The Complex Dynamics of Arrays of Evaporating and Condensing Droplets

本项目的目的是在提出者之前关于蒸发固着液滴的工作的基础上，探索凝结(即干燥)固着液滴这一新颖而具有挑战性的问题。当纯液体液滴暴露在大气中时，它通常会蒸发。然而，当多组分液滴暴露在含有高浓度其中一种组分的大气中时，可能会发生凝结。这在有限区域和多个液滴紧密接近的情况下尤其常见，因此近年来它已经成为几个实验研究的主题。一种天真的方法可能只是期望这个系统与广泛研究的蒸发情况相反。然而，在实践中，由于与空气相比，液滴中的扩散速度较低，因此系统要复杂得多。因此，为证明蒸发的扩散受限模型而作的常见假设通常不适用于冷凝液滴。特别是，必须准确跟踪液滴内组分的随时间变化的浓度。据我们所知，凝结固着液滴的唯一分析处理依赖于接近液体沸点的温度，而在大多数情况下不是这样。因此，本项目的重点将是开发和分析一个更普遍适用(因此更有用)的凝结数学模型，该模型捕捉了关键的物理机制，但仍然可以在不借助大量(和耗时的)数值计算的情况下进行分析。固体液滴凝结的最小数学模型不可避免地比蒸发模型更复杂，但作者在最近的《流体力学杂志》和《物理评论流体》论文中使用的技术非常适合于解决这类问题中可能出现的混合边值问题。此外，大多数最有趣的场景通常涉及近距离多个液滴之间的竞争(或合作)。然而，理解和分析这种多液滴系统蒸发的技术才刚刚由提出者开发出来。这些技术为研究更广泛的情况打开了可能性，包括蒸发，并希望也冷凝，液滴，和主管在该领域的尖端专业知识的理想地位，使我们在这一快速发展的多学科研究领域取得快速进展。最后，我们注意到，拟议的项目与Strathclyde的几个战略主题密切相关，特别是能源。例如，凝聚液滴在能源收集应用中很常见，在这一基础科学问题上的进展可能对中长期的能源研究产生重要影响。

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.