Disintegration process of surface stabilized sol–gel <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si0008.gif" display="inline" overflow="scroll"><mml:msub><mml:mrow><mml:mi>TiO</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math> nanoparticles by population balances

Gokhale, Yashodhan Pramod; Kumar, Rajesh; Kumar, Jitendra; Hintz, Werner; Warnecke, Gerald; Tomas, Jürgen

doi:10.1016/j.ces.2009.09.015

Cited by 22 publications

(2 citation statements)

References 12 publications

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“…The processes of coagulation and fragmentation occur in several fields of pure and applied science to design the dynamics of particulate processes like high shear granulation, condensation of water vapor in the atmosphere, depolymerization, astrophysics, and so forth [1][2][3]. The usual interpretation of the system of particles is the merging of particles and break-up into tiny particles.…”

Section: Introductionmentioning

confidence: 99%

Convergence and error estimation of weighted finite volume scheme for coagulation‐fragmentation equation

Bariwal

Kumar

2022

Numerical Methods Partial

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This article is dedicated to analyze a finite volume scheme for solving coagulation and multiple fragmentation equation. The rates of coagulation and fragmentation are chosen locally bounded and unbounded (singularity near the origin), respectively. It is shown that using weak L 1 compactness method, the numerically approximated solution tends to the weak solution of the continuous problem under a stability condition on the time step for non-uniform mesh. Further, considering a uniform mesh, first order error approximation is demonstrated when kernels are in W 1,∞ loc space. The accuracy of the scheme is also authenticated numerically for several test problems.

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Section: Introductionmentioning

confidence: 99%

Convergence and error estimation of weighted finite volume scheme for coagulation‐fragmentation equation

Bariwal

Kumar

2022

Numerical Methods Partial

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“…Events of particle fragmentation (or breakage) occur in several industrial sectors such as chemical engineering [1][2][3][4], food processing [5][6][7], pharmaceutical [8][9][10], communition in mineral processing [11][12][13][14], etc., and, in different natural and astrophysical phenomenons [15][16][17]. Therefore, theoretical researchers have gained interest to discuss on different model equations involving particle breakage [18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

On the approximate solutions of fragmentation equations

2018

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A numerical model based on the finite volume scheme is proposed to approximate the binary breakage problems. Initially, it is considered that the particle fragments are characterized by a single property, i.e. particle’s volume. We then investigate the extension of the proposed model for solving breakage problems considering two properties of particles. The efficiency to estimate the different moments with good accuracy and simple extension for multi-variable problems are the key features of the proposed method. Moreover, the mathematical convergence analysis is performed for one-dimensional problems. All mathematical findings and numerical results are validated over several test problems. For numerical validation, we propose the extension of Bourgade & Filbet (2008 Math. Comput. 77 , 851–882. ( doi:10.1090/S0025-5718-07-02054-6 )) model for solving two-dimensional pure breakage problems. In this aspect, numerical treatment of the two-dimensional binary breakage models using finite volume methods can be treated to be the first instance in the literature.

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