Proximity force approximation

Derjaguin used this approach to calculate the interaction between two ellipsoids [84]. The same approximation was also introduced in 1977 by Blodd et al. [85] for calculating interaction forces between nuclei of atoms. They coined the term proximity forces in their publication. While the term Derjaguin approximation is stUl the standard term in surface science, the term proximity force approximation has become popular among physicists in the field of nuclear physics and the Casimir force (see Section 2.6). 

Casimir Force for Nontriviai Geometries As in the case of the normal van der Waals forces, the Derjaguin approximation can be used to calculate the Casimir force for geometries other than that of parallel plates. Note that in many papers on the Casimir force, this approach is called "proximity force approximation due to historic reasons (see Section 2.3). It was shown that the error introduced by this approximation should be smaller than 0.4 D/R for D < 300 nm [129]. Full calculations without approximation have been done for some configurations, for example, sphere/plate [130], but these are usually cumbersome. An alternative approach for approximate calculations was introduced by Jaffe and Scardicchio [131]. It is based... 

The Derjaguin approximation (also called proximity force approximation) allows the calculation of the van der Waals interaction between macroscopic bodies with complex geometries from the knowledge of the interaction potential between planar surfaces, as long as the radii of curvature of the objects are large compared to the separation between them. 

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... 

Compressing ammonia gas under high pressure forces the molecules into close proximity. In a normal gas, the separation between each molecule is generally large - approximately 1000 molecular diameters is a good generalization. By contrast, the separation between the molecules in a condensed phase (solid or liquid) is more likely to be one to two molecular diameters, thereby explaining why the molar volume of a solid or liquid is so much smaller than the molar volume of a gas. 

In the case of molecules which do not dissociate, the electromotive force must be due to the orientation of the molecules in the surface layer, which molecules must have a definite electric moment. In the few cases where the electromotive force can be accurately compared with the surface concentration such as n-but3rric, ri-valeric and n-caproic acids, the E.M.F. is almost approximately proportional to the surface concentration F, as would be the case if the moment of a molecule were independent of the proximity of its neighbours. 

Rigorous formulations of the problems associated with solvation necessitate approximations. From the computational point of view, we are forced to consider interactions between a solute and a large number of solvent molecules which requires approximate models [75]. The microscopic representation of solvent constitutes a discrete model consisting of the solute surrounded by individual solvent molecules, generally only those in close proximity. The continuous model considers all the molecules surrounding the solvent but not in a discrete representation. The solvent is represented by a polarizable dielectric continuous medium characterized by macroscopic properties. These approximations, and the use of potentials, which must be estimated with empirical or approximate computational techniques, allows for calculations of the interaction energy [75],... 

At a first approximation, the hydrodynamic phenomenon observed also may be explained by the interplay between two force components acting on the fluid. At the distal portion of the coil, both the strong radial force field and the reduced relative flow of the two phases establish a clear and stable interface between the two liquid phases. At the proximal portion of the spiral column, where the strength of the radial-force component is minimized, the effect of the Archimedean screw force becomes visualized as agitation at the interface caused by the relative movement of two liquid layers [2]. 

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