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The present paper reviews the methodologies for representing the droplet motion and vaporization history in two-phase flow computations. The focus is on the use of droplet models that are realistic in terms of their efficient implementation in comprehensive spray simulations, representation of important physical processes, and applicability under a broad range of conditions. The methodologies available at present to simulate droplet motion in complex two-phase flows may be broadly classified into two categories. First one is based on the modified BBO equation. This approach is more comprehensive, but requires modifications and/or correlations at higher droplet Reynolds number. The second approach aims at developing correlations, using detailed numerical simulations or laboratory experiments, for the effects of flow nonuniformity and droplet relative acceleration on the instantaneous drag and lift coefficients. Recent advances made in the droplet vaporization models are also discussed. The advanced vaporization models include the effects of transient liquid heating, gas-phase convection, and variable thermo physical properties. All of these models are discussed, and recommendations are made for their inclusion in comprehensive two-phase computations.

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Separation of fine coal in froth flotation relies upon the wettability difference between the coal-rich and mineral-rich particles in the aqueous solution. Two methods were used to measure the wettability of six ranks of coal as well as coal samples treated with various levels of dispersed collector in aqueous solution. Wettability was determined by measuring the distribution of critical wetting surface tension, i.e., surface energy, using the film flotation technique and by measuring the induction time, i.e., bubble−particle attachment time, of the material. The wetting of coal particles is strongly dependent upon the coalification processes and can be affected by ash content. For anthracite coal with a high ash content, very high surface energy and intermediate induction time were measured, but intermediate floatability with a very good ash rejection was obtained. Sub-bituminous coal with low mineral inclusion was found to have a relatively low surface energy, and thus a high floatability, but very poor selectivity was observed, which was reflected in lengthened induction time. When dynamics of flotation behaviors are involved, flotation results can be better interpreted by induction time. For dispersed collector-treated coal samples, an increase in collector dispersion (i.e., a decrease in kerosene droplet size), by direct liquid collector mechanical agitation, ultrasonic energy emulsification, or atomization, caused decreases in surface energy and induction time and closely matched the increase of flotation recovery and selectivity. With similar particle density, mineral liberation conditions, and particle size, the induction time was found to be closely related to the mean critical surface tension for untreated coal samples and for HV-bituminous coal samples treated by various levels of dispersed collector.