Rivulet evolution in gravity-driven thin-film flows

The evolution of a perfectly wetting, gravity-driven, thin, continuously-fed liquid film down an inclined planar substrate is modelled using the long-wave approximation with, as ob-served experimentally, a periodic pattern of flnger-like rivulets forming at the unstable advancing front. The required long-time solution, with the merger of neighbouring rivulets a possibility, is obtained using a purpose designed eficient multigrid methodology incorporating complementary error-controlled automatic spatio-temporal adaptivity and mesh devolution strategies. Critical wavelengths are extracted from the various solutions showing the effect of inclination angle and comparison drawn with the results of a linear stability analysis (LSA) based on the same flow conditions.