A bimodal population balance method for the dynamic process of engineered nanoparticles

Jindong Shen; Honghui Jiang; Mingzhou Yu; Bo Kong

doi:10.1016/j.ijheatmasstransfer.2022.122605

A bimodal population balance method for the dynamic process of engineered nanoparticles

Jindong Shen^*, Honghui Jiang, Mingzhou Yu^*, Bo Kong

^*Corresponding author for this work

Chemical Engineering

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

The evolution of size distribution of engineered nanoparticles (ENPs) from the gas phase to the product in chemical reactors is a complicated heat and mass transfer process, whose mathematical description is commonly characterized by the population balance equation (PBE) in terms of particle number concentration. This study presents a new population balance model (PBM) for resolving the evolution of PBE for ENPs using a bimodal inverse Gaussian distributed method of moments (BIGDMOM). In this method, engineered nanoparticles’ size distribution is constructed by superposing two inverse Gaussian subdistribution. A close model for arbitrary moments is then obtained for achieving the final solution of the population balance equation for ENPs. The precision of BIGDMOM, which is verified in the test cases of two representative ENPs dynamics, is acceptable compared with widely used methods, such as log-normal MOM (log MOM), third-order Taylor-series expansion MOM, and unimodal IGDMOM, for key statistical quantities determining ENP size distributions, including kth moments (k = 0, 1/3, 2/3, and 2), shape factor, mean, and variance, sometimes is even better. Therefore, this study provides a new bimodal particle size distribution for the moment method, which can be used as an option to explore the specific bimodal practical problems of ENPs in the future.

Original language	English
Journal	International Journal of Heat and Mass Transfer
DOIs	https://doi.org/10.1016/j.ijheatmasstransfer.2022.122605
State	Published - 1 Jun 2022

Keywords

Engineered nanoparticles dynamics
Inverse Gaussian distribution
Method of moments
Population balance equation

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10.1016/j.ijheatmasstransfer.2022.122605

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title = "A bimodal population balance method for the dynamic process of engineered nanoparticles",

abstract = "The evolution of size distribution of engineered nanoparticles (ENPs) from the gas phase to the product in chemical reactors is a complicated heat and mass transfer process, whose mathematical description is commonly characterized by the population balance equation (PBE) in terms of particle number concentration. This study presents a new population balance model (PBM) for resolving the evolution of PBE for ENPs using a bimodal inverse Gaussian distributed method of moments (BIGDMOM). In this method, engineered nanoparticles{\textquoteright} size distribution is constructed by superposing two inverse Gaussian subdistribution. A close model for arbitrary moments is then obtained for achieving the final solution of the population balance equation for ENPs. The precision of BIGDMOM, which is verified in the test cases of two representative ENPs dynamics, is acceptable compared with widely used methods, such as log-normal MOM (log MOM), third-order Taylor-series expansion MOM, and unimodal IGDMOM, for key statistical quantities determining ENP size distributions, including kth moments (k = 0, 1/3, 2/3, and 2), shape factor, mean, and variance, sometimes is even better. Therefore, this study provides a new bimodal particle size distribution for the moment method, which can be used as an option to explore the specific bimodal practical problems of ENPs in the future.",

keywords = "Engineered nanoparticles dynamics, Inverse Gaussian distribution, Method of moments, Population balance equation",

author = "Jindong Shen and Honghui Jiang and Mingzhou Yu and Bo Kong",

year = "2022",

month = jun,

day = "1",

doi = "10.1016/j.ijheatmasstransfer.2022.122605",

language = "英语",

journal = "International Journal of Heat and Mass Transfer",

issn = "0017-9310",

publisher = "Elsevier Ltd.",

}

TY - JOUR

T1 - A bimodal population balance method for the dynamic process of engineered nanoparticles

AU - Shen, Jindong

AU - Jiang, Honghui

AU - Yu, Mingzhou

AU - Kong, Bo

PY - 2022/6/1

Y1 - 2022/6/1

N2 - The evolution of size distribution of engineered nanoparticles (ENPs) from the gas phase to the product in chemical reactors is a complicated heat and mass transfer process, whose mathematical description is commonly characterized by the population balance equation (PBE) in terms of particle number concentration. This study presents a new population balance model (PBM) for resolving the evolution of PBE for ENPs using a bimodal inverse Gaussian distributed method of moments (BIGDMOM). In this method, engineered nanoparticles’ size distribution is constructed by superposing two inverse Gaussian subdistribution. A close model for arbitrary moments is then obtained for achieving the final solution of the population balance equation for ENPs. The precision of BIGDMOM, which is verified in the test cases of two representative ENPs dynamics, is acceptable compared with widely used methods, such as log-normal MOM (log MOM), third-order Taylor-series expansion MOM, and unimodal IGDMOM, for key statistical quantities determining ENP size distributions, including kth moments (k = 0, 1/3, 2/3, and 2), shape factor, mean, and variance, sometimes is even better. Therefore, this study provides a new bimodal particle size distribution for the moment method, which can be used as an option to explore the specific bimodal practical problems of ENPs in the future.

AB - The evolution of size distribution of engineered nanoparticles (ENPs) from the gas phase to the product in chemical reactors is a complicated heat and mass transfer process, whose mathematical description is commonly characterized by the population balance equation (PBE) in terms of particle number concentration. This study presents a new population balance model (PBM) for resolving the evolution of PBE for ENPs using a bimodal inverse Gaussian distributed method of moments (BIGDMOM). In this method, engineered nanoparticles’ size distribution is constructed by superposing two inverse Gaussian subdistribution. A close model for arbitrary moments is then obtained for achieving the final solution of the population balance equation for ENPs. The precision of BIGDMOM, which is verified in the test cases of two representative ENPs dynamics, is acceptable compared with widely used methods, such as log-normal MOM (log MOM), third-order Taylor-series expansion MOM, and unimodal IGDMOM, for key statistical quantities determining ENP size distributions, including kth moments (k = 0, 1/3, 2/3, and 2), shape factor, mean, and variance, sometimes is even better. Therefore, this study provides a new bimodal particle size distribution for the moment method, which can be used as an option to explore the specific bimodal practical problems of ENPs in the future.

KW - Engineered nanoparticles dynamics

KW - Inverse Gaussian distribution

KW - Method of moments

KW - Population balance equation

U2 - 10.1016/j.ijheatmasstransfer.2022.122605

DO - 10.1016/j.ijheatmasstransfer.2022.122605

M3 - 文章

SN - 0017-9310

JO - International Journal of Heat and Mass Transfer

JF - International Journal of Heat and Mass Transfer

ER -

A bimodal population balance method for the dynamic process of engineered nanoparticles

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Keywords

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