Growth and translation of a liquid-vapour compound drop in a second liquid. Part 2. Heat transfer

Abstract

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.

Boiling of small droplets

“…They find the rate of heat transfer to the droplet and compare it to experimental results obtained by photographing droplets boiling while rising through water. Tochitani and coworkers [9,10] also develop an analytical model of heat transfer to a boiling droplet using a geometric model of the droplet similar to that of Sideman and Taitel, but assume that the flow around the Other researchers examine boiling droplets using more sophisticated models of the geometry of the bubble and droplet [12,13]. Raina and Grover [14] study the effects of sloshing of the droplet around the bubble.…”

On the thermocapillary motion of partially engulfed compound drops

“…The heat transfer characteristics of a partially engulfed gas-liquid compound drop translating in a different immiscible fluid appear to have been first studied by Sideman & Taitel (1964), who used pentane and butane drops as the dispersed phase evaporating in a continuous phase of distilled water. Vuong & Sadhal (1989b) computed the evaporation of a pentane drop in glycerol. Dammel & Beer (2003) have studied the case of heat transfer from a continuous liquid to a drop of a second immiscible liquid, which rises due to buoyancy and simultaneously evaporates.…”

Thermocapillary motion of hybrid drops

“…19 The heat transfer characteristics of a partially engulfed gas-liquid compound drop translating in a different immiscible fluid appear to have been first studied by Sidemen and Taitel 20 who used pentane and butane drops as the dispersed phase evaporating in a continuous phase of distilled water. Vuong and Sadhal 21 computed the evaporation of a pentane drop in glycerol. They assumed that the shape was solely determined by the interfacial tensions and solved the flow fields analytically in the limit of the Stokes flow.…”