We developed a sharp-interface level-set method for immiscible pore-scale two-phase flow with a thin wetting film on the solid surface. The lubrication approximation is used to model the thin-film equation efficiently. The incompressible Navier–Stokes, level-set, and thin-film evolution equations are coupled sequentially. Hamilton–Jacobi level-set reinitialization is employed to construct the signed-distance function, which takes into account the thin film on the solid surface. The level-set simulation method is validated and shown to match the augmented Young–Laplace equation for a meniscus in a capillary tube. Viscous bending of an advancing interface over a precursor film is captured by the level-set method and agrees with the Cox–Voinov theory. We model the evolution of an advancing bubble surrounded by a wetting film. The predicted film thickness compares well with both theory and experiments. We then demonstrate that the multiscale level-set approach can model immiscible two-phase flow with a capillary number as low as 10−6.
|Acceptance of Terms and Conditions||Click here to agree|