Title: Modeling, analysis, and control of droplet dynamics

Abstract: Thin liquid films flowing down vertical fibers spontaneously exhibit complex interfacial dynamics, leading to irregular wavy patterns and traveling liquid droplets. Such droplet dynamics are fundamental components in many engineering applications, including mass and heat exchangers for thermal desalination, as well as water vapor and particle capture. Recent experiments demonstrate that critical flow regime transitions can be triggered by varying inlet geometries and external fields. Similar interacting droplet dynamics have also been observed on hydrophobic substrates, arising from interfacial instabilities in volatile liquid films. In this talk, I will describe lubrication theory and weighted residual models for falling droplets. The coarsening dynamics of condensing droplets will be described by a simplified dynamical system. I will also present our recent results on developing optimal boundary control and mean-field control for droplet dynamics.