Derjaguin approximation transform

The Derjaguin idea, a mainstay in colloid science since its 1934 publication, was rediscovered by nuclear physicists in the 1970s. In the physics literature one speaks of "proximity forces," surface forces that fit the criteria already given. The "Derjaguin transformation" or "Derjaguin approximation" of colloid science, to convert parallel-surface interaction into that between oppositely curved surfaces, becomes the physicists "proximity force theorem" used in nuclear physics and in the transformation of Casimir forces.23... 

The interaction between two spherical colloids can be transformed by the Derjaguin approximation [29] to the interaction between two flat surfaces (see Appendix A). The net osmotic pressure in an electric double layer is the difference between the internal force, F n, and the external or bulk force, Fex, and is related to the force between two colloids Posm = F n — Fex/a, where a is the area. 

According to the Derjaguin approximation (see Appendix B), the force between the surfaces is related to the free energy per area between two flat surfaces. Then, standard thermodynamics can be used to transform the free energy into the osmotic pressure ... 

L2.3.A. Interactions between two semi-infinite media, 182 L2.3.B. Layered systems, 190 L2.3.C. The Derjaguin transform for interactions between oppositely curved surfaces, 204 L2.3.D. Hamaker approximation Hybridization to modern theory, 208 L2.3.E. Point particles in dilute gases and suspensions, 214 L2.3.F. Point particles and a planar substrate, 228 L2.3.G. Line particles in dilute suspension, 232... 

The Derjaguin transform or approximation converts the interaction between plane-parallel surfaces into the interaction between oppositely curved surfaces such as spheres. This procedure and its reverse are allowed in the limit in which the closest separation is much smaller than radii of curvature. 

The general equation (13.4), which was first derived by Evans and Napper (1978), can be simplified for those systems where the Deijaguin integration transforms a flat plate potential into a sphere potential. If "Fttotal potential energy per unit area between two parallel flat plates separated by a distance h, then the Derjaguin integration can be approximated by... 

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