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Analysis of the aggregation-fragmentation population balance equation with application to coagulation
ETH, Inst Chem & Bioengn, Dept Chem & Appl Biosci.ORCID iD: 0000-0001-7995-3151
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
Abstract [en]

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.
Keyword [en]
Aggregation, Breakage, Colloidal clusters, Population balance equation, Scaling, Self-similarity, Turbulent coagulation
National Category
Chemical Process Engineering
Identifiers
URN: urn:nbn:se:kth:diva-87898DOI: 10.1016/j.jcis.2007.08.029ISI: 000250987500026OAI: oai:DiVA.org:kth-87898DiVA: diva2:502006
Note
QC 20120301Available from: 2012-02-14 Created: 2012-02-14 Last updated: 2017-12-07Bibliographically approved

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Bäbler, Matthäus

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