Thin film dynamics using lattice Boltzmann method: Role of aspect ratio and surface wettability gradient

Abstract

This study investigates the possibility of solving film problems using the phase-field lattice Boltzmann method (LBM). The mesoscopic nature of fluid interface makes the lattice Boltzmann method (LBM) a suitable tool to model two-phase systems. Experimental and theoretical observations for a film spreading on an inclined plane have been reproduced using LBM, justifying the use of LBM in film problems. We present a detailed analysis of the effect of the aspect ratio (the ratio of the film thickness far away from the contact point to the characteristic length), viscosity ratio, and surface wettability gradient. The study of the effect of the aspect ratio confirms that the dimensionless height of the tip of the ridge approaches unity exponentially as we move toward the thick film where lubrication approximation no longer holds. The ridge completely vanishes at a critical value of the aspect ratio (εc). εc is found to be independent of the advancing contact angle, and increasing the aspect ratio beyond εc results in fluid protrusion ahead of the contact point. The film is more prone to instability in a more viscous surrounding where free-surface assumption is not valid. Furthermore, the study of the effect of the chemically induced wettability gradient on the solid substrate reveals that the contact point velocity and the interfacial profile depend on the local surface wettability.