Convective transport from drops in complex shearing flows

Abstract

This work broadly deals with transport in two-phase systems. The two-phase system of direct rele- vance to this study is an emulsion, where one of the phases is dispersed as droplets in the other (ambi- ent/continuous) phase. In this work, we analyse the transport in such a system, where we analytically calculate the transport rate in the convection dominant regime (as characterised by large P eclet numbers, Pe 1) from a single neutrally buoyant drop suspended in an ambient three-dimensional linear ow, for an arbitrary value of the drop-to medium viscosity ratio ( ). The scenario we are interested in pertains to the Stokesian regime (Re = 0) or near-Stokesian regime (Re 1) and the transport rate is calculated as a dimensionless Nusselt number (Nu), which depends on the geometry of the ow (as characterized by the streamline topology) on the surface of the drop. Correspondingly, we consider two separate scenarios where the surface streamlines on the drop are either open or closed. The emphasis in our study is on being able to tailor the transport-rate (Nu) calculation to non-trivial surface or near-surface streamline topologies; in contrast to examples from textbooks, or those in the existing literature, that are restricted to simple symmetric ambient ow con gurations. The results of this study are categorised into ve chap- ters and a brief description of them follows.