New Jersey Institute of Technology
Department of Mathematical Sciences

Capstone Laboratory

Thin film flow inside a funnel

Supported in part by the NSF Grant No. CBET-1604351 and DMS-1815613.

Instructor: Lou Kondic

Lab Assistant: Ryan Allaire

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) .

Well developed instability of a converging thin film in a funnel.

An example of experimental results showing well developed instability of a converging thin film in a funnel: the view is from above, and one can see a number of finger-like fluid structures (dark) that spontaneously develop during flow evolution

Experimental videos for 60 degree funnel

Experimental videos for 45 degree funnel

Experimental videos for 35 degree funnel

Experimental videos for 10 degree funnel