Evolution of the cluster-size distribution in stirred suspensions

Abstract

Based on combinatorics, a simple model for predicting the steady-state cluster or drop-size distribution in suspensions undergoing simultaneous coagulation and break-up due to rapid stirring was recently proposed (R. D. Cohen, J. Chem. Soc. Faraday Trans., 1990, 86, 2433). This work extends that model to account for the evolution of the size distribution in stirred systems. The method utilizes the concept of the distribution entropy, and suggests a means for predicting the characteristics of the size distribution as the system approaches steady state. Among the important results is that the distribution functions (size, volume etc.) are path dependent. Furthermore, along the ‘most probable entropy path’, the cluster-size distribution remains closely related to the Poisson distribution up to and including steady state. Another interesting finding is that, along the mentioned path, the distribution functions are concentration specific (intensive property) as long as they are in their transient state. These ultimately become number specific (extensive property) once they reach steady state.