The probability of capture and its impact on floc structure

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Abstract
A simple method, utilizing statistical mechanics, is presented for calculating the capture probability for a Brownian particle approaching a charged surface. The model, although restricted to a particle being trapped at the secondary energy well of the DLVO interaction potential curve, accounts for the possibility of surface roughness. It is concluded that, in the absence of hydrodynamical and inertial effects, the capture probability is primarily governed by the magnitude of the DLVO secondary energy well, V*, and the nature of the surface roughness. The results are also shown to provide an analytical tool for investigating the evolution of jlocs, particularly those which involve the single-particle addition concept. Applying the model to construct a small aggregate reveals that the capture probability is strongly affected by the structure of the floc. Furthermore, the existence of a critical value of V* is established which, for practical purposes, lies within the order of 0.3 kBT for small flocs. This, interestingly, appears to have a significant transitional impact on certain features regarding floc configurations.

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