I worked out all the details of the flat surface thin film fluid equation. You can download the pdf here: /uploads/2/9/5/2/2952473/derivation.pdf . I'm currently working on the derivation for a curved substrate and as soon as I finish I will start the implementation.
I have been working on the implementation of the 1D Thin Film fluid equation according to Diez in Computing Three-Dimensional Thin Film Flows Including Contact Lines. Until recently, I wasn't sure that my implementation was giving the correct results. According to the paper, their implementation is validated against an analytical solution to the PDE. The problem was that the analytical solution they gave did not seem to actually be a solution to the problem, at least in the 1D setting. I noticed this when I differentiated the given equation and they didn't zero out. My suspicion was confirmed when I decided to plug some real numbers to the equation and found out that it was definitely not a solution to the PDE I was solving. I decided to look back at the literature that they referenced in the paper and after a couple of redirections, I finally found the original equation in Smyth's High-order nonlinear diffusion paper. I made sure to understand the derivation of the solution, so that I had a clear notion of what to validate against. I changed the implementation so that it solved the PDE that does have the analytical solution and the results can be seen in the following video, for the diffusion.