Mathematical framework for higher order breakage scenarios

Marchetti, Jorge Mario; Patruno, L.E.; Jakobsen, Hugo A.; Svendsen, Hallvard F.

doi:10.1016/j.ces.2010.08.008

Cited by 11 publications

(5 citation statements)

References 18 publications

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“…For fluid particles, the fragmentation of the mother entity into two daughter entities has been assumed in the majority of modeling investigations . Only a few models are proposed that allow for multiple breakup. ,− …”

Section: Introductionmentioning

confidence: 99%

Definition of the Single Drop Breakup Event

Solsvik

Maaß²,

Jakobsen

2016

Ind. Eng. Chem. Res.

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Experiments are performed to record data of single drop breakup events in turbulent flow (stirred tank conditions) for improved understanding of the breakup phenomena. Different interpretations can be made of a multiple breakup event, in particular, either the initial breakup can be evaluated, or the entire breakup cascade can be considered. The examining of these two breakup definitions in the present study reveals that the binary breakup event, which is the most frequent used assumption for the number of daughter drops in the literature, is only a rough assessment of the physical truth. For a 1 mm toluene drop up to 47 daughter drops as a consequence of an entire breakup sequence were counted and the arithmetic average value was 11.7 with standard deviation of 7.7. The corresponding average value for the initial breakup was 2.39. By high-speed imaging it is possible to break down the breakup cascade into binary breakups. However, the isolation of these individual breakups is a strong simplification of the breakup process. The breakups in the cascade are triggered by the initial breakup and are not statistically independent. It is more meaningful to evaluate not only the initiation of a drop breakup but the whole sequence of the breakup cascade. The breakup time of the two breakup definitions appears significantly different. For a 1 mm toluene drop the difference in the arithmetic breakup time was 129 ms. The relative number distribution of the breakup time is wider for the breakup cascade than for the initial breakup as it is influence by the wider range and higher number of daughter drops. Resolution limitations of the camera used did not allow determination of the complete daughter size distribution of the final drop population of the breakup cascade with sufficient accuracy. Two different experimental set-ups were used to verify the general trends of the breakup definitions.

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Section: Introductionmentioning

confidence: 99%

Definition of the Single Drop Breakup Event

Solsvik

Maaß²,

Jakobsen

2016

Ind. Eng. Chem. Res.

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“…In particular, the Lagrange interpolant polynomials throughout the GaussLobatto and Gauss-Legendre-Lobatto quadrature points are used. Using approximation 21 in expression 18 and taking systematically ν = i ∀i = 0, 1, ..., N, we get…”

Section: Methodsmentioning

confidence: 99%

“…For this reason, we adopted models that have been used for other physical problems that require the same constraints of this work: binary breakage, mass balance, and number balance for the particles. Marcheti et al 21 studied several redistribution functions that mathematically satisfy these constraints. We selected the more appropriate model in terms of accuracy between the experimental and simulated results, and accurate prediction of the daughter fibers' length.…”

Section: Models For the Redistribution Functionmentioning

confidence: 99%

“…2) show daughter fibers having two-thirds the length of the parent ones. Marchetti et al 21 have reviewed several kernels for the size redistribution function in binary breakage. A normal distribution and a beta distribution function were adopted in this work:…”

Section: Models For the Redistribution Functionmentioning

confidence: 99%

“…This case has not physical basis due to the fact that longer fibers of the same diameter are easier to brake as a consequence of their decreased resistance to shearing flow. 21 For this reason, the simulations corresponding to the combination [b 0 ; h 1 ] did not converge, while large error was obtained using b 0 and h 2 . The optimal combination between the breakage rate and the redistribution function was [b 2 ; h 2 ].…”

Section: Analysis Of Sensitivity Of the Model Over Changes In The Brementioning

confidence: 99%

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Novel Approach for Modeling the Dynamics of Fiber Breakage in Polymer Matrix Composites during Capillary Extrusion

et al. 2015

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ABSTRACT:In this work, a population balance equation (PBE) model is used to predict the evolution of the fiber breakage in thermoplastic polymer/short-fiber composites during capillary extrusion. The least squares spectral method was used to solve the resulting integrodifferential equation. The differences found between the experimental and simulated data were attributed to the selected breakage and redistribution functions. An experimental setup is proposed to find accurate breakage functions for this problem. The results indicate that the application of the PBE for such a breakage process could be a powerful tool for the design of injection molding molds. C 2015 Wiley Periodicals, Inc. Adv Polym Technol 2015, 0, 21635; View this article online at wileyonlinelibrary.com.

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