Dynamics of drop formation in viscous flows

Abstract

This paper presents numerical results of the dynamics of a viscous liquid drop that is being formed directly at the tip of a vertical, circular tube and breaks into an ambient, viscous fluid. A model is developed to predict the evolution of the drop shape and its breakup based on the volume-of-fluid/continuum-surface-force method, which is a solution algorithm for computing transient, two-dimensional, incompressible fluid flow with surface tension on free surfaces of general topology (Richards et al. (1995 Physics of Fluids, 257, 111–145)). The full Navier–Stokes system is solved by using finite-difference formulation on a Eulerian mesh. The mesh is fixed in space, with the flow and interface moving through it to ensure accurate calculations of complex free surface flows and topology, including surface breakup and coalescence. The nonlinear dynamics of drop growth and breakup are simulated for describing and predicting the universal features of drop formation. The focus here is on dynamic effects of a quiescent or flowing ambient fluid on drop breakup and the subsequent generation of satellite droplets. The effects of finite inertial, capillary, viscous, and gravitational forces are accounted for in order to classify drastically different formation dynamics and to elucidate the fate of satellite droplets. The numerical predictions are compared with experimental measurements for a typical system of 2-ethyl-1-hexanol drops forming and breaking into quiescent water, and the results show excellent agreement.