Population balance Monte Carlo simulation of self-assembly of core (micro-Al2O3)-shell (nano-TiO2) structure in aqueous suspensions

Zhao, Hanqing; Xu, Zuwei; Zhao, Haibo

doi:10.1016/j.ces.2018.12.059

Cited by 6 publications

(1 citation statement)

References 26 publications

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“…The abundance of engineering processes that involve aggregation and breakup has provided the impetus for the continuing development of stochastic simulation methods for population balances. Areas of application include droplets, bubbles and particles in multiphase systems [24,35,48,61,87,112,164,164], crystal precipitation [20,39], atmospheric and combustion aerosols [61,64,88,100,100,111,111,115,116,150], biological systems [75,89] and granulation [13,54,77,93,94,104].…”

Section: Monte Carlo Simulationmentioning

confidence: 99%

Challenges and opportunities concerning numerical solutions for population balances: a critical review

Singh

Ranade²,

Shardt³

et al. 2022

J. Phys. A: Math. Theor.

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Population balance models are tools for the study of dispersed systems, such as granular materials, polymers, colloids and aerosols. They are applied with increasing frequency across a wide range of disciplines, including chemical engineering, aerosol physics, astrophysics, polymer science, pharmaceutical sciences, and mathematical biology. Population balance models are used to track particle properties and their changes due to aggregation, fragmentation, nucleation and growth, processes that directly affect the distribution of particle sizes. The population balance equation is an integro-partial differential equation whose domain is the line of positive real numbers. This poses challenges for the stability and accuracy of the numerical methods used to solve for size distribution function and in response to these challenges several different methodologies have been developed in the literature. This review provides a critical presentation of the state of the art in numerical approaches for solving these complex models with emphasis in the algorithmic details that distinguish each methodology. The review covers finite volume methods, Monte Carlo method and sectional methods; the method of moments, another important numerical methodology, is not covered in this review.

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