Abstract
Initial wetting of crystals by binder droplets is a key rate process in spherical agglomeration, however there are no models to predict the kinetics and formation of agglomerate nuclei. Two new mathematical models are introduced for agglomerate nucleation by an immersion mechanism; immersion rate limited model and collision rate limited model. The agglomerate nucleation number developed in this work predicts different regimes; immersion rate limited, collision rate limited and intermediate. In an immersion rate limited regime, agglomerate size increases with square root of time. In a collision rate limited regime, size increases linearly with time if the bulk crystal volume fraction, φPb, is constant, or with an exponential decay rate for batch crystallisation with decreasing φPb. The timescale for nucleation is less than ten minutes for a broad range of conditions, significantly less than most crystallisation timescales. These models have great promise for population balance modelling and spherical agglomeration optimisation.
Highlights
Crystallisation has become an essential unit operation for the production, recovery and purification of products
We evaluate the mechanism of immersion nucleation more closely, in terms of increases in agglomerate nuclei size with time due to layering; the acquisition of crystal particles suspended in the mother solution
The dimensionless volume derived in Eq (42) can be a good parameter for such comparison between model results and experimental data. c) A comprehensive validation of the kinetic models can be achieved by a careful design of a spherical agglomeration experiment in which the immersion is the dominant mechanism for the agglomerate nucleation and the other rate processes, such as agglomeration and breakage, are hindered. Such experimental design and model validation are to be performed in a future work. d) The new nucleation models can be incorporated in a population balance framework, along with other rate processes, for modelling and optimal design of spherical agglomeration processes. This is the first study to investigate the kinetics of agglomerate nucleation by the immersion mechanism in spherical agglomeration
Summary
Please cite this article as: O. Arjmandi-Tash, J.D. Tew, K. Pitt, R. Smith, J.D. Litster, A new mathematical model for nucleation of spherical agglomerates by the immersion mechanism, Chemical Engineering Science (2019), doi: http://dx.doi.org/10.1016/j.ces.2019.115258 This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Omid Arjmandi-Tash, Jonathan D. Tew, Kate Pitt, Rachel Smith and James D. Litster* EPSRC Future Continuous Manufacturing and Advanced Crystallisation Research Hub (CMAC), Department of Chemical and Biological Engineering, University of Sheffield, UK
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