The modified Cassie's equation and contact angle hysteresis

In this paper, we derive a modified Cassie's equation for wetting on chemically patterned surfaces from a homogenization approach. The derivation reveals that effective contact angle is a local average of the static contact angle along the contact line which describes all possible equilibrium states including the local minimum of the free energy of the system. The usual Cassie's state which corresponds to the global minimum is only a special case. We then discuss the contact angle hysteresis on chemically patterned surfaces.