Dynamics of drops and fluid interfaces: A level set study

The deformation and breakup of liquid drops is a problem of fundamental importance with application to a wide range of systems. We study this problem numerically using a level set method to follow the interface. The level set method has been applied to many problems involving interface motion but has yet to be used in a comprehensive study of drop deformation and breakup.; We develop a numerical method that solves the Navier-Stokes equations (including interfacial tension) using a level set representation of the interface. For systems with three or more fluids we develop a projection method to treat the motion of multiple junctions (such as contact lines) in the level set formulation. This method is shown to reproduce expected results in various scenarios.; Following this, we apply the method to a number of problems in interfacial dynamics. In the first problem, we examine the dynamics of a single phase drop under shear. We obtain results that are in good agreement with the literature for steady drop shapes as well as unsteady behavior, including breakup. We define a standard stretching protocol and used to compare drop deformation and breakup under varying flow conditions.; We then apply the techniques used for the single phase drop to an encapsulated drop, consisting of a concentric core and shell. We first consider the effect of core interfacial tension on steady drops, and then turn to unsteady drop behavior. Using the standard stretching protocol, we observe a wide variety of behavior as the core interfacial tension is varied. We show that the core can alter both the elongation and breakup of the drop, often in surprising ways. This can lead to significant changes in the final morphology after shear is terminated.; We also show that the shear-driven behavior of a drop lying on a fluid interface involves a new flow topology. Finally, we discuss aspects of the dynamic contact line and late stage coarsening in a fluid undergoing spinodal decomposition.