  In this paper, we propose an alternative approach to implement the contact
angle boundary condition on immersed surfaces for phase-field simulations of
two-phase flows using the Cahn-Hilliard equation on a Cartesian mesh. This
simple and effective method was inspired by previous works on the geometric
formulation of the wetting boundary condition. In two dimensions, by making
full use of the hyperbolic tangent profile of the order parameter, we were able
to obtain its unknown value at a ghost point from the information at only one
point in the fluid. This is in contrast with previous approaches using
interpolations involving several points. The special feature allows this method
to be easily implemented on immersed surfaces (including curved ones) that cut
through the grid lines. It is verified through the study of two examples: (1)
the shape of a drop on a circular cylinder with different contact angles; (2)
the spreading of a drop on an embedded inclined wall with a given contact
angle.
