Date
Thu, 22 Oct 2020
Time
16:00 - 17:00
Location
Virtual
Speaker
Howard Stone
Organisation
Princeton

There are many examples of thin-film flows in fluid dynamics, and in many cases similarity solutions are possible. In the typical, well-known case the thin-film shape is described by a nonlinear partial differential equation in two independent variables (say x and t), which upon recognition of a similarity variable, reduces the problem to a nonlinear ODE. In this talk I describe work we have done on 1) Marangoni-driven spreading on pre-wetted films, where the thickness of the pre-wetted film affects the dynamics, and 2) the drainage of a film on a vertical substrate of finite width. In the latter case we find experimentally a structure to the film shape near the edge, which is a function of time and two space variables. Analysis of the corresponding thin-film equation shows that there is a similarity solution, collapsing three independent variables to one similarity variable, so that the PDE becomes an ODE. The solution is in excellent agreement with the experimental measurements.

Further Information

We return this term to our usual flagship seminars given by notable scientists on topics that are relevant to Industrial and Applied Mathematics. 

 

Please contact us for feedback and comments about this page. Last updated on 03 Apr 2022 01:32.