Tracer mixing dynamics during aggregation and fragmentation

Abstract

For many chemical systems consisting of particles, liquid droplets, or gas bubbles undergoing concurrent (reversible) aggregation and fragmentation in a stirred immiscible fluid, evolution of the particle distribution and mixing of chemical species are important fundamental issues. A dynamic model for dispersive mixing systems presented here illustrates the time dependence of the particle-size distribution (PSD) and the tracer mass distribution (TMD). For rapid tracer diffusion, the population balance equations (PBEs) for the PSD and TMD are identical (only the initial conditions differ) for binary aggregation and fragmentation rate coefficients that do not depend on particle size or tracer mass. The integrodifferential PBE is solved by a numerical method, and results agree with the moment solution. Measures for the degree of tracer mixing are related to the variance or polydispersity index and to the mixing entropy. The kinetics are reversible, allowing the PSD, TMD, and mixing entropy to approach stationary states. Results are partially compared with a similarity solution for the PSD.