The Complex Dynamics of Arrays of Evaporating and Condensing Droplets

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The aim of the present project is to build on the proposers' previous work on evaporating sessile droplets to explore the novel and challenging problem of condensing (i.e., desiccating) sessile droplets.When a droplet of pure liquid is exposed to the atmosphere, it will typically evaporate. However, a multi-component droplet, when exposed to an atmosphere containing a high concentration of one of its components, can undergo condensation. This is especially common in confined regions and with multiple droplets in close proximity, and as a result it has been the subject of several experimental studies in recent years.The dynamics of such systems are complicated. A naive approach might simply expect the system to be the inverse of the extensively-studied evaporating case. However, in practice the system is much more complicated due to the lower rate of diffusion in the droplets compared to the air. As a result, common assumptions made to justify the diffusion-limited model of evaporation do not, in general, apply, to condensing droplets. In particular, the time-varying concentration of the components inside the droplets must be tracked accurately.To our knowledge, the only analytical treatment of condensing sessile droplets relies on the temperatures being close to the boiling point of the liquid, which will not be the case in most situations. As a result, the focus of this project will be on developing and analysing a more generally applicable (and hence more useful) mathematical model of condensation which captures the key physical mechanisms but is still amendable to analysis without resorting to extensive (and time consuming) numerical calculations. While the minimal mathematical model for condensation of sessile droplets is inevitably more complicated than that for evaporation, the techniques exploited by the proposers in their recent Journal of Fluid Mechanics and Physical Review Fluids papers are ideally suited to solving mixed boundary value problems of the type that are expected to arise in such problems.In addition, the majority of the most interesting scenarios often involve the competition (or cooperation) between multiple droplets in close proximity. However, the techniques to understand and analyse the evaporation of such multi-droplet systems have only just been developed by the proposers. These techniques open the possibility of studying a much wider range of situations involving evaporating, and hopefully also condensing, droplets, and the supervisors' cutting-edge expertise in the area ideally positions us to make rapid progress in this fast-moving, multidisciplinary research area.Finally, we note that the proposed project is closely aligned with several of Strathclyde's Strategic Themes, notably Energy. For example, condensing droplets are commonly found in energy harvesting applications, and progress on this fundamental scientific problem could have important implications for energy research in the medium to long term.