Multiscale level-set method for accurate modeling of immiscible two-phase flow with deposited thin films on solid surfaces

We developed a multiscale sharp-interface level-set method for immiscible two-phase flow with a pre-existing thin film on solid surfaces. The lubrication approximation theory is used to model the thin-film equation efficiently. The incompressible Navier-Stokes, level-set, and thin-film evolution equations are coupled sequentially to capture the dynamics occurring at multiple length scales. The Hamilton-Jacobi level-set reinitialization is employed to construct the signed-distance function, which takes into account the deposited thin-film on the solid surface. The proposed multiscale method is validated and shown to match the augmented Young-Laplace equation for a static meniscus in a capillary tube. Viscous bending of the advancing interface over the precursor film is captured by the proposed level-set method and agrees with the Cox-Voinov theory. The advancing bubble surrounded by a wetting film inside a capillary tube is considered, and the predicted film thickness compares well with both theory and experiments. We also demonstrate that the multiscale level-set approach can model immiscible two-phase flow with a capillary number as low as 10−6.