Fluid accumulation in thin-film fl ows driven by surface tension and gravity (I): Rigorous analysis of a drainage equation

Details Fluid accumulation in thin-film fl ows driven by surface tension and gravity (I): Rigorous analysis of a drainage equation Fluid accumulation in thin-film fl ows driven by surface tension and gravity (I): Rigorous analysis of a drainage equation

2011-07-29

arxiv.org/abs/1107.5917v1

Mathematics

Analysis of PDEs

33 pages, 3 figures

Scientific paper

We derive a boundary layer equation describing accumulation regions within a thin-film approximation framework where gravity and surface tension balance. As part of the analysis of this problem we investigate in detail and rigorously the 'drainage' equation (phi"'+1)phi^3=1. In particular, we prove that all solutions that do not tend to 1 as the independent variable goes to infinity are oscillatory, and that they oscillate in a very specific way. This result and the method of proof will be used in the analysis of solutions of the afore mentioned boundary layer problem.

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