Film Dynamics Over a Topographical Surface Using Lattice Boltzmann Method

In this work, the dynamics of a spreading liquid film on a planar and topographical substrate are numerically modeled using the phase-field lattice Boltzmann Method (PFLBM). A two-phase interface is inherently mesoscopic in nature, making the PFLBM a suitable technique for modeling. Interfacial patterns generated using PFLBM perfectly match the experimental and analytical results obtained within the lubrication assumption. PFLBM simulations uncovered that steady-state solutions are not possible for large topographies and the fluid-fluid interface results in a series of droplets, leaving the topographical feature in the downstream direction. This unsteady pattern is found to be highly dependent on the advancing contact angle. A decrease in viscosity ratio (bottom to top fluid) increases the height of the capillary ridge formed, making the film more prone to instability. We also explore the effect of multiple obstacles on the capillary ridges formed by each and obtain the condition for independent ridges. Finally, a detailed analysis will be presented for the effect of aspect ratio (film thickness away from contact point versus capillary length) on planar surfaces with contact-line spreading. Our study unveils that at a critical value of the aspect ratio, the maximum value of dimensionless capillary ridge height reaches unity, and this critical value is found to be independent of the inclination angle. On further increasing the value of this parameter, a nose-like structure appears near the contact point, which is strongly dependent on contact angle values.