Intermediate asymptotics of the capillary-driven thin-film equation.
We present an analytical and numerical study of the two-dimensional capillary-driven thin-film equation. In particular, we focus on the intermediate asymptotics of its solutions. Linearising the equation enables us to derive the associated Green's function and therefore obtain a complete set of solutions. Moreover, we show that the rescaled solution for any summable initial profile uniformly converges in time towards a universal self-similar attractor that is precisely the rescaled Green's function. Finally, a numerical study on compact-support initial profiles enables us to conjecture the extension of our results to the nonlinear equation.
Laboratoire de Physico-Chimie Théorique, UMR CNRS Gulliver 7083, ESPCI, Paris, France.
Michael
M
Benzaquen
Thomas
T
Salez
Elie
E
Raphaël
D002197:Capillary Action; D044085:Microfluidics; D008956:Models, Chemical