Microscopic approach of Hamaker between cylinder surfaces

5 Microscopic approach of Hamaker between cylinder surfaces 

Equation (553) shows the important simplification of the dispersion interaction potential between two crossed cylinders, and thus this geometry is preferred for use in the surface force apparatus, which we will see in Section 7.4. 

6 Comparison of sphere-surface and sphere-sphere interactions with surface-surface interactions Langbein approximation 

It is clear that the geometry of particles has an important effect on the interaction potential with other particles and surfaces. It is, then, a good idea to investigate the effective area of the interaction. For the same dispersion interaction potentials, if we consider sphere-surface and surface-surface interactions, by equalizing Equations (538) and (550), we have 

If we remember that Equation (538) is derived for a unit area = 1 of parallel slabs, it is clear from Equation (554) that the dispersion interaction potentials are the same if the effective interaction area in a sphere-surface interaction is equal to 

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