Numerical simulation of shear driven film instability over heterogeneous surfaces via enhanced lubrication theory

The prediction of the transition between continuous film, ensemble of rivulets and moving droplets is crucial in applications such as in-flight icing on airfoil wings or a number of chemical reactors. Here, lubrication theory is used to numerically investigate the stability of a continuous liquid film, driven by shear, over a heterogeneous surface. The disjoining pressure is used to model surface wettability, while the full implementation of the film curvature allows to investigate contact angles up to 60◦. Different heterogeneous surface configurations occurring in real problems are investigated. An extended computational campaign records the transition from continuous film to rivulet regime and, if present, the further transition from rivulet to droplets at different flow conditions. A moving grid approach allows for accurate prediction of instability phenomena at low computational cost. The numerical results are successfully validated with experimental evidence in case of critical flow rate leading to a stable dry patch and compared with literature results involving the inherently multiscale in-flight icing phenomenon, providing useful statistical information, required to transfer the present detailed small-scale information into larger scale CFD computational approaches.