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In this paper, we propose an alternative approach to implement the contactangle boundary condition on immersed surfaces for phase-field simulations oftwo-phase flows using the Cahn-Hilliard equation on a Cartesian mesh. Thissimple and effective method was inspired by previous works on the geometricformulation of the wetting boundary condition. In two dimensions, by makingfull use of the hyperbolic tangent profile of the order parameter, we were ableto obtain its unknown value at a ghost point from the information at only onepoint in the fluid. This is in contrast with previous approaches usinginterpolations involving several points. The special feature allows this methodto be easily implemented on immersed surfaces (including curved ones) that cutthrough 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 contactangle.

An Alternative Method to Implement Contact Angle Boundary Condition on Immersed Surfaces for Phase-Field Simulations