In this dissertation, we present a numerical method for tracking surfactants on an interface in multiphase flow, along with applications of the method to two physical problems. We also present an extension of our method to track charged droplets. Our method combines a traditional volume of fluid (VOF) method with marker tracking. After describing this method in detail, we present a series of tests we used to validate our method. The applications we consider are the coalescence of surfactant-laden drops, and the rising of surfactant-laden drops in stratifications.
In our study of the coalescence of surfactant-laden drops, we describe conditions under which coalescence is partial, rather than total. In particular, we examine the dependence of the critical Ohnesorge number, above which coalescence is total, on surfactant effects. We find that the surfactant potency has a surprising non-monotonic effect on the critical Ohnesorge number. This effect is explained by a balancing interface area loss and tangential stresses, which we describe using a scaling argument. Our argument is confirmed by forming a predicted critical Ohnesorge number profile, which qualitatively matches the data. We also discuss gravity effects, varying initial conditions, and daughter drops resulting from partial coalescence.
In our study of rising drops, we examine three distinct physical setups. In the first setup, we examine a drop coated in insoluble surfactant rising in a uniform ambient. Our results for an unstratified ambient show good agreement with earlier work, and fill a gap between results for zero Reynolds number and intermediate Reynolds number. In our second setup, we study drops rising in a linear density stratification, with and without surfactant. Entrainment effects on the rising drop are isolated and used to compute an effective buoyancy of entrained fluid. In our third setup, we present velocity profiles of a clean drop entering a layer of soluble surfactant. The surfactant layer "sucks" the drop in, before it transitions to a terminal Rising speed.
Lastly, we extend our method to track electric fields and charges in the bulk fluid and on the surface. Such a numerical method has applications to electrically induced drop deformation, the coalescence of charged droplets, and electro-wetting. This extension of our method is validated by examining a simple test case.