Microfluidics is the science of processing microliters or less of fluid at a time in a channel with dimensions on the order of microns. The small size of the channels allows fluid properties to be studied in a world dominated by viscosity, surface tension, and diffusion rather than gravity and inertia. Microfluidic droplet generation is a well studied and understood phenomena, which has attracted attention due to its potential applications in biology, medicine, chemistry and a wide range of industries. This dissertation adds to the field of microfluidic droplet studies by studying individual droplet deformation and the process of scaling-up microfluidic devices for industrial use. The study of droplet deformation under extensional and mixed shear and extensional flows was performed within a microfluidic device. Droplets were generated using a flow-focusing device and then sent through a hyperbolic contraction downstream of the droplet generator. The hyperbolic contraction allowed the smallest droplets to be deformed by purely extensional flows and for the larger droplets to experience mixed extensional and shear flows. The shear resulted from the proximity of the droplet to the walls of the microfluidic channel. The continuous phase in all of these devices was oil and the dispersed phase was water, an aqueous surfactant solution, or an aqueous suspension of colloidal particles. Droplet deformation dynamics are affected by the use of surfactants and colloidal particles, which are commonly used to stabilize emulsion droplets again coalescence. Microfluidic droplet generating devices have many potential industrial applications, however, due to the low output of product from a single droplet generating device, their potential has not been realized. Using six parallel flow-focusing droplet generators on a single chip, the process of microfluidic droplet formation can be scaled up, thus resulting in a higher output of droplets. The tuning of droplet size and production frequency can be achieved on chip by varying the outlet tubing lengths, thus allowing for a single device to be used to generate a range of droplet sizes.

Numerical approaches have been conducted to investigate the effect of droplet deformation and internal circulation on droplet dynamics. Although droplet drag is a classical area of study, there are still theoretical gaps in understanding the motion of large droplets. In applications such as spray combustion, droplets of various sizes are generated and move with the flow. Large droplets tend to deform in the flow, and they have complex interactions with the flow because of this deformation. To better model spray, the physical understanding of droplets needs to be improved. Under spray conditions, droplets are subjected to a high-temperature-and-pressure environment, and the coupling between liquid and gas is enhanced. Therefore the deformation and internal circulation will affect the droplet drag coefficient more significantly than they would under atmospheric conditions. To study the mechanism of how droplet shape and internal circulation influence droplet dynamics, we have used direct numerical simulation (DNS) to simulate a droplet falling at its terminal velocity in high-pressure air. An in-house code developed for interface-capturing DNS of multiphase flows is employed for the simulation. The drag coefficient is calculated, and the results are consistent with the existing literature for slightly deformed droplets. The results show that the drag coefficient is directly related to the droplet deformation and droplet internal circulation. This paper also develops an analytical theory to account for the effect of the Weber number and fluid properties on droplet deformation. / Master of Science / This study investigates how larger droplets interact with airflow in spray conditions. Classical droplet drag models are not accurate under extreme conditions due to the neglect the droplet deformation and droplet internal circulation. To better understand droplet dynamics and to improve the accuracy of droplet models, direct numerical simulations were conducted. In our simulations, a non-evaporating falling droplet in high-pressure air was modeled. Results show a direct link between drag coefficient and droplet shape and internal flow. We also derived an analytical scaling law to explore the parameters related to droplet deformation. This research enhances our understanding of droplet dynamics in spray conditions.

We develop a viscoelastic version of the volume of fluid algorithm for tracking deformable interfaces. The code uses the piecewise linear interface calculation method to reconstruct the interface, the continuous surface force formulation to model interfacial tension forces and utilizes the semi-implicit Stokes solver (enabling computations at low Reynolds numbers). The algorithm is primarily designed to simulate the flow of superposed fluids and the drop in a flow problem in 2D shear flows of viscoelastic and/or Newtonian fluids. The code is validated against linear stability theory for the two-layer flow case and against experimental and other documented numerical investigations for the droplet-matrix case. / Ph. D.

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[pt] A motivação deste trabalho consiste no uso do four-roll mill para aumentar a separação de fases de emulsões água em óleo (A/O) presente no processamento primário da indústria de petróleo. A partir da conservação de massa e momento, a fase contínua foi modelada como escoamento incompressível, bi-dimensional e isotérmico. Simulações numéricas utilizando o método de elementos finitos foram implementadas para revelar a influência das diversas configurações de escoamento no comportamento mecânico do material. A partir dos resultados obtidos, a habitual forma de classificar o escoamento no four-roll mill de acordo com a literatura se demonstrou ineficiente. Este trabalho sugere classificações locais de escoamento a cada posição dependendo se a mesma está ocupada pela fase contínua ou dispersa da emulsão. O efeito da fase dispersa é descrito via pós-processamento. Microelementos no formato de vetores foram inseridos no domínio e investigou-se suas deformações e trajetórias. Consequentemente, analisou-se a deformação de gotas e a sua respectiva influência na instabilidade da emulsão. / [en] The motivation of this work consists in the use of four-roll mill in order to increase the phase separation of water-in-oil emulsions (W/O) present in the primary process of oil industry. With mass and momentum conservation, the continuous phase is modeled by an incompressible, bi-dimensional and isothermal flow. Numerical simulations employing the finite element method were implemented to reveal the influence of the several flow configurations in the material mechanical behavior. From the obtained results, the standard way of classifying the flow in the four-roll mill according to the literature was proved inefficient. This work suggests local flow classifications for each position depending if it is occupied by the continuous or dispersed phase. The effect of the dispersed phase was described by a post-processing scheme. Microelements in shape of vectors were inserted in the domain and their deformations and pathlines were investigated. Thus, the deformation of droplets and their respective influences in the emulsion instability were analyzed.

Ce travail porte sur l’étude expérimentale et théorique du comportement des gouttelettes d’eau (instabilité, déformation, coalescence), déposées à la surface d’un isolateur composite haute tension, en présence d’un champ électrique. La déformation des gouttelettes d’eau est étudiée en fonction de plusieurs paramètres tels que le volume, le nombre et la conductivité des gouttelettes ainsi que leurs positions par rapport aux électrodes. Un intérêt particulier est porté à la charge accumulée sur la surface d’une gouttelette. L’influence des gouttelettes sur la répartition du champ électrique ainsi que le facteur d’amplification du champ électrique par une méthode numérique sont étudiés. Une formulation mathématique de la déformation d’une gouttelette d’eau posée sur une surface d’isolateur est développée. Les mécanismes ainsi que les paramètres impliqués dans la coalescence d’une paire de gouttelettes d’eau sous l’effet du champ électrique sont également traités. Un modèle mathématique permettant d’analyser la coalescence d’une paire de gouttelettes d’eau posées sur la surface d’un isolateur en présence du champ électrique est proposé. Ce modèle est basé sur une approche à interface diffuse qui consiste essentiellement en un couplage entre les équations de Navier-Stokes, le calcul de la force électrique et une équation de type Cahn-Hilliard décrivant l’évolution de l’interface en prenant en compte les phénomènes de tensions superficielles. La démarche suivie et les résultats présentés dans ce travail ouvrent de multiples perspectives tant d’un point de vue expérimental que d’un point de vue de la modélisation et de la simulation numérique des phénomènes physiques intervenant sur des isolateurs de lignes de transport et de distribution de l’énergie électrique dans des conditions d’humidité (pluie, rosée ...). / This work is devoted to experimental and theoretical study of the behavior of water droplets (instability, deformation, coalescence), located on the surface of a high voltage composite insulator, in presence of electric field. The deformation of droplets is investigated according to several parameters such as volume, number and conductivity of the droplets as well as their positions with respect to the electrodes. A particular interest is focused on the electric charge accumulated on the droplet surface. The droplet influences on the electric field distribution as well as the amplification factor of the electric field are studied by a numerical method. A mathematical formulation of the deformation of water droplet located on a surface of insulator is developed. The mechanisms as well as parameters involved in coalescence of a pair of water droplets under the electric field stress are also investigated. A mathematical model is developed for analyzing the coalescence of a pair of water droplets sitting on the surface of an insulator in presence of the electric field. It is based on a diffuse interface model that essentially consists of a coupling between Navier-Stokes equations, the computing of electric force and a Cahn-Hilliard type equation describing the interface evolution including capillary phenomena. The approach followed and the results presented in this work open several perspectives as well from an experimental point of view as from a point of view of modeling and numerical simulation of physical phenomena affecting insulators of high voltage transport and distribution lines in humidity conditions (rain, dew...).