A theoretical study of the approach and collision of liquid-drop pairs is performed with results obtained numerically. The collision process is modeled by a squeeze-flow problem involving both planar and non-planar geometry, with attention given to the deformation of the interacting interfaces. Based on the nature of the collision process, an analogy is made between the fluidic systems of colliding liquid bodies and a mechanical mass- spring-damper system. Examination of the analogous mechanical system yields the derivation of an effective damping ratio, ζ*, which is used to predict the outcome of the drop-drop collisions. Predictions made by utilizing the effective damping ratio are then compared to experimental results presented in literature. / text

<p>Surface energy-powered motion is useful for a variety of autonomous functions such as passive cooling and self-cleaning, where independence from external forces is highly desirable. Drop coalescence offers a convenient process to release surface energy, which can be harvested to power self-propelled fluid motion. </p><p>On superhydrophobic surfaces, out-of-plane jumping motion spontaneously results from drop coalescence. However, less than 4\% of the released surface energy is converted to useful kinetic energy giving rise to the jumping motion. Using three-dimensional interfacial flow simulations that are experimentally validated, we elucidate the mechanism of low energy conversion efficiency. The non-wetting substrate interferes with the expanding liquid bridge between the coalescing drops at a relatively late stage, forcing a small fraction of the merged drop to "bounce" back from the non-wetting substrate. The substrate breaks the symmetry of surface energy release, leading to self-propelled jumping that is perpendicular to the solid substrate. The intercepting substrate imparts a relatively small translational momentum on the overall merged drop, giving rise to a small energy conversion efficiency. </p><p>This mechanistic understanding has provided guidance on how to increase the energy conversion efficiency by changing the geometry of the intercepting solid surface, e.g. to a pillared substrate which has additional intercepting planes, or to a cylindrical fiber which interferes with the coalescence process at a much earlier stage. These topographical changes have already led to a 10-fold increase in energy conversion efficiency. The directional control of surface energy-powered motion is achieved by breaking the symmetry of oscillations induced by drop coalescence, such as by adding additional intercepting planes on pillared substrates. The work has applications ranging from self-sustained dropwise condensers, drop coalescers to ballistospore discharge in some fungi species in nature. </p><p> The ballistospore discharge process is powered by surface energy released from the coalescence between a spherical Buller's drop and an adaxial drop on the spore. The disturbance to the adaxial drop from coalescing Buller's drop results in the capillary-inertial oscillations of the liquid system. The oscillations redirect the mass and momentum transfer and yields a tensile force along the adaxial direction with negligible momentums in other directions, ensuring the preferable launching along the adaxial direction. The findings offer insights for applications of biomimicry involving self-propelled jumping with payloads which takes advantage of the high power density of the process.</p> / Dissertation

<div>Free surface flows where the shape of the interface separating two fluids is unknown <i>apriori</i> are an important area of interest in fluid dynamics. The study of free surface flows such as the breakup and coalescence of drops, and thinning and rupture of films lends itself to a diverse range of industrial applications, such as inkjet printing, crop spraying, foam and emulsion stability, and nanolithography, and helps develop an understanding of natural phenomena such as sea spray generation in oceans, or the dynamics of tear films in our eyes. In free surface flows, singularities are commonly observed in nite time, such as when the radius of a thread goes to zero upon pinchoff or when the thickness of a film becomes zero upon rupture. Dynamics in the vicinity of singularities usually lack a length scale and exhibit self-similarity. In such cases, universal scaling laws that govern the temporal behavior of measurable physical quantities such as the thickness of a lm can be determined from asymptotic analysis and veried by high-resolution experiments and numerical simulations. These scaling laws provide deep insight into the underlying physics, and help delineate the regions of parameter space in which certain forces are dominant, while others are negligible. While the majority of previous works on singularities in free-surface flows deal with Newtonian fluids, many fluids in daily use and industry exhibit non-Newtonian rheology, such as polymer-laden, emulsion, foam, and suspension flows.</div><div><br></div><div><div>The primary goal of this thesis is to investigate the thinning and rupture of thin films of non-Newtonian fluids exhibiting deformation-rate-thinning (power-law) rheology due to attractive intermolecular van der Waals forces. This is accomplished by means of intermediate asymptotic analysis and numerical simulations which utilize a robust Arbitrary Eulerian-Lagrangian (ALE) method that employs the Galerkin/Finite-Element Method for spatial discretization. For thinning of sheets of power-law fluids, a signicant finding is the discovery of a previously undiscovered scaling regime where capillary, viscous and van der Waals forces due to attraction between the surfaces of the sheet, are in balance. For thinning of supported thin films, the breakdown of the lubrication approximation used almost exclusively in the past to study such systems, is shown to occur for films of power-law fluids through theory and conrmed by two dimensional simulations. The universality of scaling laws determined for rupture of supported films is shown by studying the impact of a bubble immersed in a power-law fluid with a solid wall.</div></div><div><br></div><div><div>Emulsions, which are ne dispersions of drops of one liquid in another immiscible liquid, are commonly encountered in a variety of industries such as food, oil and gas, pharmaceuticals, and chemicals. Stability over a specied time frame is desirable in some applications, such as the shelf life of food products, while rapid separation into its constituent phases is required in others, such as when separating out brine from crude oil. The timescale over which coalescence of two drops of the dispersed phase occurs is crucial in determining emulsion stability. The drainage of a thin film of the outer liquid that forms between the two drops is often the rate limiting step in this process. In this thesis, numerical simulations are used to decode the role played by fluid inertia in causing drop rebound, and the subsequent increase in drainage times, when two drops immersed in a second liquid are brought together due to a compressional flow imposed on the outer liquid. Additionally, the influence of the presence of insoluble surfactants at the drop interface is studied. It is shown that insoluble surfactants cause a dramatic increase in drainage times by two means, by causing drop rebound for small surfactant concentrations, and by partially immobilizing the interface for large surfactant concentrations.</div></div>