The force F(h) between two bodies is related to the interaction free energy U(h) as
where h is the surface-to-surface separation. Conversely, when the force profile is known, one can evaluate the interaction energy as
When one considers two planar walls, the corresponding quantities are expressed per unit area. The disjoining pressure is the force per unit area and can be expressed by the derivative
where W(h) is the surface free energy per unit area. Conversely, one has
The main restriction of the Derjaguin approximation is that it is only valid at distances much smaller than the size of the objects involved, namely h ≪ R and h ≪ R. Furthermore, it is a continuum approximation and thus valid at distances larger than the molecular length scale. Even when rough surfaces are involved, this approximation has been shown to be valid in many situations. Its range of validity is restricted to distances larger than the characteristic size of the surface roughness features (e.g., root mean square roughness).