Droplets on a wall: moving contact lines with the Immersed Boundary Method

In this work, we propose and test four techniques for simulating the 2D Immersed Boundary (IB) method for moving droplets on a wall. The first technique defines a moving contact line (MCL) model and implements Navier slip at an immersed solid boundary. The static and dynamic contact line angle are endogenous instead of prescribed. The second technique simulates both a surface tension force and an unbalanced Young's force with one general equation that does not involve estimating local curvature. The third technique splices the liquid-gas interfaces to handle the coalescence and separation of liquid droplets or gas bubbles. The forth technique re-samples the liquid-gas interface markers to ensure a near-uniform distribution without exerting artificial forces. Then, we test our techniques using some benchmark cases, including a slipping droplet on a wall and a rising bubble, some convergence tests, and some other qualitative tests.