Emergence of falsified kinetics as a consequence of multi-particle interactions in dense-phase comminution processes

Capece, Maxx; Bilgili, Ecevit; Davé, Rajesh N.

doi:10.1016/j.ces.2011.08.001

Cited by 10 publications

(7 citation statements)

References 46 publications

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“…= 0, which conclude the result (11). To extend the interval of solution from [0, t 0 ] to [0, T], consider the equation…”

Section: Hypothesessupporting

confidence: 60%

“…Therefore, the reaction rate of this is taken to be proportional to the numbers of particle per unit volume of the colliding particles. 1 Nonlinear breakage has significant impact in many engineering processes such as fluidized beds, [2][3][4][5] the bulk distribution of raindrops, [6][7][8][9] comminution systems, [10][11][12][13] and several types of milling process. [14][15][16][17] Binary collisional breakage is the specific case of the nonlinear breakage, one where the breaking behavior is influenced through the sole of collisions between two particles.…”

Section: Introductionmentioning

confidence: 99%

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An existence‐uniqueness result for the pure binary collisional breakage equation

Paul

Kumar

2018

Math Methods in App Sciences

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The study of collision‐induced breakage phenomenon in the particulate process has much current interest. This is an important process arising in many engineering disciplines. In this work, the existence of continuous solution of the pure collisional breakage model is developed beneath some restrictions on the breakage kernels. Furthermore, the mass conservation and uniqueness of solution are investigated in the absence of “shattering transition.” The underlying theory is based on the compactness result of Arzelà‐Ascoli and Banach contraction mapping principle.

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“…= 0, which conclude the result (11). To extend the interval of solution from [0, t 0 ] to [0, T], consider the equation…”

Section: Hypothesessupporting

confidence: 60%

Section: Introductionmentioning

confidence: 99%

An existence‐uniqueness result for the pure binary collisional breakage equation

Paul

Kumar

2018

Math Methods in App Sciences

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“…In these cases, particle breakage is dependent on the instantaneous PSD due to mechanical interactions amongst feed particles, which results in non-first-order breakage kinetics and a time-variant specific breakage rate constant (Bilgili and Scarlett, 2005;Bilgili et al, 2006). Consideration of the proper breakage kinetics is paramount in modeling and prediction of the PSD for milling processes as shown by previous studies (Capece et al, 2011b(Capece et al, , 2013. While the observation and origination of non-linear breakage kinetics have been discussed at length elsewhere (Bilgili and Scarlett, 2005), most analysis is inferred from process scale modeling since mechanical multi-particle interactions have not been quantified or measured directly in the milling processes.…”

Section: Conclusion and Future Perspectivementioning

confidence: 95%

Insight into first-order breakage kinetics using a particle-scale breakage rate constant

Capece

Bilgili

Davé

2014

Chemical Engineering Science

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“…No PBM can yield accurate parameters in the inverse problem if it does not account for key, fundamental physics such as relevant particle change mechanisms, either mechanistically or phenomenologically (modeling errors). In fact, this is the number one reason for falsified breakage kinetics [9,19,20]. Let us reconsider the underlying assumptions for the PBMs described in Equations ( 1)-( 4).…”

Section: Principle I: Reduce Modeling Errorsmentioning

confidence: 99%

Population Balance Modeling of Milling Processes: Are We Falsifying Breakage Kinetics and Distribution via Back-Calculation Methods?

Bilgili

2024

Powders

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Population balance models (PBMs) for milling processes are based on two fundamental concepts: specific breakage rate function and breakage distribution function, which vary with particle size as well as design–operation conditions. The solution of the inverse problem, i.e., the estimation of these two functions’ parameters, may cause falsified kinetics and breakage distribution mechanisms. This perspective article aims to expose and mitigate various aspects of potential falsification, thus enabling the development of a robust PBM. Through an in-depth analysis of historical approaches to the PBM inverse problem and experimental observations, as well as the author’s recent contributions to the inverse methodology within the context of back-calculation methods, six principles have been offered: (i) include the governing physical phenomena and reduce errors in model building; (ii) reduce the number of model parameters via size–operation-dependent functional forms, hybrid approaches for back-calculation, and combination with CFD–DEM and other mechanistic models; (iii) generate a dense particle size distribution data set obtained at various milling times and/or locations; (iv) ensure a grid-independent solution with a sufficient number of size classes; (v) use a global optimization-based back-calculation method for parameter estimation and provide standard errors of the estimates; and (vi) test the predictive capability of the PBM. This perspective article boosts awareness of various challenges involved in the solution of the inverse PBM problem as pertinent to milling processes and provides researchers with six principles to minimize falsified kinetics.

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Emergence of falsified kinetics as a consequence of multi-particle interactions in dense-phase comminution processes

Cited by 10 publications

References 46 publications

An existence‐uniqueness result for the pure binary collisional breakage equation

An existence‐uniqueness result for the pure binary collisional breakage equation

Insight into first-order breakage kinetics using a particle-scale breakage rate constant

Population Balance Modeling of Milling Processes: Are We Falsifying Breakage Kinetics and Distribution via Back-Calculation Methods?

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