Exact solutions of the population balance equation including particle transport, using group analysis

2018 ◽  
Vol 59 ◽  
pp. 255-271 ◽  
Author(s):  
Fubiao Lin ◽  
Sergey V. Meleshko ◽  
Adrian E. Flood
Keyword(s):  
Exact Solutions ◽  
Balance Equation ◽  
Particle Transport ◽  
Group Analysis ◽  
Population Balance ◽  
Population Balance Equation

Studies on population balance equation involving aggregation and growth terms via symmetries

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Zehra Pinar
Keyword(s):  
Analytical Solutions ◽  
Balance Equation ◽  
Elementary Function ◽  
Group Analysis ◽  
Population Balance ◽  
Numerical Approach ◽  
Population Balance Equation ◽  
Auxiliary Equation ◽  
Approximate Methods ◽  
Reduced Equations

Abstract The population balance equation (PBE) is one of the most popular integro-differential equations modeled for several industrial processes. The solution to this equation is usually solved using a numerical approach as the analytical solutions of such equations are not obtained easily. Typically, the available analytical solutions are limited and are based on momentous Laplace transform. In this study, the reduced equations of the PBE are obtained via the group analysis method. Two particulate cases involving aggregation, growth and nucleation are selected, the determining equations are solved and the reduced equations are solved via approximate methods. The approximate method involves the target solution of the nonlinear evolution equation, here the PBE, to be expressed as a polynomial in an elementary function which satisfies a particular ordinary differential equation termed as an auxiliary equation.

scholarly journals Analytical time-stepping solution of the discretized population balance equation

2020 ◽  
Vol 135 ◽  
pp. 106741
Author(s):  
Mohamed Ali Jama ◽  
Wenli Zhao ◽  
Waqar Ahmad ◽  
Antonio Buffo ◽  
Ville Alopaeus
Keyword(s):  
Balance Equation ◽  
Population Balance ◽  
Population Balance Equation ◽  
Time Stepping ◽  
Analytical Time

An analytical solution for the population balance equation using a moment method

Particuology ◽  
2015 ◽  
Vol 18 ◽  
pp. 194-200 ◽  
Author(s):  
Mingzhou Yu ◽  
Jianzhong Lin ◽  
Junji Cao ◽  
Martin Seipenbusch
Keyword(s):  
Analytical Solution ◽  
Balance Equation ◽  
Moment Method ◽  
Population Balance ◽  
Population Balance Equation

Bubble-size Experiments and Predictions for Polyurethane Foam using a Population Balance Equation.

2020 ◽  
Author(s):  
Rekha Rao ◽  
Lisa Mondy ◽  
Weston Ortiz ◽  
Christine Roberts ◽  
Melissa Soehnel
Keyword(s):  
Polyurethane Foam ◽  
Bubble Size ◽  
Balance Equation ◽  
Population Balance ◽  
Population Balance Equation
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