We consider a system of diffusing particles, which coagulate when they get close. Macroscopically the system is described by the long established Smoluchowski equation for the particle densities. There has been recent progress in deriving this equation from a microscopic model, given by a stochastic process for the time evolution of each individual particle. The results indicate, that the relation between microscopic and macroscopic interaction rates depends on the scaling regime of the hydrodynamic limit.
We propose a systematic investigation of a range of coagulation models in the hydrodynamic limit, which will contribute to the fundamental issue of Statistical Mechanics concerning the relation of microscopic and macroscopic models. We shall first extend existing results of the proposed Fellow for the moderate-limit scaling, to include the case of arbitrarily large particles. Then we shall investigate the dependence of the macroscopic coagulation rate on the interaction-range scaling, from the moderate limit down to the constant mean-free-path regime. Finally we shall study the large-particle-number limit for spatial coagulation involving complex particle shapes, which may themselves evolve under coagulation.
Field of science
- /natural sciences/physical sciences/classical mechanics/statistical mechanics
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