Abstract
In this article, we show that significant deviations from the classical quasi-steady models of droplet evaporation can arise solely due to transient effects in the gas phase. The problem of fully transient evaporation of a single droplet in an infinite atmosphere is solved in a generalized, dimensionless framework with explicitly stated assumptions. The differences between the classical quasi-steady and fully transient models are quantified for a wide range of the 10-dimensional input domain and a robust predictive tool to rapidly quantify this difference is reported. In extreme cases, the classical quasi-steady model can overpredict the droplet lifetime by 80%. This overprediction increases when the energy required to bring the droplet into equilibrium with its environment becomes small compared with the energy required to cool the space around the droplet and therefore establish the quasi-steady temperature field. In the general case, it is shown that two transient regimes emerge when a droplet is suddenly immersed into an atmosphere. Initially, the droplet vaporizes faster than classical models predict since the surrounding gas takes time to cool and to saturate with vapour. Towards the end of its life, the droplet vaporizes slower than expected since the region of cold vapour established in the early stages of evaporation remains and insulates the droplet.
Highlights
Since Maxwell’s seminal work [1], continued commitment to understand evaporation processes has fostered a rich scientific literature on topics as diverse as spray cooling, combustion, climate science, medical treatments, cosmetics and manufacturing processes [2,3,4,5,6]
Gas phase transient effects are studied in isolation of liquid phase transients by careful selection of initial conditions
The QS problem is summarized for two main reasons; firstly, to provide the definitions of BM and BT which readily derive from the QS solution; and secondly, to define the QS droplet lifetimetev,QS which is used as a benchmark to compare with the fully transient model
Summary
Since Maxwell’s seminal work [1], continued commitment to understand evaporation processes has fostered a rich scientific literature on topics as diverse as spray cooling, combustion, climate science, medical treatments, cosmetics and manufacturing processes [2,3,4,5,6]. The preceding models that result in d2-law behaviour once the steady droplet temperature is reached are based on the classical theory assumption that the gas is quasi-steady (QS). Tonini & Cossali [33] modelled evaporation of various fluids under ambient conditions of 1 bar/500◦C They found that the effect of a moving droplet surface can cause a 20% difference in the time to reach 95% of initial droplet size between the QS and fully transient models. Gas phase transient effects are studied in isolation of liquid phase transients (droplet heating and cooling) by careful selection of initial conditions This reveals that significant deviation from the classical theory can occur solely due to gas phase transients. The dimensionless approach and large number of cases considered allows general conclusions to be made that increase the fundamental understanding of droplet evaporation physics
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