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

In this work, we use the immersed boundary method with four extensions to simulate a moving liquid-gas interface on a solid surface. We first define a moving contact line model and implements a static-dynamic friction condition at the immersed solid boundary. The dynamic contact angle is endogenous instead of prescribed, and the solid boundary can be non-stationary with respect to time. Second, we simulate both a surface tension force and a Young's force with one general equation that does not involve estimating local curvature. In the third extension, we splice liquid-gas interfaces to handle topological changes, such as the coalescence and separation of liquid droplets or gas bubbles. Finally, we re-sample 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. Published under an exclusive license by AIP Publishing.