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Volumn 33, Issue 1, 2009, Pages 112-121

On sectional techniques for the solution of the breakage equation

Author keywords

Breakage equation; Moments of the distribution; Numerical solution; Population balances; Sectional techniques

Indexed keywords

COAGULATION; NUMERICAL METHODS; PARTICLE SIZE ANALYSIS; POPULATION STATISTICS;

EID: 56949093064     PISSN: 00981354     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compchemeng.2008.07.002     Document Type: Article
Times cited : (25)

References (38)
  • 1
    • 33745065434 scopus 로고    scopus 로고
    • Statistical models of brittle fragmentation
    • Astrom J.A. Statistical models of brittle fragmentation. Advances in Physics 55 (2006) 247
    • (2006) Advances in Physics , vol.55 , pp. 247
    • Astrom, J.A.1
  • 2
    • 0037381515 scopus 로고    scopus 로고
    • Optimal moving and fixed grids for the solution of discretized population balances in batch and continuous systems: Droplet breakage
    • Attarakih M.M., Bart H.J., and Faqir N.M. Optimal moving and fixed grids for the solution of discretized population balances in batch and continuous systems: Droplet breakage. Chemical Engineering Science 58 (2003) 1311
    • (2003) Chemical Engineering Science , vol.58 , pp. 1311
    • Attarakih, M.M.1    Bart, H.J.2    Faqir, N.M.3
  • 3
    • 18144368563 scopus 로고    scopus 로고
    • Prediction of multimodal distributions in breakage processes
    • Canu P. Prediction of multimodal distributions in breakage processes. Industrial Engineering Chemistry Research 44 (2005) 2649
    • (2005) Industrial Engineering Chemistry Research , vol.44 , pp. 2649
    • Canu, P.1
  • 4
    • 0037152845 scopus 로고    scopus 로고
    • A moment methodology for coagulation and breakage problems. Part 3. Generalized daughter distribution functions
    • Diemer R.B., and Olson J.H. A moment methodology for coagulation and breakage problems. Part 3. Generalized daughter distribution functions. Chemical Engineering Science 57 (2002) 4187
    • (2002) Chemical Engineering Science , vol.57 , pp. 4187
    • Diemer, R.B.1    Olson, J.H.2
  • 5
    • 0032529379 scopus 로고    scopus 로고
    • New parameterization for a discrete batch grinding equation
    • Eyre D., Everson R.C., and Campbell Q.P. New parameterization for a discrete batch grinding equation. Powder Technology 98 (1998) 265
    • (1998) Powder Technology , vol.98 , pp. 265
    • Eyre, D.1    Everson, R.C.2    Campbell, Q.P.3
  • 7
    • 0141513782 scopus 로고    scopus 로고
    • Beyond log-normal distributions: Hermite spectra for solving population balances
    • Hamilton R.A., Curtis J.S., and Ramkrishna D. Beyond log-normal distributions: Hermite spectra for solving population balances. AIChE Journal 49 (2003) 2328
    • (2003) AIChE Journal , vol.49 , pp. 2328
    • Hamilton, R.A.1    Curtis, J.S.2    Ramkrishna, D.3
  • 8
    • 0030106387 scopus 로고
    • New discretization procedure for the breakage equation
    • Hill P.J., and Ng K.M. New discretization procedure for the breakage equation. AIChE Journal 42 (1995) 1600
    • (1995) AIChE Journal , vol.42 , pp. 1600
    • Hill, P.J.1    Ng, K.M.2
  • 9
    • 33744539046 scopus 로고    scopus 로고
    • Population balance modelling of phase inversion in liquid-liquid pipeline flows
    • Hu B., Matar O.K., Hewit G.F., and Angeli P. Population balance modelling of phase inversion in liquid-liquid pipeline flows. Chemical Engineering Science 61 (2006) 4994
    • (2006) Chemical Engineering Science , vol.61 , pp. 4994
    • Hu, B.1    Matar, O.K.2    Hewit, G.F.3    Angeli, P.4
  • 12
    • 37749012006 scopus 로고    scopus 로고
    • Extended cell average technique for the solution of coagulation equation
    • Kostoglou M. Extended cell average technique for the solution of coagulation equation. Journal of Colloid and Interface Science 306 (2007) 72
    • (2007) Journal of Colloid and Interface Science , vol.306 , pp. 72
    • Kostoglou, M.1
  • 13
    • 0037120789 scopus 로고    scopus 로고
    • An assessment of low order methods for solving the breakage equation
    • Kostoglou M., and Karabelas A.J. An assessment of low order methods for solving the breakage equation. Powder Technology 127 (2002) 116
    • (2002) Powder Technology , vol.127 , pp. 116
    • Kostoglou, M.1    Karabelas, A.J.2
  • 14
    • 4143062491 scopus 로고    scopus 로고
    • Optimal low order methods of moments for solving the fragmentation equation
    • Kostoglou M., and Karabelas A.J. Optimal low order methods of moments for solving the fragmentation equation. Powder Technology 143-144 (2004) 280
    • (2004) Powder Technology , vol.143-144 , pp. 280
    • Kostoglou, M.1    Karabelas, A.J.2
  • 15
    • 27444433145 scopus 로고    scopus 로고
    • Towards a unified framework for the derivation of breakage functions based on the statistical theory of turbulence
    • Kostoglou M., and Karabelas A.J. Towards a unified framework for the derivation of breakage functions based on the statistical theory of turbulence. Chemical Engineering Science 60 (2005) 6584
    • (2005) Chemical Engineering Science , vol.60 , pp. 6584
    • Kostoglou, M.1    Karabelas, A.J.2
  • 16
    • 38649130630 scopus 로고    scopus 로고
    • An efficient numerical technique for solving population balance equation involving aggregation, breakage, growth and nucleation
    • Kumar J., Peglow M., Warnecke G., and Heinrich S. An efficient numerical technique for solving population balance equation involving aggregation, breakage, growth and nucleation. Powder Technology 182 (2008) 81
    • (2008) Powder Technology , vol.182 , pp. 81
    • Kumar, J.1    Peglow, M.2    Warnecke, G.3    Heinrich, S.4
  • 17
    • 33644988295 scopus 로고    scopus 로고
    • Improved accuracy and convergence of discretized population balance for aggregation: The cell average technique
    • Kumar J., Peglow M., Warneke G., Heinrich S., and Morl L. Improved accuracy and convergence of discretized population balance for aggregation: The cell average technique. Chemical Engineering Science 61 (2006) 3327
    • (2006) Chemical Engineering Science , vol.61 , pp. 3327
    • Kumar, J.1    Peglow, M.2    Warneke, G.3    Heinrich, S.4    Morl, L.5
  • 18
    • 56949105021 scopus 로고    scopus 로고
    • Kumar, J., & Warnecke, G. (2008a). Convergence analysis of sectional methods for solving breakage population balance equations-I. The fixed pivot technique, preprint nr. 07-39. Faculty of Mathematics, Otto-von-Guericke University Magdeburg.
    • Kumar, J., & Warnecke, G. (2008a). Convergence analysis of sectional methods for solving breakage population balance equations-I. The fixed pivot technique, preprint nr. 07-39. Faculty of Mathematics, Otto-von-Guericke University Magdeburg.
  • 19
    • 56949083634 scopus 로고    scopus 로고
    • Kumar, J., & Warnecke, G. (2008b). Convergence analysis of sectional methods for solving breakage population balance equations-II. The cell average technique, preprint nr. 07-40. Faculty of Mathematics, Otto-von-Guericke University Magdeburg.
    • Kumar, J., & Warnecke, G. (2008b). Convergence analysis of sectional methods for solving breakage population balance equations-II. The cell average technique, preprint nr. 07-40. Faculty of Mathematics, Otto-von-Guericke University Magdeburg.
  • 20
    • 0030128282 scopus 로고    scopus 로고
    • On the solution of population balance equations by discretizations. I. A fixed pivot technique
    • Kumar S., and Ramkrishna D. On the solution of population balance equations by discretizations. I. A fixed pivot technique. Chemical Engineering Science 51 (1996) 1311
    • (1996) Chemical Engineering Science , vol.51 , pp. 1311
    • Kumar, S.1    Ramkrishna, D.2
  • 21
    • 0030127313 scopus 로고    scopus 로고
    • On the solution of population balance equations by discretization. II. A moving pivot technique
    • Kumar S., and Ramkrishna D. On the solution of population balance equations by discretization. II. A moving pivot technique. Chemical Engineering Science 51 (1996) 1333
    • (1996) Chemical Engineering Science , vol.51 , pp. 1333
    • Kumar, S.1    Ramkrishna, D.2
  • 22
    • 0346997983 scopus 로고    scopus 로고
    • New wavelet-based adaptive method for the breakage equation
    • Liu Y., and Tade M.O. New wavelet-based adaptive method for the breakage equation. Powder Technology 139 (2004) 61
    • (2004) Powder Technology , vol.139 , pp. 61
    • Liu, Y.1    Tade, M.O.2
  • 23
    • 34047202715 scopus 로고    scopus 로고
    • Breakage behavior characterization of micron-scale particles
    • Livk I., and Illievski D. Breakage behavior characterization of micron-scale particles. AIChE Journal 53 (2007) 780
    • (2007) AIChE Journal , vol.53 , pp. 780
    • Livk, I.1    Illievski, D.2
  • 24
    • 19944373089 scopus 로고    scopus 로고
    • Transient and asymptotic behaviour of the binary breakage problem
    • Mantzaris N.V. Transient and asymptotic behaviour of the binary breakage problem. Journal of Physics A-Mathematical and General 38 (2005) 5111
    • (2005) Journal of Physics A-Mathematical and General , vol.38 , pp. 5111
    • Mantzaris, N.V.1
  • 25
    • 8544249139 scopus 로고    scopus 로고
    • Modeling for size reduction of agglomerates in nanoparticle fluidization
    • Matsuda S., Hatano H., Muramoto T., and Tsutsumi A. Modeling for size reduction of agglomerates in nanoparticle fluidization. AIChE Journal 50 (2004) 2763
    • (2004) AIChE Journal , vol.50 , pp. 2763
    • Matsuda, S.1    Hatano, H.2    Muramoto, T.3    Tsutsumi, A.4
  • 27
    • 0032103301 scopus 로고    scopus 로고
    • A simulation model for analysis and design of continuous grinding mills
    • Mihalyko C., Blickle T., and Lacatos B.G. A simulation model for analysis and design of continuous grinding mills. Powder Technology 97 (1998) 51
    • (1998) Powder Technology , vol.97 , pp. 51
    • Mihalyko, C.1    Blickle, T.2    Lacatos, B.G.3
  • 29
    • 28844472607 scopus 로고    scopus 로고
    • Olesen, P., Ferkinghoff-Borg, J., Jensen, M. H., & Mathiesen, J. (2005). Diffusion, fragmentation, and coagulation processes: Analytical and numerical results. Physical Review E, 72, paper no. 031103.
    • Olesen, P., Ferkinghoff-Borg, J., Jensen, M. H., & Mathiesen, J. (2005). Diffusion, fragmentation, and coagulation processes: Analytical and numerical results. Physical Review E, 72, paper no. 031103.
  • 30
    • 0000118047 scopus 로고
    • The collisions of asteroids
    • Piotrowsky S. The collisions of asteroids. Acta Astronomica A 5 (1953) 115
    • (1953) Acta Astronomica A , vol.5 , pp. 115
    • Piotrowsky, S.1
  • 32
    • 34548510325 scopus 로고    scopus 로고
    • Numerical solution of population balance equations for nucleation growth and aggregation processes
    • Qamar S., and Warnecke G. Numerical solution of population balance equations for nucleation growth and aggregation processes. Computers and Chemical Engineering 31 (2007) 1576
    • (2007) Computers and Chemical Engineering , vol.31 , pp. 1576
    • Qamar, S.1    Warnecke, G.2
  • 33
    • 33845412491 scopus 로고    scopus 로고
    • Solving population balance equations for two component aggregation by a finite volume scheme
    • Qamar S., and Warnecke G. Solving population balance equations for two component aggregation by a finite volume scheme. Chemical Engineering Science 62 (2007) 679
    • (2007) Chemical Engineering Science , vol.62 , pp. 679
    • Qamar, S.1    Warnecke, G.2
  • 34
    • 0020336029 scopus 로고
    • A simple model of particle coalescence and breakup
    • Shrivastava R.C. A simple model of particle coalescence and breakup. Journal of Atmospheric Science 39 (1982) 1317
    • (1982) Journal of Atmospheric Science , vol.39 , pp. 1317
    • Shrivastava, R.C.1
  • 35
    • 3042645390 scopus 로고    scopus 로고
    • Modelling end-chain scission and recombination of linear polymers
    • Staggs J.E.J. Modelling end-chain scission and recombination of linear polymers. Polymer Degradation and Stability 85 (2004) 759
    • (2004) Polymer Degradation and Stability , vol.85 , pp. 759
    • Staggs, J.E.J.1
  • 36
    • 30744439327 scopus 로고    scopus 로고
    • Discrete bond-weighted random scission of linear polymers
    • Staggs J.E.J. Discrete bond-weighted random scission of linear polymers. Polymer 47 (2006) 897
    • (2006) Polymer , vol.47 , pp. 897
    • Staggs, J.E.J.1
  • 37
    • 0033119084 scopus 로고    scopus 로고
    • Discretization procedure for the breakage equation
    • Vanni M. Discretization procedure for the breakage equation. AIChE Journal 45 (1999) 916
    • (1999) AIChE Journal , vol.45 , pp. 916
    • Vanni, M.1
  • 38
    • 0000856723 scopus 로고
    • Kinetics of polymer degradation
    • Ziff R.M., and McGrady E.D. Kinetics of polymer degradation. Macromolecules 19 (1986) 2513
    • (1986) Macromolecules , vol.19 , pp. 2513
    • Ziff, R.M.1    McGrady, E.D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.