dedicated to develop simple models to investigate the effect of water spray system on the premixed hydrogen-air combustion in the nuclear power plants. Specific simple models are developed to describe the water droplet evaporation in the flame, particle cloud dispersion after the shock wave passage, and turbulence length scale evolution with the presence of a water spray. A methodology is proposed to evaluate the spray evaporation effects on the propagation of the turbulent hydrogen flame inside a closed volume and a simple model is developed for the quantification of the laminar velocity deceleration with the droplets evaporation inside the flame. An analytical model is proposed for the prediction of particle cloud dispersion after the shock passage in the one-way formalism and another analytical model is dedicated to describe the spray-shock interaction mechanism and predict the appearance of a particle number density peak using the two-way formalism. A review of the important criteria and physical modelings related to the particle-induced turbulence modulation is given and a mechanistic model is used for the estimation of the turbulent integral length scales induced by the injection of particle clouds. These developed numerical models can be coupled to implement in the large-scale numerical simulations of the spray system effects on the accidental hydrogen explosions in the nuclear power plants

This study is devoted to some of the most important issues for advancing inkjet printing for possible application in the coating industry with a focus on piezoelectric droplet on demand (DOD) inkjet technology. Current problems, as embodied in liquid filament breakup along with satellite droplet formation and reduction in droplet sizes, are discussed and then potential solutions identified. For satellite droplets, it is shown that liquid filament break-up behavior can be predicted by using a combination of two pi-numbers, including the Weber number, We and the Ohnesorge number, Oh, or the Reynolds number, Re, and the Weber number, We. All of these are dependent only on the ejected liquid properties and the velocity waveform at the print-head inlet. These new criteria are shown to have merit in comparison to currently used criteria for identifying filament physical features such as length and diameter that control the formation of subsequent droplets. In addition, this study performs scaling analyses for the design and operation of inkjet printing heads. Because droplet sizes from inkjet nozzles are typically on the order of nozzle dimensions, a numerical simulation is carried out to provide insight into how to reduce droplet sizes by employing a novel input waveform impressed on the print-head liquid inflow without changing the nozzle geometry. A regime map for characterizing the generation of small droplets based on We and a non-dimensional frequency, Ω is proposed and discussed. In an attempt to advance inkjet printing technology for coating purposes, a prototype was designed and then tested numerically. The numerical simulation successfully proved that the proposed prototype could be useful for coating purposes by repeatedly producing mono-dispersed droplets with controllable size and spacing. Finally, the influences of two independent piezoelectric characteristics - the maximum head displacement and corresponding frequency, was investigated to examine the quality of filament breakup quality and favorable piezoelectric displacements and frequencies were identified.

Recent experiments [P. Brunet, J. Eggers, and R. Deegan, Phys. Rev. Lett. 99, 114501 (2007)] have shown that a liquid droplet on an inclined plane can be made to move uphill by sufficiently strong, vertical oscillations. In order to investigate this counterintuitive phenomenon we will derive three different models that qualitatively reproduce the main features of the experiment. For the first model the liquid's inertia and viscosity are assumed negligible, so that the motion of the droplet is dominated by the applied acceleration due to the oscillation of the plate, gravity and surface tension and that the droplet is thin. We explain how the leading order motion of the droplet can be separated into a spreading mode and a swaying mode. For a linear contact line law, the maximum rise velocity occurs when the frequencies of oscillation of the two modes are in phase. We show that, both with and without contact angle hysteresis, the droplet can climb uphill and also that, for certain contact line laws, the motion of the droplet can produce footprints similar to experimental results. We show that if the two modes are out of phase when there is no contact angle hysteresis, the inclusion of hysteresis can force them into phase. This in turn increases the rise velocity of the droplet and can, in some cases, cause a sliding droplet to climb. For the second model we use a two-dimensional flow where the Reynolds number is assumed large enough for viscosity to be neglected. We show that the leading order motion of the droplet can be separated into the same two modes and the net motion of the droplet is an oscillatory function of the frequency. For increasingly non-wetting droplets we discover that the rise velocity begins to oscillate very rapidly as a function of the static contact angle. What we also discover is that the change in the free surface of the droplet is actually a wave travelling travelling across the droplet, and the amount of modes present coincide with the rapid change in the rise velocity. Using a cubic contact line law and contact angle hysteresis we observe a droplet that can climb uphill for parameter values similar to that of the experiment. With the addition of a time dependent term within the contact line law we show that it is possible to obtain a multi-valued relationship between the velocity of the contact line and the respective contact angles, reproducing experimental observations seen for unsteady, moving contact lines. For the third model we again assume that the liquid's viscosity is negligible, similar to model 2, only now for a three-dimensional, thin droplet. For very small amplitudes the motion of the droplet is a combination of a swaying mode and a spreading mode that interact causing a net motion of the droplet. This motion is found to be an oscillatory function of the driving frequency and the magnitude of the peak rise velocity is proportional to one over the frequency squared. By examining the velocity of the centre of the droplet and the displacement of the contact line we see that the absolute maximums of both of these, over one period of oscillation, contain natural frequencies, which are evenly spaced with respect to the square root of the frequency of the oscillation.

This thesis investigates symmetry breaking phenomena and motile steady states in droplets driven by stresses generated by active (out-of-equilibrium) liquid crystals. First, we show that in a fluid droplet with active polar liquid crystal an asymmetric polarisation field is sufficient to drive steady state motility. We are able to approximate the forces and flows generated in such a system analytically, and show how the force distribution on the droplet interface is characteristic of this motion. Second, we consider the case of a passive fluid droplet immersed in an active liquid crystal. Here we see that strong anchoring at the droplet interface can create an asymmetric equilibrium configuration, and thus any active stress can drive propulsion of the drop. Third we analytically perform linear stability analysis calculations on two kinds of active droplet to determine how active stresses can make these systems unstable to symmetry breaking events. Finally, we produce 2D simulations of these systems so that we can find the resulting steady states of these systems. We observe a rich phase space of behaviour, with steady state flows in the droplets that result in motion, symmetric deformations and rotation.

Hot-dip galvanising is commonly used in industry to increase the corrosion resistance of cold-rolled steel products for commercial use such as roofing and walling of buildings. Traditionally, the zinc coated steel surface is characterised by a relatively smooth surface with large spangle relief which is detrimental to corrosion resistance. One of the techniques to modify the surface appearance consists of a water-mist spray solution which allows for the creation of a large number of nucleation sites giving rise to micro rather than macro spangles, thereby producing a much smoother surface. In addition, controlling the spray parameters allows the hot, zinc coated, steel surface to be ‘roughened’ facilitating its bonding to concrete or for lamination. The proper control of water droplet impact parameters such as impact velocity, droplet diameter and crater size is essential for a successful implementation of this technique. Certain aspects of the second of these processes, the production of rough, non-skid galvanised steel sheet surfaces, has been addressed by this thesis.Although an experimental investigation of the effect of such water droplet parameters on the formation of zinc surface characteristics such as crater diameter and depth would provide a great deal of valuable data it is fraught with difficulties. The presence of hot metal surfaces exceeding 450oC and the boiling and evaporation of water droplets taking place at very small timescales (microseconds) all combine to make an experimental study difficult to implement not to say unsafe. On the other hand computer simulations with a properly constructed mathematical model are a valuable tool for the investigation of these parameters.A comprehensive modelling of the process would include the process of heat transfer: such as conduction through a vapour layer, internal droplet and vapour convection, radiation from the hot surface, solidification of the zinc liquid layer; as well as the fluid dynamical aspects: such as surface tension at the droplet-air, droplet-zinc and zinc-air interfaces, the droplet impact phenomena such as spreading and splashing and the formation of impact craters and wave propagation in a thin viscous zinc layer. As a first stage in the modelling exercise this thesis will concentrate on an investigation of single water droplet impact on a thin liquid zinc layer with a steel substrate which provides a simplified and computationally tractable model of the spraying process.The objectives of this thesis are twofold: firstly, the development and construction of an accurate, robust mathematical model and, secondly, the solution of the model for the impact of a single water droplet onto a thin liquid layer of zinc on a steel substrate. This model must be able to deal with rapidly deforming moving interfaces and maintain stability in the presence of very large density and viscosity ratios. This moving boundary problem requires the tracking of three fluid interfaces while also maintaining incompressibility. The Godunov-Marker-Particle Projection Scheme developed in this thesis is able to satisfy these requirements. Through a combination of approximate projection methods, Godunov convective differencing, Marker-Particle interface tracking and velocity filters the method is able to treat viscous, multi-fluid free surface flows. The modelling of free surface flows with more than two separate immiscible fluids, to the author’s knowledge not yet published in the literature, is a secondary aim of the thesis. A major part of the thesis deals with the thorough testing of each aspect of the combination of numerical methods used: firstly, the Poisson solver with discontinuous coefficients and homogeneous boundary conditions used in the approximate projection method, analytical solutions for the construction of an initial solenoidal velocity field, testing of the projection and velocity filters and kinematic tests of the Marker-Particle method for tracking of fluid interfaces; secondly, dynamical tests of the viscous incompressible Navier-Stokes equations for: an exact solution, the Lid-Driven Cavity and the Rayleigh-Taylor instability. The combined method is also successfully tested on the limited two-fluid droplet-solid and droplet-liquid impact problems before solving the thesis problem.It is shown that, for the impact of a single water droplet onto a thin liquid zinc layer, impact crater growth, diameter and depth, are linearly dependent on impact velocity. For a given impact velocity, crater diameter is not effected by increasing zinc layer depth although crater depth is linearly dependent. The time at which the droplet commences penetration of the zinc layer is inversely dependent on impact velocity and the maximum crater diameter and depth are nonlinearly dependent on impact velocity. The model shows that, within the convective timescale, droplet impact on thin liquid zinc layers can be approximately described by droplet spreading on a solid zinc surface. The droplet is shown to spread preferentially to the zinc layer splashing after completion of spreading. This shows that adjustment of the droplet impact velocity or zinc layer depth can vary the surface roughness appropriately.

The oscillating droplet technique is an experimental technique that is used to measure the surface tension and viscous damping coefficients of a liquid droplet. This technique has been the subject of much analysis; theoretical, numerical, and experimental with a number of different external forces used to confine the droplet. These external forces are found to modify the oscillation frequency and damping rates, which need to be quantified in order for the measurement technique to be used. The dynamics of the droplet are three-dimensional but previous numerical work has largely focused on axisymmetric cases. This work uses numerical techniques to extend the previous analysis to include the full three-dimensional effects. In this work a three-dimensional numerical model is designed, developed and applied to study the dynamics of a liquid droplet both in free space and with a high DC magnetic field used to balance gravitational forces. The numerical model is a grid point formulation of the pseudo-spectral collocation method discretised in a spherical coordinate system with the implicit Euler method used to advance the solution in time. A coordinate transformation method is used to ensure the direct surface tracking required for modelling the surface shape oscillations. The study covers the laminar fluid flow regime within a droplet exhibiting translational and surface shape oscillations providing a greater understanding of the physical behaviour of the droplet along with a qualitative and quantitative comparison with theoretical results. Initially a droplet oscillating in free space is considered, with a range of surface oscillation modes used to demonstrate the three-dimensional dynamics. Then the influence of electromagnetic forces on a diamagnetic droplet is studied, this includes the field from a solenoid magnet used to levitate a diamagnetic droplet. Finally the dynamics of an electrically conducting droplet in an external static magnetic field are modelled. In each case a number of methods are used to analyse the surface displacement in order to determine the surface tension and viscous damping coefficients. The numerical study of a freely oscillating droplet shows good agreement with the low order theoretical results for droplets in the limit of low viscosity. The high accuracy of the surface tracking method allows the non-linear effects of mode coupling and frequency shift with amplitude to be observed. There is good agreement with the theoretical values available for inviscid axisymmetric oscillations and the numerical study provides the opportunity to determine these effects for three-dimensional viscous oscillations. The magnetic field from a solenoid is used to study the levitation of a diamagnetic droplet and the oscillation frequencies of the droplet are compared with a theoretical model. The magnetic field is analysed and the accuracy of the field calculation used when determining the modification to the oscillation frequencies is considered with the use of a theoretical model. Analysis is made into the splitting of the frequency spectrum due to the magnetic field. The theoretical model that is available for an electrically conducting droplet in a static magnetic field predicts different fluid flow within the droplet and oscillation frequency and damping rate changes. These changes are compared qualitatively and quantitatively with the numerical model results with good agreement.