Solitary waves on falling liquid films in the low Reynolds number regime

We study the problem of a thin liquid film falling down an inclined slope. We use a simplified model to study the evolution and morphology of the solitary waves on a thin film with a periodic forcing at the inlet. In recent work by Denner et al (2016 Phys. Rev. E 93, 033121), the regime for high Re was studied and results obtained on the geometry and dispersion of the waves. We wish to establish whether similar results are observed in a regime of smaller Re and examine quantities which can be compared with experiment, such as the maximum and minimum film height as a function of a rescaled Reynolds number which accounts for the inclination of the substrate. Our results show some evidence that h min collapses onto a single curve when plotted as a function of Re*, and approaches the absolute value of h min/h N = 0.375 in agreement with results obtained at higher Re. We also obtain a curve for d/λ which can be compared with the results reported in (Denner et al 2016 Phys. Rev. E 93, 033121).