Classical fluid mechanics confronts modern research questions: Virus transport, a novel similarity solution, and an N-body problem

I will provide a brief overview of recent projects in my group where we identify new analytical and physical features of flows common to modern research questions. First, I will share some of our work (experimental and numerical) on fluid dynamics themes related to virus transmission by speech, which has largely been neglected, but may be relevant when thinking about asymptomatic transmission of a pathogen. Second, I consider the drainage of a liquid film on a vertical substrate of finite width. We measured experimentally the film shape near an edge, which is a function of time and two space variables. Analysis of the corresponding nonlinear thin-film equation shows that there is a similarity solution, collapsing three independent variables to one similarity variable, so that the nonlinear PDE becomes a nonlinear ODE. This novel similarity solution (three variables to one) is in excellent agreement with the experimental measurements. Finally, if there is time, I will introduce an evaporation problem involving N droplets, and show how a 19th-century approach appears to be more effective than modern (mostly numerical) studies of the problem.