Derjaguin approximation

The Derjaguin approximation (or sometimes also referred to as the proximity approximation) due to 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 The Derjaguin approximation (or sometimes also referred to as the proximity approximation) due to 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 Reff the effective radius. When the two bodies are two spheres of radii R1 and R2, 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)/Reff. 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