A level-set approach for simulations of flows with multiple moving contact lines with hysteresis

The level-set method of Sussman et al. [J. Comput. Phys. 148 (1999) 81] is extended such that flows with multiple moving contact lines can be simulated, accounting for inertia, a relation between contact-line speed and contact angle, slip and contact-line hysteresis. The convergence properties of the method are investigated, with particular attention on the resolution of the contact-line stress singularity. Results are compared with a lubrication theory for spreading droplets.