The Derjaguin approximation (or sometimes also referred to as the proximity approximation), named after the Russian scientist Boris Derjaguin, expresses the force profile acting between finite size bodies in terms of the force profile between two planar semi-infinite walls. This approximation is widely used to estimate forces between colloidal particles, as forces between two planar bodies are often much easier to calculate. The Derjaguin approximation expresses the force F(h) between two bodies as a function of the surface separation as
where W(h) is the interaction energy per unit area between the two planar walls and R the effective radius. When the two bodies are two spheres of radii R and R, respectively, the effective radius is given by
Experimental force profiles between macroscopic bodies as measured with the surface forces apparatus (SFA) or colloidal probe technique are often reported as the ratio F(h)/R.