The fluid dynamics associated with a compound drop consisting of a vapour bubble, partly surrounded by its own liquid in another immiscible liquid is considered. The fluid motion is analysed in the limit of Stokes flow and at the same time the surface tension forces are considered to be large enough to allow the interfaces to have uniform curvature. The flow field consists of translation and growth that can arise from change of phase.An exact analytical solution for the axisymmetric flow field is obtained. The important results of physical interest are the drag force and the flow behaviour. In the case without growth, the drag force lies between the bubble and the solid-sphere limits for a sphere of the same volume as the total liquid and vapour dispersed phase. The maximum drag force is observed when the liquid and vapour volumes are nearly the same. This is the effect of weak circulation due to the smaller available space as compared with a spherical drop. With growth this effect appears to be enhanced. The flow streamlines exhibit secondary vortices in the dispersed phase when there is growth. The velocity field and the drag results here are applied to the heat transfer problem for the compound drop in Part 2 of this two-part series.

The present work is a comprehensive theoretical study of the heat transfer associated with a 3-singlet compound drop that is growing because of change of phase. The geometry is the same as in Part 1, i.e. a vapour bubble partially surrounded by its own liquid in another immiscible liquid. The attempt here is to gain fundamental understanding of the transport processes that take place in connection with direct-contact heat exchange. The fluid dynamics associated with its growth and translation is treated in Part 1. Here, that flow field solution is used to obtain the temperature field and hence the evaporation rate. The energy equation for the system consisting of a single compound drop is solved numerically by finite-difference methods. The results give the complete time history of evaporation of the drop. In addition, useful quantities such as the Nusselt number are given and compared with existing experimental data. Most of the results have good agreement with experimental data.