Considering a given subvolume formula_17 containing a surface of discontinuity, the volume is divided by the mathematical surface into two parts A and B, with volumes formula_18 and formula_19, with formula_20 exactly. Now, if the two parts A and B were homogeneous fluids (with pressures formula_21, formula_22) and remained perfectly homogeneous right up to the mathematical boundary, without any surface effects, the total grand potential of this volume would be simply formula_23. The surface effects of interest are a modification to this, and they can be all collected into a surface free energy term formula_24 so the total grand potential of the volume becomes: