Contact line driven fingering instability of thin fluid film flows over diverging surfaces: Spherical and Conical surfaces

While thin fluid film flows over flat surfaces are well studied and understood little work has been done in understanding film flows over curved surfaces. In this work we explore flow of a completely wetting Newtonian fluid over a spherical and conical surface, with particular focus on contact line instabilities at the fluid front. Understanding contact line driven instability

in this configuration has inherent difficulties due to the presence of curvature and divergent nature of the flow imposed by the geometry. In this study we derive a thin film equation based on long wave approximation for a fluid film on a spherical and conical surface and using numerical simulations we provide some basic insights into the flow dynamics. We observe that unlike thin film flow over flat surfaces the contact line driven instability is engendered multiple times as the flow progresses.