In both engineering and medical applications it is often useful to use the knowledge of the conditions under which adhering liquid droplets appear, deform and interact with surrounding fluids, in order to either remove or create them. Examples include the de-wetting of aircraft surfaces and the process of injecting glue into the bloodstream in the treatment of aneurysms. In this study, we look at various methods of modelling a particular class of droplets - those attached to a wall in the presence of an external shear flow.

In addition to theory, this study focuses on practical application and computer implementation in a coherent introduction to boundary integrals, boundary element and singularity methods for steady and unsteady flow at zero Reynolds numbers.

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.

The Droplet Deformation and Breakup Model was used to predict deformation of droplets approaching the leading edge stagnation line of an airfoil. The quasi-steady model was solved for each position along the droplet path. A program was developed to solve the non-linear, second order, ordinary differential equation that governs the model. A fourth order Runge-Kutta method was used to solve the equation. Experimental slip velocities from droplet breakup studies were used as input to the model which required slip velocity along the particle path. The center of mass displacement predictions were compared to the experimental measurements from the droplet breakup studies for droplets with radii in the range of 200 to 700 mm approaching the airfoil at 50 and 90 m/sec. The model predictions were good for the displacement of the center of mass for small and medium sized droplets. For larger droplets the model predictions did not agree with the experimental results. Vargas, Mario Glenn Research Center WBS 648987.02.02.03.10

The Droplet Deformation and Breakup Model was used to predict deformation of droplets approaching the leading edge stagnation line of an airfoil. The quasi-steady model was solved for each position along the droplet path. A program was developed to solve the non-linear, second order, ordinary differential equation that governs the model. A fourth order Runge-Kutta method was used to solve the equation. Experimental slip velocities from droplet breakup studies were used as input to the model which required slip velocity along the particle path. The center of mass displacement predictions were compared to the experimental measurements from the droplet breakup studies for droplets with radii in the range of 200 to 700 mm approaching the airfoil at 50 and 90 m/sec. The model predictions were good for the displacement of the center of mass for small and medium sized droplets. For larger droplets the model predictions did not agree with the experimental results.

The Droplet Deformation and Breakup Model was used to predict deformation of droplets approaching the leading edge stagnation line of an airfoil. The quasi-steady model was solved for each position along the droplet path. A program was developed to solve the non-linear, second order, ordinary differential equation that governs the model. A fourth order Runge-Kutta method was used to solve the equation. Experimental slip velocities from droplet breakup studies were used as input to the model which required slip velocity along the particle path. The center of mass displacement predictions were compared to the experimental measurements from the droplet breakup studies for droplets with radii in the range of 200 to 700 mm approaching the airfoil at 50 and 90 m/sec. The model predictions were good for the displacement of the center of mass for small and medium sized droplets. For larger droplets the model predictions did not agree with the experimental results.