A height function based momentum balance model to simulate contact angle dynamics with hysteresis

We report a combined method to deal with the contact angle dynamics with hysteresis. The momentum balance model is applied to obtain the transient contact angle by balancing the inertia and the capillary force where the curvatures are estimated by the height function at the contact line. This integrated approach provides a great convenience that no need for a prior knowledge of the contact angle, and possesses the good property of the sharp interface approximation. In order to facilitate the wider use of the present method, we incorporate a dynamic contact line model to estimate the contact angle when the contact line starts to move. This combination plus the hysteresis region will take the ability to solve most of problems related to wetting with more physical sense. This proposed model is finally validated by the droplet equilibrium, spreading, and sliding tests.