A theoretical framework for comprehensive modeling of steadily fed evaporating droplets and the validity of common assumptions

• Published in: International journal of thermal sciences 2020-12, Vol.158, p.106529, Article 106529
• Main Authors: Akkus, Yigit, Çetin, Barbaros, Dursunkaya, Zafer
• Format: Article
• Language: English
• Subjects: Buoyancy; Droplet evaporation; Gas convection; Steadily fed droplet; Stefan flow; Thermocapillarity
• ISSN: 1290-0729; 1778-4166
• DOI: 10.1016/j.ijthermalsci.2020.106529

A theoretical framework is established to model the evaporation from continuously fed droplets, promising tools in the thermal management of high heat flux electronics. Using the framework, a comprehensive model is developed for a hemispherical water droplet resting on a heated flat substrate incorporating all of the relevant transport mechanisms: buoyant and thermocapillary convection inside the droplet and diffusive and convective transport of vapor in the gas domain. At the interface, mass, momentum, and thermal coupling of the phases are also made accounting for all pertinent physical aspects including several rarely considered interfacial phenomena such as Stefan flow of gas and the radiative heat transfer from interface to the surroundings. The model developed utilizes temperature dependent properties in both phases including the density and accounts for all relevant physics including Marangoni flow, which makes the model unprecedented. Moreover, utilizing this comprehensive model, a nonmonotonic interfacial temperature distribution with double temperature dips is discovered for a hemispherical droplet having internal convection due to buoyancy in the case of high substrate temperature. Proposed framework is also employed to construct several simplified models adopting common assumptions of droplet evaporation and the computational performance of these models, thereby the validity of commonly applied simplifying assumptions, are assessed. Benchmark simulations reveal that omission of gas flow, i.e. neglecting convective transport in gas phase, results in the underestimation of evaporation rates by 23–54%. When gas flow is considered but the effect of buoyancy is modeled using Boussinesq approximation instead of assigning temperature dependent density throughout the gas domain, evaporation rate can be underestimated by up to 16%. Deviation of simplified models tends to increase with increasing substrate temperature. Moreover, presence of Marangoni flow leads to larger errors in the evaporation rate prediction of simplified models. •Liquid and gas domains are modeled using temperature dependent thermophysical properties.•The effects of buoyancy, thermocapillarity, Stefan flow, radiation from the interface, and species diffusion in the gas are modeled.•Surface temperature variation with double dips is discovered for a hemispherical droplet having internal convection due to buoyancy.•Using Boussinesq approximation instead of assigning temperature depende