Analysis of the aggregation-fragmentation population balance equation with application to coagulation
2007 (English)In: Journal of Colloid and Interface Science, ISSN 0021-9797, E-ISSN 1095-7103, Vol. 316, no 2, 428-441 p.Article in journal (Refereed) Published
Coagulation of small particles in agitated suspensions is governed by aggregation and breakage. These two processes control the time evolution of the cluster mass distribution (CMD) which is described through a population balance equation (PBE). In this work, a PBE model that includes an aggregation rate function, which is a superposition of Brownian and flow induced aggregation, and a power law breakage rate function is investigated. Both rate functions are formulated assuming the clusters are fractals. Further, two modes of breakage are considered: in the fragmentation mode a particles splits into w ≥ 2 fragments of equal size, and in the erosion mode a particle splits into two fragments of different size. The scaling theory of the aggregation-breakage PBE is revised which leads to the result that under the negligence of Brownian aggregation the steady state CMD is self-similar with respect to a non-dimensional breakage coefficient θ. The self-similarity is confirmed by solving the PBE numerically. The self-similar CMD is found to deviate significantly from a log-normal distribution, and in the case of erosion it exhibits traces of multimodality. The model is compared to experimental data for the coagulationof a polystyrene latex. It is revealed that the model is not flexible enough to describecoagulation over an extended range of operation conditions with a unique set of parameters. In particular, it cannot predict the correct behavior for both a variation in the solid volume fraction of the suspension and in the agitation rate (shear rate).
Place, publisher, year, edition, pages
2007. Vol. 316, no 2, 428-441 p.
Aggregation, Breakage, Colloidal clusters, Population balance equation, Scaling, Self-similarity, Turbulent coagulation
Chemical Process Engineering
IdentifiersURN: urn:nbn:se:kth:diva-87898DOI: 10.1016/j.jcis.2007.08.029ISI: 000250987500026OAI: oai:DiVA.org:kth-87898DiVA: diva2:502006
QC 201203012012-02-142012-02-142012-03-01Bibliographically approved