A Simple Model for Simulation of Particle Deaggregation of Few-Particle Aggregates Erik Kaunisto and Anders Rasmuson Dept. of Chemical Engineering, Chalmers University of Technology, Gothenburg SE-412 96, Sweden Johan Bergenholtz Dept. of Chemistry and Molecular Biology, University of Gothenburg, Gothenburg SE-412 96, Sweden Johan Remmelgas, Lennart Lindfors, and Staffan Folestad AstraZeneca R&D, M€ olndal SE-431 83, Sweden DOI 10.1002/aic.14363 Published online January 27, 2014 in Wiley Online Library (wileyonlinelibrary.com) A proper mechanistic understanding of the deaggregation process of small colloidal particle aggregates is of generic importance within many fields of science and engineering. The methodology for modeling colloidal deaggregation is currently limited to analytical solutions in the two-particle case and time consuming numerical algorithms, such as Brownian Dynamics (BD) simulations, for many-particle aggregates. To address this issue, a simplified alternative model that describes deaggregation of few-particle aggregates is presented. The model includes end-particle deaggrega- tion and a particle reconfiguration mechanism, which are the two most important mechanisms for deaggregation. Com- parison of the calculated first passage time distribution for various two-, three-, four-, and five-particle aggregates with the corresponding result using BD simulations confirms the validity of the model. It is concluded that the dominating mechanism behind deaggregation can be quantified using a deaggregation number, which reflects the time scale for reconfiguration relative to the time scale for end-particle deaggregation. V C 2014 American Institute of Chemical Engineers AIChE J, 60: 1863–1869, 2014 Keywords: colloids (ionic systems in water), diffusion, mathematical modeling, particle technology Introduction Deaggregation of colloidal species plays an important role in many engineering fields, for example, drug release from tablet formulations, 1 subsurface transport of contaminants, 2 filtration, bioremediation, and water treatment. 3 In contrast to aggregation, the fundamental mechanisms behind deaggre- gation are currently not well understood. However, earlier work on agglomeration in milling processes has shown that the stability factor, which accounts for electrostatic and van der Waals interactions between particles, seems to play an important role. 4 Similarly, a recent pharmaceutical study has shown that the addition of ionic surfactant at subcritical micelle concentrations enhances drug dissolution from drug particle aggregates, making the dissolution process approach that of a nonaggregated system. 5 These findings both suggest that colloidal interactions and DLVO theory, 6,7 may provide at least a partial qualitative explanation of the deaggregation process. Colloidal interactions and stability are mainstay topics of research within colloid science and they have been extensively studied in the literature. Based on the theory of hydrodynami- cally interacting Brownian particles 8 and the Smoluchowski equation, that are relevant for describing the dynamics of colloidal-size particles, Chan and Halle 9 derived an analytical expression for the so-called mean first passage time (MFPT), that is, the mean time it takes for two particles to deaggregate, for a pair of weakly flocculated particles subject to, for exam- ple, a DLVO interaction-potential. A similar mathematical treatment related to diffusion-controlled reactions has also been presented by Szabo et al., 10 from which also the full first passage time distribution (FPTD) can be obtained. Unfortu- nately, these methods are in practice limited to two-particle aggregates and cannot be directly applied to study more gen- eral many-particle aggregates. An alternative methodology that can be used in these cases is Brownian dynamics (BD) simulations. 11 In a recent study by Kaunisto et al., 1 it was found that BD simulations can be used to calculate and ana- lyze FPTD:s and MFPT:s of three- and four-particle aggre- gates. Kaunisto et al. 1 also found that BD simulations are very time consuming and quickly become infeasible as the number of particles increases. The general applicability of BD simulations is thus limited and computationally less expensive models are required. The objective of this work is to develop a simplified model for deaggregation of small particle aggregates that can replace otherwise time and resource consuming BD sim- ulations. For this purpose, this work is based upon a previous result due to Kaunisto et al., 1 who found that deaggregation of at least small aggregates seems to be governed mainly by Correspondence concerning this article should be addressed to A. Rasmuson at rasmuson@chalmers.se. V C 2014 American Institute of Chemical Engineers AIChE Journal 1863 May 2014 Vol. 60, No. 5