RESUMO

Advanced mathematical (analytical/numerical) techniques used in recent studies in published literature to evaluate the drag coefficients and transport rates pertaining to direct-contact heat and mass transfer processes with liquid droplet(s) have been reviewed. Illustrations of the actual applications of these techniques are provided. In some instances, where necessary, earlier contributions are recalled and discussed for the sake of completeness. Critical observations and comments are made where appropriate. This article is a companion article to the one published recently by the author [5] in which the focus was on the physics.
This review is classified under various subdivisions depending on the continuous phase Reynolds number. However, two spherico-symmetric (stationary droplet) studies of vaporization and combustion, one dealing with a slurry droplet and the other with a droplet in a high-pressure, high-temperature environment, have also been included. The remainder deals with studies involving convective effects. With the drop in laminar motion, three different direct-contact transfer problem classifications are recognized as belonging to the low, intermediate, or high Reynolds number. The subject matter is further subdivided into two classes: (1) transport without phase-change at the interface, (2) transport with phase-change at the interface. For low Reynolds number creeping flows, the inertia of the fluid is not significant, and, consequently, in many cases the flow fields and transport rates may be determined by matched-asymptotic (singular perturbation) procedures. At intermediate Reynolds numbers (Re ∼ O(10) − O(100), fully numerical or semianalytical (series-truncation, spectral-type) methods are usually required. At high Reynolds numbers, boundary layer approximations are possible, but these preclude the accurate determination of the drag coefficient and transport in the rear of the droplet. Presence of a phase-change, in any of the above circumstances, immensely complicates the formulations and the solution procedures, as the discussions in this article reveal. Most analytical/numerical studies of direct-contact transfer have considered an isolated spherical drop in laminar motion. This review article has mostly addressed such situations. Droplet deformation, droplet-interaction, and the many-droplet problems are briefly discussed.