Simulating liquid-gas interfaces and moving contact lines using the immersed boundary method

In this work, we combine the immersed boundary method with several techniques to simulate a moving liquid-gas interface on a solid surface. The first technique defines a moving contact line model and implements an extended Generalized Navier Boundary Condition at the immersed solid boundary. The static and dynamic contact line angles are endogenous instead of prescribed, and the solid boundary can be non-stationary with respect to time. The second technique simulates both a surface tension force and an unbalanced Young force with one general equation that does not involve estimating local curvature. The third technique splices liquid-gas interfaces to handle topological changes such as the coalescence and separation of liquid droplets or gas bubbles. Finally, the forth technique re-samples liquid-gas interface markers to ensure a near-uniform distribution without exerting artificial forces. We demonstrate empirical convergence of our methods on non-trivial examples and apply them to several benchmark cases, including a slipping droplet on a wall and a rising bubble.