Abstract Multiphase Droplet Interactions with a Single Fiber By: Noor M. Farhan A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at Virginia Commonwealth University. Virginia Commonwealth University, 2019 Director: Hooman V. Tafreshi, Professor, Department of Mechanical and Nuclear Engineering Formulating the physics of droplet adhesion to a fiber is interesting intellectually and important industrially. A typical example of a droplet–fiber system in nature is the dew droplets on spider webs, where droplets first precipitate and grow on the fibers, but they eventually fall when they become too heavy. Obviously, quantifying the force of adhesion between a droplet and a fiber is crucial in designing fog harvesting devices or manufacturing filtration media for liquid–gas or liquid–liquid separation, among many other industrial applications. This study is aimed at developing a mathematical framework for the mechanical forces between a droplet and a fiber in terms of their physical and wetting properties. To this end, a series of experiments were conducted to detach ferrofluid droplets of varying volumes from fibers with different diameters and Young–Laplace contact angles (YLCAs) in a controlled magnetic field. The force of detachment was measured using a sensitive scale and used along with the results of numerical simulations to develop a semi-analytical expression for the force required to detach a droplet from a fiber. This universally-applicable expression allows one to predict the force detachment without the need to run an experiment or a computer simulation. This work also reports on the use of magnetic force to measure the force of detachment for nonmagnetic droplets for the first time. This is accomplished by adding a small amount of a ferrofluid to the original nonmagnetic droplet to create a compound droplet with the ferrofluid nesting inside or cloaking the nonmagnetic droplet. The ferrofluid is then used to induce a body force to the resulting compound droplet and thereby detach it from the fiber. The recorded detachment force is used directly (the case of nesting ferrofluid) or after scaling (the case of cloaking ferrofluid) to obtain the force of detachment for the original nonmagnetic droplet. The accuracy of these measurements was examined through comparison with numerical simulations as well as available experimental data in the literature. In addition, a simple method is developed to directly measure the intrinsic contact angle of a fiber (i.e., Young–Laplace Contact angle of the fiber material) with any arbitrary liquid. It is shown that the intrinsic contact angle of a fiber can be obtained by simply measuring the angle between the tangent to the fiber surface and the tangent to the droplet at the contact line, if the droplet possesses a clamshell conformation and is viewed from the longitudinal direction. The novelty of the proposed method is that its predictions are not affected by the volume of the droplet used for the experiment, the wettability of the fiber, the surface tension of the liquid, or the magnitude of the body force acting on the droplet during the experiment. Also, a liquid droplet interaction with granular coatings is simulated and the droplet apparent contact angle (ACA) and the transition from Cassie (fully dry) to Wenzel (fully wet) state as a function to the roughness wavelength have been studied. For a fixed droplet volume, two different granular coatings have been used, spherical and hemispherical bumps. It is demonstrated that the chemistry (YLCA) and geometrical parameters for the granular microtexture play an important effect on the droplet ACA and its transition from Cassie to Wenzel state.

Multiphase flows abound in nature and enterprises. Our daily interactions with fluids - washing, drinking, and cooking, for example - occur at a free surface and within the realm of multiphase flows. The applications of multiphase flows within the context of emulsions, which are caused by mixing two immiscible fluids, have been of interest since the nineteenth century: compartmentalizing one fluid in another is particularly of interest in applications in pharmaceutical, materials, microfluidics, chemical, and biological engineering. Even more control in compartmentalization and delivery can be obtained through the usage of double emulsions, which are emulsions of smaller drops (i.e., inner drop) within larger drops (i.e., outer drop). The goal of this work is to understand the dynamic behavior of compound drops in confined flow at low Reynolds numbers. These behaviors include the migration patterns, limit cycles, and equilibrium locations in confined flows such as channel flows.<br> <br>Firstly, we look at non-concentric compound drops that are subject to simple shear flows. The eccentricity in the inner drop is either within the place of shear, normal to the plane of shear, or mixed. We show unreported motions that persist throughout time regardless of the initial eccentricity, given that the deformations of the inner and outer drops are small. Understanding the temporal dynamics of compound drops within the simple shear flow, one of the simplest background flows that may be imposed, allows us to probe at the dynamics of more complicated background flows.<br> <br>Secondly, we look at the lateral migration of compound drops in a Poiseuille flow. Depending on the initial condition, we show that there are multiple equilibria. We also show that the majority of initial configurations results in the compound drop with symmetry about the short wall direction. We then show the time it takes for the interfaces to merge if a given initial configuration does not reach the aforementioned symmetry.<br> <br>Thirdly, while the different equilibria of compound drops offer some positional differences at different radii ratio, we show that the lift force profiles at non-equilibrium locations offer distinctly different results for compound drops with different radii ratio. We then look at how this effect is greater than changes that arise due to viscosity ratio changes, and offer insights on what may create such a change in the lift force profile.