Non-additive behavior of van der Walls dispersion forces due to material   and surface geometry effects
  We present a series of calculations of van der Waals (vdW) forces that show non-additive behavior. The results reveal effects of geometrical dependences of the dispersion forces, that are in strong contradictions to the results from additivity approaches like the Lennard-Jones (LJ) pairwise interaction and the proximity force approximation (PFA). For the simple geometries treated here deviations appear when the effects of the materials are taken into account. We obtain these results with a general and simple numerical method that allows for a detailed study of the vdW interactions. The method is also accurate and fast, and due to its generality makes the study of interactions between three-dimensional (3D) objects, with arbitrary geometries and configurations, feasible. We present results for normal, lateral and rotational forces. 
Carlos E Roman-Velazquez and Bo E Sernelius