Numerical Simulation of rivulet build up via lubrication equations

A number of engineering problems involve the evolution of a thin layer of liquid over a non-wettable substrate. For example, CO2 chemical absorption is carried out in packed columns, where ost-combustion CO2 flows up while liquid solvent falls down through a collection of corrugated sheets. Further application include, among others, in-flight icing simulations, moisture ondensation on de-humidifier fins, fogging build up and removal. Here, we present a development of an in-house code numerically solving the 2D lubrication equation for a film flowing down an nclined plate. The disjoining pressure approach is followed, in order to model both the contact line discontinuity and the surface wettability. With respect to the original implementation, the full odeling of capillary pressure terms according to Young- Laplace relation allows to investigate contact angles close to /2. The code is thus validated with literature numerical results, obtained by fully 3D approach (VOF), showing satisfying agreement despite a strong reduction in terms of computational cost. Steady and unsteady wetting dynamics of a developing rivulet are investigated and validated) under different load conditions and for different values of the contact angles.