Wave breaking in Newtonian and viscoplastic vertical falling liquid films

We examine the onset of wave breaking in highly viscous gravity-driven vertical falling liquid films in a quiescent atmosphere via multiphase direct numerical simulations. Both Newtonian and Herschel–Bulkley liquids are considered. Analysis of the force balance acting on wave humps shows that the transition from travelling waves to breaking states is governed primarily by the competition between gravitational and capillary forces. The transition is primarily characterised by a criterion based on the Eötvös number (quantifying gravitational to capillary forces), which we identify through a comprehensive parameter study involving over 500 simulations, where we vary the Reynolds number, the plasticity number and the power-law index. We provide a regression model for italic Eo Subscript italic crit Eo crit $\textit{Eo}_{\textit{crit}}$ in terms of these parameters, as well as for the corresponding wetting rate. The parameter study indicates that breaking generally occurs for large film thicknesses and high viscosities, yielding large Eötvös numbers while remaining in the wavy–laminar flow regime. Close to the onset of breaking, we observe overhanging travelling wave solutions, where the wave front deforms into a steady overhang, and this state generally precedes wave breaking irrespective of the investigated rheologies. Our results establish a concise criterion for predicting wave breaking in falling films involving both Newtonian and complex fluids representative of different industrial processes, and have implications for heat and mass transfer, bubble entrainment and liquid residence time.