Approximate moment methods for population balance equations in particulate and bioengineering processes

R Dürr, A Bück - Processes, 2020 - mdpi.com
Population balance modeling is an established framework to describe the dynamics of
particle populations in disperse phase systems found in a broad field of industrial, civil, and …

[HTML][HTML] Extended method of moment for general population balance models including size dependent growth rate, aggregation and breakage kernels

A Falola, A Borissova, XZ Wang - Computers & chemical engineering, 2013 - Elsevier
Among the various methods for the solution of population balances (PB) equations, the
moments based methods are some of the most successful and popular. Moment based …

Integral formulation of the population balance equation: Application to particulate systems with particle growth

M Attarakih - Computers & Chemical Engineering, 2013 - Elsevier
Numerical solution of the population balance equation (PBE) is widely used in many
scientific and engineering applications. Available numerical methods, which are based on …

Population balance modeling. Promise for the future

D Ramkrishna, AW Mahoney - Chemical engineering science, 2002 - Elsevier
Population balance modeling has received an unprecedented amount of attention during
the past few years from both academic and industrial quarters because of its applicability to …

Solution of the population balance equation using the sectional quadrature method of moments (SQMOM)

MM Attarakih, C Drumm, HJ Bart - Chemical Engineering Science, 2009 - Elsevier
A discrete framework is introduced for simulating the particulate physical systems governed
by population balance equations (PBE) with particle splitting (breakage) and aggregation …

New developments of the extended quadrature method of moments to solve population balance equations

M Pigou, J Morchain, P Fede, MI Penet… - Journal of Computational …, 2018 - Elsevier
Abstract Population Balance Models have a wide range of applications in many industrial
fields as they allow accounting for heterogeneity among properties which are crucial for …

Numerical methods for the solution of population balance equations coupled with computational fluid dynamics

M Shiea, A Buffo, M Vanni… - Annual review of …, 2020 - annualreviews.org
This review article discusses the solution of population balance equations, for the simulation
of disperse multiphase systems, tightly coupled with computational fluid dynamics. Although …

[HTML][HTML] A Gauss/anti-Gauss quadrature method of moments applied to population balance equations with turbulence-induced nonlinear phase-space diffusion

M Pütz, M Pollack, C Hasse, M Oevermann - Journal of Computational …, 2022 - Elsevier
Many particulate systems occurring in nature and technology are adequately described by a
number density function (NDF). The numerical solution of the corresponding population …

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

M Singh, V Ranade, O Shardt… - Journal of Physics A …, 2022 - iopscience.iop.org
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 …

[HTML][HTML] A new framework for numerical modeling of population balance equations: Solving for the inverse cumulative distribution function

JD Peterson, I Bagkeris, V Michael - Chemical Engineering Science, 2022 - Elsevier
Population balance equations (PBE) are a class of integro-partial differential equations with
applications spanning a broad range of engineering disciplines. When the state of a …