Numerical simulation of thin liquid films over a solid non-wettable substrate assuming lubrication approximation.

When a continuous film flows over a non-wettable surface, it may break up with the consequent formation of a dry-patch. The actual shape of the resulting water layer is of great interest in several engineering applications, such as in-flight icing simulations, finned dehumidifier behavior modeling, coating process and chemical absorption/distillation through structured packing. A 2D numerical solver for the prediction of film flow is presented. The lubrication approximation is assumed, allowing for the description of liquid film flowing down an inclinate plate, driven by both gravity and shear. The effects of contact line and surface wettability are introduced combining the precursor film model and the disjoining pressure terms. The capillary pressure, which is usually modeled through the small slope approximation, is here defined imposing the membranal equilibrium of the gas-liquid free-surface, in order to investigate higher values of the imposed equilibrium contact angle between liquid and solid substrate. The in-house solver is first validated with both experimental and numerical results, available in literature. Numerical simulations are then performed with the aim of studying the beahvior of liquids in absorption/distillation process through structured packing. The lubrication theory is finally extended to the most general case of a 3D curved substrate, allowing to investigate problems involving complex geometries and configurations. Thus, a liquid film flowing down a packing layer, which is a wrinked surface composing the packed column used in absorption process, is simulated. Such a problem has been investigated in literature by means of a fully 3D approach only, but the huge computational costs do not allow to investigate several configurations, resulting in a lack of knowledge of the hydrodinamics driving the liquid flowing through the packing layers. The full modeling of the capillary pressure and the extension to general curved substrates clearly put a new effort to the well known lubrication theory and allow to simulate phenomena, that were not covered by such a theory.