Instability of a Film Falling Down a Bounded Plate and Its Application to Structured Packing

The instability of a film falling down a vertical plate with lateral walls, which is the base configuration describing the structured packing geometry, is numerically investigated via the lubrication theory. The solid substrate wettability is imposed through the disjoining pressure, while the assumption of a tiny, precursor film thickness allows for modelling a moving contact line. Contact angles up to 60∘, which falls in the range of structured packing applications, are investigated, thanks to the full implementation of the capillary pressure instead of the small slope approximation. Parametric computations are run for a film falling down a vertical plate bounded by lateral walls, changing the plate width and the flow characteristics. An in-house, finite volume method (FVM) code, previously developed in FORTRAN language and validated in the case of film instability and rivulet flow, is used. The number of observed rivulets, triggered by the instability induced by the lateral walls, is traced for each computation. The numerical results suggest that rivulets with a given wavelength, equal to the one provided by the linear stability analysis, are generated, but only those characterized by a wavelength greater than a minimum threshold, which depends on the substrate wettability, induce partial dewetting of the domain. This allowed for the development of a simplified, statistically based model to predict the effective interface area and the rivulet holdup (required to estimate the mass transfer rate in absorption/distillation applications). Compared to the literature models of the structured packing hydrodynamics, which usually assume a continuous wetting layer, the influence of the flow pattern (continuous film or ensemble of rivulets) on the liquid holdup and on the interfacial area is introduced. The predicted flow regime is successfully verified with evidence from the literature, involving a flow down a corrugated sheet.