Dynamics of Retracting Films and Filaments Near Singularities

Free surface flows in the vicinity of space-time singularities such as those that arise during the breakup or coalescence of drops and bubbles have diverse industrial applications including inkjet printing, emulsions, foam formation and stability, and personalized drug delivery, among others. In addition to these wide ranging practical applications, the breakup and coalescence of drops or bubbles can be observed in everyday life with rain drops, sea foams and sea sprays in crashing waves, and the myriad bubbles that are present in carbonated beverages. In drop breakup, both large (mother or parent or primary) and small (daughter or satellite) drops are produced. The formation of the latter drops often involves retraction of long slender filaments that lead to either stable contraction to a single spherical drop or the disintegration of the contracting filament into multiple droplets. In drop or bubble coalescence, two drops or bubbles touch at a point and form a small fluid bridge; the fluid bridge grows in time as the two drops or bubbles merge into one. The dynamics in the vicinity of the point where the drops have come together is tantamount to a hole that grows in time in the thin sheet (film) of fluid that separates the two drops. Therefore, the primary goal of this thesis is to develop an improved understanding of the retraction of filaments and films in the context of the breakup and coalescence of drops and bubbles. To accomplish this goal, a robust Arbitrary Eulerian-Lagrangian (ALE) method utilizing the Galerkin/Finite Element Method (G/FEM) is used to solve the fully 3D axisymmetric Navier-Stokes system and simulate free surface flows in the vicinity of the breakup and coalescence singularities. In drop breakup, a significant finding is the discovery of a new mode of breakup that had heretofore been missed in the literature, and exhibits unique and unexpected dynamics. In drop coalescence in air, it is shown that all coalescence events begin in a Stokes regime where viscous and capillary forces are in balance but fluid inertia is negligible, thereby resolving the long-standing controversy on the nature of the dominant forces at the incipience of drop coalescence. Single-fluid coalescence simulations are generalized and a complete description is provided of the scaling laws that govern coalescence in liquid-liquid emulsions and dispersions of gas bubbles in liquids