In recent years, computational fluid dynamics (CFD) has become a valuable tool for the design of extraction processes. CFD simulations have been combined with population balances to account for coalescence and breakage. In this work, another approach to account for drop interactions is shown, namely, the incompressible Cahn-Hilliard/Navier-Stokes equations. To apply the Cahn-Hilliard equations, they have to be combined with a thermodynamic model. Here, a Koningsveld-Kleintjens approach is used to account for the mixing gap of the binary mixture. The suggested method was applied to analyze drops in a shear field and to investigate drop coalescence.