Derjaguin approximation

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.^[1] 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^[2]

${\displaystyle F(h)=2\pi R_{\rm {eff}}W(h),}$

where W(h) is the interaction energy per unit area between the two planar walls and R_eff the effective radius. When the two bodies are two spheres of radii R₁ and R₂, respectively, the effective radius is given by

${\displaystyle R_{\rm {eff}}^{-1}=R_{1}^{-1}+R_{2}^{-1}.}$

Experimental force profiles between macroscopic bodies as measured with the surface forces apparatus (SFA)^[3] or colloidal probe technique^[4] are often reported as the ratio F(h)/R_eff.