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Population balance equation
About: Population balance equation is a research topic. Over the lifetime, 972 publications have been published within this topic receiving 25791 citations.
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1,471 citations
TL;DR: In this paper, phenomenological models are proposed to describe drop breakup and coalescence in a turbulently agitated liquid-liquid dispersion, and the breakage and rate functions are developed and used to solve the general population balance equation describing drop interactions in a continuous flow vessel.
1,041 citations
Book•
26 Jul 2000
TL;DR: The Framework of Population Balances as discussed by the authors is a generalization of Population Balance Equations (PBE) and the solution of population balance equations (SBE) for the same purpose.
Abstract: Foreword. Preface. Introduction. The Framework of Population Balances. Birth and Death Functions. The Solution of Population Balance Equations. Similarity Behavior of Population Balance Equations. Inverse Problems in Population Balances. The Statistical Foundation of Population Balances. Index.
1,026 citations
TL;DR: In this paper, the population balance for batch aggregation of particulate suspensions is recast in a form that may be solved simply and accurately with the introduction of only one additional parameter, which is found to be a constant for all cases.
Abstract: The population balance for batch aggregation of particulate suspensions is recast in a form that may be solved simply and accurately. The transformed equation is deduced with the introduction of only one additional parameter, which is found to be a constant for all cases. The transformed equation is tested by comparison with some analytical solutions with which it is found to be in excellent agreement. In particular, the equation is shown to predict correctly the rate of change of total particle number and volume. Compatible descriptions of linear growth and nucleation are developed with similar success.
The method is then applied to modeling the in vitro growth and aggregation of kidney stones (calcium oxalate monohydrate crystals). It is found that these phenomena are well described by McCabe's ΔL law, a size-independent coalescence kernel, and first-order kinetics. Simulated particle size distributions and their moments are in excellent agreement with the experimental results.
917 citations
TL;DR: A new framework for the discretization of continuous population balance equations (PBEs) is presented and a numerical technique has been developed that is applicable to binary or multiple breakage, aggregation, simultaneous breakage and aggregation and yields excellent predictions in all cases.
829 citations