Study of film dynamics using lattice Boltzmann method*

In this work the dynamics of a spreading film is numerically modelled using the phase-field lattice Boltzmann approach. The fluid-fluid interface is mesoscopic in nature, making the lattice Boltzmann method (LBM) a useful technique for modelling two-phase systems. A geometry-based wetting boundary condition has been used to model the three-phase contact point. The two-dimensional interfacial pattern obtained using LBM  matches with the profile obtained using the analytical model derived within the lubrication limit for a thin film spreading on an inclined plane. We present a detailed analysis of the effect of aspect ratio (film-thickness versus capillary length) and viscosity ratio (bottom to top fluid) on the spreading dynamics. The study reveals that the dimensionless height of the ridge's tip approaches unity rapidly as we approach the thick films away from the validity of the lubrication approximation. The ridge completely vanishes at a critical aspect ratio and is shown to be independent of the advancing contact angle. A protruding structure at the contact point has been observed for aspect ratios beyond the critical value and is also found sensitive to contact angle. Furthermore, the viscous effects of surrounding fluid have been investigated on the interfacial pattern of spreading film. Increasing the viscous effects of surrounding fluid results in an enhanced ridge height and, as a result, makes the film more prone to instability.