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

Lin, Fubiao; Meleshko, Sergey V.; Flood, Adrian E.

doi:10.1016/j.cnsns.2017.11.022

Cited by 14 publications

(17 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…New applications of this model framework are continuously developed in various fields, e.g. for the description of crystallization-based enantioseparation processes like Viedma Ripening or Preferential Crystallization [3][4][5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

“…Population balance equations (PBEs) present a sophisticated and well-studied mathematical basis to describe and optimize crystallization-based processes. The general equations were developed over the past decades and have been studied intensively since then. , New applications of this model framework are continuously developed in various fields, e.g., for the description of crystallization-based enantioseparation processes like Viedma ripening or preferential crystallization. − …”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Measurement and Evaluation of the Crystallization Kinetics of l-Asparagine Monohydrate in the Ternary l-/d-Asparagine/Water System

Temmel

Gänsch

Lorenz

et al. 2018

Crystal Growth & Design

View full text Add to dashboard Cite

Growth kinetics of L-asparagine monohydrate in racemic aqueous solutions as well as nucleation, growth and dissolution kinetics of the same enantiomer crystallized from pure Lasparagine solutions are measured and the kinetic parameters are estimated applying a recently developed shortcut-method. The corresponding experimental procedure is based on a small number of preferential (seeded) cooling crystallizations where the crystal size distribution is monitored with an online microscope. Afterwards, image analysis yields the transient particle size evolution of initially provided crystals, from which the response of the solid phase to the liquid phase driving force can be extracted. Subsequently, parameter estimation is carried out applying this data together with the information of concentration and composition of the liquid phase, to discriminate between different model approaches. The kinetics are validated finally with independent experiments to evaluate their quality. It is proven that growth kinetics of L-and D-asparagine monohydrate from water are identical. In contrast, it can be shown and quantified, that growth kinetics from racemic and enantiopure solutions of asparagine differ significantly from each other. The corresponding calculation of the driving force of enantiomeric systems is discussed in detail by means of ternary phase diagrams.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Measurement and Evaluation of the Crystallization Kinetics of l-Asparagine Monohydrate in the Ternary l-/d-Asparagine/Water System

Temmel

Gänsch

Lorenz

et al. 2018

Crystal Growth & Design

View full text Add to dashboard Cite

show abstract

“…On the other hand, the obtained symmetries can also be used to construct the self‐similar solutions. Such as the literatures 14‐16 …”

Section: Admitted Scaling Group Of Equation ()mentioning

confidence: 99%

“…Conversely, one can use the developed Lie group analysis 12,13 to deal with symmetries of integro‐differential equations. In recent years, the developed Lie group analysis 12,13 was applied to solve integro‐differential, stochastic and delay equations, and so on 14‐25 . The main obstacle of this method is in finding the general solutions of the determining equations, approaches of solving determining equations of integro‐differential equations depend on the studied equations, there is no a general approach for solving determining equations of integro‐differential equations 14‐26 …”

Section: Introductionmentioning

confidence: 99%

Symmetries and exact solutions of the population balance equation with growth and breakage processes, using group analysis

Lin

Zhang

2020

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

Population balance equation which may be employed to handle a wide variety of particle processes has certainly received unprecedented attention, but the absence of explicit exact solutions necessitates the use of numerical approaches. The one‐dimensional population balance equation with time independent but size dependent growth and breakage rate is investigated. The corresponding system of equation is solved analytically by use of the Lie group analysis method. Symmetries, reduced equations, invariant solutions, explicit exact, and unphysical solutions are presented in this paper.

show abstract

“…[21]. Considerable research studies on particle dynamics are carried out by many researchers [7,[24][25][26][27][28][29][30][31] to overcome the complexity and difficulty in theoretical and experimental studies on PBE. Generally, PBE proposed by Friedlander [22] is adequate to describe typical aerosol dynamic processes including nucleation, condensation, and coagulation etc.…”

Section: Introductionmentioning

confidence: 99%

Numerical study on fractal-like soot aggregate dynamics of turbulent ethylene-oxygen flame

Liu

Chan

Lin

et al. 2019

Fuel

View full text Add to dashboard Cite

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

Cited by 14 publications

References 12 publications

Measurement and Evaluation of the Crystallization Kinetics of l-Asparagine Monohydrate in the Ternary l-/d-Asparagine/Water System

Measurement and Evaluation of the Crystallization Kinetics of l-Asparagine Monohydrate in the Ternary l-/d-Asparagine/Water System

Symmetries and exact solutions of the population balance equation with growth and breakage processes, using group analysis

Numerical study on fractal-like soot aggregate dynamics of turbulent ethylene-oxygen flame

Contact Info

Product

Resources

About