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On the solution of bivariate population balance equations for aggregation: Pivotwise expansion of solution domain

Chiney, Abhinandan and Kumar, Sanjeev (2012) On the solution of bivariate population balance equations for aggregation: Pivotwise expansion of solution domain. In: CHEMICAL ENGINEERING SCIENCE, 76 . pp. 14-25.

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Official URL: http://dx.doi.org/10.1016/j.ces.2012.04.006

Abstract

The solution of a bivariate population balance equation (PBE) for aggregation of particles necessitates a large 2-d domain to be covered. A correspondingly large number of discretized equations for particle populations on pivots (representative sizes for bins) are solved, although at the end only a relatively small number of pivots are found to participate in the evolution process. In the present work, we initiate solution of the governing PBE on a small set of pivots that can represent the initial size distribution. New pivots are added to expand the computational domain in directions in which the evolving size distribution advances. A self-sufficient set of rules is developed to automate the addition of pivots, taken from an underlying X-grid formed by intersection of the lines of constant composition and constant particle mass. In order to test the robustness of the rule-set, simulations carried out with pivotwise expansion of X-grid are compared with those obtained using sufficiently large fixed X-grids for a number of composition independent and composition dependent aggregation kernels and initial conditions. The two techniques lead to identical predictions, with the former requiring only a fraction of the computational effort. The rule-set automatically reduces aggregation of particles of same composition to a 1-d problem. A midway change in the direction of expansion of domain, effected by the addition of particles of different mean composition, is captured correctly by the rule-set. The evolving shape of a computational domain carries with it the signature of the aggregation process, which can be insightful in complex and time dependent aggregation conditions. (c) 2012 Elsevier Ltd. All rights reserved.

Item Type: Journal Article
Additional Information: Copyright for this article belongs to Elesevier
Keywords: Population balance; Particulate processes; Mixing; Agglomeration; Mathematical modelling; Discretization methods
Department/Centre: Division of Mechanical Sciences > Chemical Engineering
Date Deposited: 10 Jul 2012 07:32
Last Modified: 10 Jul 2012 07:32
URI: http://eprints.iisc.ernet.in/id/eprint/44676

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