Computational study of a thin film flow over a topographical feature using phase-field lattice Boltzmann method

Abstract

The study employs the phase-field lattice Boltzmann method (PFLBM) to explore the dynamics of a thin film flowing over a topographical feature such as a mound or a trench. The mesoscopic nature of PFLBM makes it a suitable technique for problems involving tracking the evolution of a liquid–air interface. PFLBM simulation results are validated with experimental and analytical results confirming the viability of the numerical approach for such problems. The effect of changing the topographical height, aspect ratio, viscosity ratio, and presence of multiple mounds on the film profiles are systematically analyzed. It is observed that a steady-state solution could not be obtained for large height topographical features. The transition from a steady-state interfacial pattern to an unsteady-steady state is found to depend on the width of the topography. Geometry-based condition is employed to deal with the contact points present in the film dynamics beyond rupture. For large contact angles, the unsteady cases result in film rupture and form a continuous array of droplets of equivalent dimensions at a periodic interval. Increasing the aspect ratio reduces the width of the capillary ridge formed above the topographical feature, while the viscosity ratio reduces the maximum height of the ridge. The shapes of the capillary ridges formed over multiple mounds in the flow direction are independent if the separation between the successive mounds is beyond a critical value. This critical value strongly depends on the capillary number and is independent of the dimensions of the mound.