This Capstone projects focuses on the problem of analysis of converging flows, such a flow on the inside of a funnel. Figure shows an example of a physical experiment where thin film is released close to the upper edge of a funnel, and then let to evolve. While this setup is related to a number of classical problems involving thin films, it introduces a novel twist related to converging nature of the flow. The participating students have carried out four separate but related projects (i) physical experiments, image analysis, and quantification of the instabilities that develop during the flow; (ii) asymptotic analysis, (iii) numerical simulations, and (iv) self-similar type of analysis of a simplified setup. The direct comparison between experimental, analytical, and numerical results allowed to the participating students to develop better understanding of fluid instabilities, and, more broadly, of the techniques used in applied mathematics research.
The instructor thanks to Joshua Dijksman (Wageningen University, The Netherlands) for significant help with the experimental aspects of the project, and to Te-Sheng Lin (National Chiao Tung University, Taiwan) for his support with numerical and analytical aspects. Combined experimental theoretical study was published in J. Fluid Mechanics (2021) .