Numerical simulation of static and sliding drop with contact angle hysteresis

A numerical “macroscopic-scale” method for static (including hysteresis) and moving contact lines for partially wetting liquids is presented. The numerical method is based on the implementation of a “sub-grid” description of the contact line that consists in imposing the apparent angle for static and moving contact lines. The numerical simulations are validated against several well controlled bi-dimensional situations: the equilibrium shape of a drop released on a hydrophobic or hydrophilic wall, the axisymmetric spreading of a drop for a partially wetting liquid, the migration of a drop placed on a inclined wall and submitted to a Couette or Poiseuille flow.