SCALING INVARIANCE OF THE VON SMOLUCHOWSKI RATE LAW

The kinetics of flocculation for colloidal suspensions that occur in n atural environments have often been studied in terms of the von Smoluc howski rate law. Recent theoretical studies have analyzed scale-invari ant flocculation processes leading to the formation of fractal structu res which, in turn, have been observed in experiments on synthetic col loids. In this paper, these processes are described in terms of the sc aling invariance of the von Smoluchowski equation itself and are shown to be consistent with asymptotic limits of two of its well known exac t solutions, corresponding to transport- or reaction-controlled floccu lation. The resulting self-similar forms of these solutions and the as sociated fractal properties of the floccules are discussed in the cont ext of proposed universality classes. The results are applied to the c haracterization of heterogeneous colloids found in natural aqueous sys tems.