Breakup of Thin Liquid Filaments on Partially Wetting Substrates: from Micrometric to Nanometric Scales

We present theoretical and experimental results regarding the instability of a thin liquid film in the form a long filament sitted on a solid substrate. We consider this problem in two different scenarios, namely, at submillimetric and nanometric scales, and we study their free surface instability. In the first scale, we take into account the effects due to surface tension and gravity, while in the smaller scale, we add intermolecular interaction and neglect gravity. The flows are modeled within the long wave approximation, which leads to a nonlinear fourth-order differential equation for the fluid thickness. This model equation also includes the partial wetting condition between the liquid and the solid. In the theoretical models, we analyze the linear stability of the equilibrium configurations. The linear stability analyses lead to eigenvalue problems that are solved using pseudo spectral methods in the submillimetric case, and finite differences in the nanoscale. Whenever possible, the theoretical results are compared with experiments performed on a submillimetric scale (silicon oils on glass), as well as on nanometric scale (nickel films melted by laser irradiation on SiO2 substrates).