  We present an hybrid VOF/embedded boundary method allowing to model two-phase
flows in presence of solids with arbitrary shapes. The method relies on the
coupling of existing methods: a geometric Volume of fluid (VOF) method to
tackle the two-phase flow and an embedded boundary method to sharply resolve
arbitrary solid geometries. Coupling these approaches consistently is not
trivial and we present in detail a quad/octree spatial discretization for
solving the corresponding partial differential equations.
  Modelling contact angle dynamics is a complex physical and numerical problem.
We present a Navier-slip boundary condition compatible with the present cut
cell method, validated through a Taylor-Couette test case.
  To impose the boundary condition when the fluid-fluid interface intersects a
solid surface, a geometrical contact angle approach is developed. Our method is
validated for several test cases including the spreading of a droplet on a
cylinder, and the equilibrium shape of a droplet on a flat or tilted plane in
2D and 3D.
  The temporal evolution and convergence of the droplet spreading on a flat
plane is also discussed for the moving contact line given the boundary
condition (Dirichlet or Navier) used.
  The ability of our numerical methodology to resolve contact line statics and
dynamics for different solid geometries is thus demonstrated.
