PROXIMITY EFFECTS IN CLUSTERS OF PARTICLES

When two spheres are brought together, there is an enhancement in the orientation-averaged extinction per unit volume compared to isolated spheres; ''proximity effects'' such as this are expected to be most important at close separations. Using finite element methods for a pair of nearby Rayleigh spheres, this is both verified and quantified for the first time. The results are also expressed in terms of a normal mode analysis. As more spheres are added to the system there is a further growth in the extinction enhancement, which, however, depends on the topology. Arrangements of touching spheres examined included stacks, close packings, radiating structures, rings, chains, and clusters. Effective medium theory models are often used to describe composite or porous particles. It is shown that with these models the extinction predicted is significantly higher than with finite element treatment of roughly equivalent particles. Furthermore, the effects of topology, not accounted for explicitly in effective medium theory models, are found to be important. The modified prescription of effective medium theory proposed by Ossenkopf does not provide better agreement with finite element methods unless the filling factor is high, higher than typical of even compact clusters. Comparison between finite element methods and effective medium theory models in the case of a laboratory soot sample with high extinction yields a paradox that is discussed briefly.