I can hardly believe my eyes! I helped do some related research specifically concerning thin-film drainage from tubes, way back in my undergraduate days: https://doi.org/10.1016/j.expthermflusci.2018.04.015
11th problem here:
https://ortvay.elte.hu/2009/E09.pdf
I was the only one who handed in a solution for that particular problem, it was scored 70 out of 100. I no longer have my solution, but I doubt that it was very accurate, and I didn't have time for experiments.