메뉴 건너뛰기




Volumn 1, Issue , 2011, Pages 209-260

Numerical Methods on Population Balances

Author keywords

Aggregation; Breakage; Growth; Nucleation; Numerical methods; Population balances

Indexed keywords


EID: 84884620025     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/9783527631629.ch6     Document Type: Chapter
Times cited : (4)

References (60)
  • 1
    • 0029138245 scopus 로고
    • Population balance modelling of drum granulation of materials with wide size distribution
    • Adetayo, A.A., Litster, J.D., Pratsinis, S.E., Ennis, B.J., 1995. Population balance modelling of drum granulation of materials with wide size distribution. Powder Technology 82:37-50.
    • (1995) Powder Technology , vol.82 , pp. 37-50
    • Adetayo, A.A.1    Litster, J.D.2    Pratsinis, S.E.3    Ennis, B.J.4
  • 2
    • 18844444768 scopus 로고    scopus 로고
    • Part II: Dynamic evolution of the particle size distribution in particulate processes undergoing simultaneous particle nucleation, growth and aggregation
    • Alexopoulos, A.H., Kiparissides, C.A., 2005. Part II: Dynamic evolution of the particle size distribution in particulate processes undergoing simultaneous particle nucleation, growth and aggregation. Chemical Engineering Science 60:4157-4169.
    • (2005) Chemical Engineering Science , vol.60 , pp. 4157-4169
    • Alexopoulos, A.H.1    Kiparissides, C.A.2
  • 3
    • 0036898869 scopus 로고    scopus 로고
    • Experimental investigation and modelling of continuous fluidized bed drying under steady-state and dynamic conditions
    • Burgschweiger, J., Tsotsas, E., 2002. Experimental investigation and modelling of continuous fluidized bed drying under steady-state and dynamic conditions. Chemical Engineering Science 57:5021-5038.
    • (2002) Chemical Engineering Science , vol.57 , pp. 5021-5038
    • Burgschweiger, J.1    Tsotsas, E.2
  • 5
    • 0031221501 scopus 로고    scopus 로고
    • Spline method for solving continuous batch grinding and similarity equations
    • Everson, R.C., Eyre, D., Campbell, Q.P., 1997. Spline method for solving continuous batch grinding and similarity equations. Computers and Chemical Engineering 21:1433-1440.
    • (1997) Computers and Chemical Engineering , vol.21 , pp. 1433-1440
    • Everson, R.C.1    Eyre, D.2    Campbell, Q.P.3
  • 6
    • 84891567142 scopus 로고
    • New parameterization for a discrete batch grinding equation
    • Eyre, D., Everson, R.C., Campbell, Q.P., 1988. New parameterization for a discrete batch grinding equation. Powder Technology 98:256-272.
    • (1988) Powder Technology , vol.98 , pp. 256-272
    • Eyre, D.1    Everson, R.C.2    Campbell, Q.P.3
  • 7
    • 10244232991 scopus 로고    scopus 로고
    • Numerical simulation of the Smoluchowski coagulation equation
    • Filbet, F., Laurenot, P., 2004. Numerical simulation of the Smoluchowski coagulation equation. SIAM Journal of Scientific Computing 25:2004-2028.
    • (2004) SIAM Journal of Scientific Computing , vol.25 , pp. 2004-2028
    • Filbet, F.1    Laurenot, P.2
  • 8
    • 0025388799 scopus 로고
    • Modelling multicomponent aerosol particle growth by vapor condensation
    • Gelbard, F., 1990. Modelling multicomponent aerosol particle growth by vapor condensation. Aerosol Science and Technology 12:399-412.
    • (1990) Aerosol Science and Technology , vol.12 , pp. 399-412
    • Gelbard, F.1
  • 10
    • 8544278921 scopus 로고    scopus 로고
    • High resolution algorithms for multidimensional population balance equations
    • Gunawan, R., Fusman, I., Braatz, R.D., 2004. High resolution algorithms for multidimensional population balance equations. AIChE Journal 50:2738-2749.
    • (2004) AIChE Journal , vol.50 , pp. 2738-2749
    • Gunawan, R.1    Fusman, I.2    Braatz, R.D.3
  • 11
    • 34848828521 scopus 로고
    • New discretization procedure for the breakage equation
    • Hill, P.J., Ng, K.M., 1995. New discretization procedure for the breakage equation. AIChE Journal 41:1204-1216.
    • (1995) AIChE Journal , vol.41 , pp. 1204-1216
    • Hill, P.J.1    Ng, K.M.2
  • 13
    • 0024104856 scopus 로고
    • A discretized population balance for nucleation, growth and aggregation
    • Hounslow, M.J., Ryall, R.L., Marshall, V.R., 1988. A discretized population balance for nucleation, growth and aggregation. AIChE Journal 38:1821-1832.
    • (1988) AIChE Journal , vol.38 , pp. 1821-1832
    • Hounslow, M.J.1    Ryall, R.L.2    Marshall, V.R.3
  • 15
    • 2142821340 scopus 로고    scopus 로고
    • Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations
    • Springer Verlag
    • Hundsdorfer, W., Verwer, J., 2003. Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations, Springer Verlag.
    • (2003)
    • Hundsdorfer, W.1    Verwer, J.2
  • 17
    • 23944442284 scopus 로고    scopus 로고
    • Solution technique for a multi-dimensional population balance model describing granulation processes
    • Immanuel, C.D., Doyle, F.J., 2005. Solution technique for a multi-dimensional population balance model describing granulation processes. Powder Technology 156:213-225.
    • (2005) Powder Technology , vol.156 , pp. 213-225
    • Immanuel, C.D.1    Doyle, F.J.2
  • 18
  • 19
    • 0028977754 scopus 로고
    • Simulating condensational growth, evaporation and coagulation of aerosols using a combined moving and stationary size grid
    • Jacobson, M.Z., Turco, R.P., 1995. Simulating condensational growth, evaporation and coagulation of aerosols using a combined moving and stationary size grid. Aerosol Science and Technology 22:73-92.
    • (1995) Aerosol Science and Technology , vol.22 , pp. 73-92
    • Jacobson, M.Z.1    Turco, R.P.2
  • 20
    • 84884610530 scopus 로고    scopus 로고
    • Distributed product quality in fluidized bed drying
    • Proceedings of 15th International Drying Symposium
    • Kettner, C., Peglow, M., Metzger, T., Tsotsas, E., 2006. Distributed product quality in fluidized bed drying. Proceedings of 15th International Drying Symposium.
    • (2006)
    • Kettner, C.1    Peglow, M.2    Metzger, T.3    Tsotsas, E.4
  • 21
    • 0025401881 scopus 로고
    • Simulation of multicomponent aerosol condensation by the moving sectional method
    • Kim, Y.P., Seinfeld, J.H., 1990. Simulation of multicomponent aerosol condensation by the moving sectional method. Journal of Colloid and Interface Science 135:185-199.
    • (1990) Journal of Colloid and Interface Science , vol.135 , pp. 185-199
    • Kim, Y.P.1    Seinfeld, J.H.2
  • 22
    • 0003339238 scopus 로고
    • A robust upwind discretization for advection, diffusion and source terms
    • Koren, B., 1993. A robust upwind discretization for advection, diffusion and source terms. Numerical Methods for Advection-Diffusion Problems 45:117-138.
    • (1993) Numerical Methods for Advection-Diffusion Problems , vol.45 , pp. 117-138
    • Koren, B.1
  • 23
    • 0037120789 scopus 로고    scopus 로고
    • An assessment of low-order methods for solving the breakage equation
    • Kostoglou, M., Karabelas, A.J., 2002. An assessment of low-order methods for solving the breakage equation. Powder Technology 127:116-127.
    • (2002) Powder Technology , vol.127 , pp. 116-127
    • Kostoglou, M.1    Karabelas, A.J.2
  • 24
    • 4143062491 scopus 로고    scopus 로고
    • Optimal low order methods of moments for solving the fragmentation
    • 280-290
    • Kostoglou, M., Karabelas, A.J., 2004. Optimal low order methods of moments for solving the fragmentation. Powder Technology 143-144: 280-290.
    • (2004) Powder Technology , pp. 143-144
    • Kostoglou, M.1    Karabelas, A.J.2
  • 25
    • 33644988295 scopus 로고    scopus 로고
    • Improved accuracy and convergence of discretized population balances: The cell average technique
    • Kumar, J., Peglow, M., Warnecke, G., Heinrich, S., Morl, L., 2006a. Improved accuracy and convergence of discretized population balances: The cell average technique. Chemical Engineering Science 61: 3327-3342.
    • (2006) Chemical Engineering Science , vol.61 , pp. 3327-3342
    • Kumar, J.1    Peglow, M.2    Warnecke, G.3    Heinrich, S.4    Morl, L.5
  • 27
    • 84884608738 scopus 로고    scopus 로고
    • Numerical solutions of a two dimensional population balanace equation for aggregation
    • In The Fifth World Congress on Particle Technology, Orlando, FL, USA, April 2006, AIChE
    • Kumar, J., Peglow, M., Warnecke, G., Heinrich, S., Tsotsas, E., Morl, L. Numerical solutions of a two dimensional population balanace equation for aggregation. In The Fifth World Congress on Particle Technology, Orlando, FL, USA, April 2006, AIChE.
    • Kumar, J.1    Peglow, M.2    Warnecke, G.3    Heinrich, S.4    Tsotsas, E.5    Morl, L.6
  • 28
    • 0030127313 scopus 로고    scopus 로고
    • On the solution of population balance equations by discretization-i. a fixed pivot technique
    • Kumar, S., Ramkrishna, D., 1996a. On the solution of population balance equations by discretization-i. a fixed pivot technique. Chemical Engineering Science 51: 1333-1342.
    • (1996) Chemical Engineering Science , vol.51 , pp. 1333-1342
    • Kumar, S.1    Ramkrishna, D.2
  • 29
    • 0030127313 scopus 로고    scopus 로고
    • On the solution of population balance equations by discretization-ii. a moving pivot technique
    • Kumar, S., Ramkrishna, D., 1996b. On the solution of population balance equations by discretization-ii. a moving pivot technique. Chemical Engineering Science 51: 1333-1342.
    • (1996) Chemical Engineering Science , vol.51 , pp. 1333-1342
    • Kumar, S.1    Ramkrishna, D.2
  • 31
    • 0347987814 scopus 로고    scopus 로고
    • New high-resolution central schemes for nonlinear conservation laws and convectiondiffusion equations
    • Kurganov, A., Tadmor, E., 2000. New high-resolution central schemes for nonlinear conservation laws and convectiondiffusion equations. Journal of Computational Physics 160:141-182.
    • (2000) Journal of Computational Physics , vol.160 , pp. 141-182
    • Kurganov, A.1    Tadmor, E.2
  • 32
    • 84884632407 scopus 로고    scopus 로고
    • Chemical Engineering Science
    • Comments on 'an analytical solution to the population balance equation with coalescence and breakage the special case with constant number of particles' by D. Patil and J.R.G. Andrews [Chemical Engineering Science 53(3) 599-601]
    • Lage, P.L.C., 2002. Comments on 'an analytical solution to the population balance equation with coalescence and breakage the special case with constant number of particles' by D. Patil and J.R.G. Andrews [Chemical Engineering Science 53(3) 599-601]. Chemical Engineering Science 19:4253-4254.
    • (2002) , vol.19 , pp. 4253-4254
    • Lage, P.L.C.1
  • 33
    • 0037052054 scopus 로고    scopus 로고
    • A general algorithm for exact simulation of multicomponent aggregation processes
    • Laurenzi, I.J., Bartels, J.D., Diamond, S.L., 2002. A general algorithm for exact simulation of multicomponent aggregation processes. Journal of Computational Physics 177:418-449.
    • (2002) Journal of Computational Physics , vol.177 , pp. 418-449
    • Laurenzi, I.J.1    Bartels, J.D.2    Diamond, S.L.3
  • 34
    • 0034192160 scopus 로고    scopus 로고
    • Simultaneous coagulation and break-up using constant-N monte carlo
    • Lee, K., Matsoukas, T., 2000. Simultaneous coagulation and break-up using constant-N monte carlo. Powder Technology 110:82-89.
    • (2000) Powder Technology , vol.110 , pp. 82-89
    • Lee, K.1    Matsoukas, T.2
  • 35
    • 0003671760 scopus 로고
    • Numerical Methods for Conservation Laws
    • Birkhuser-Verlag
    • Leveque, R.J., 1990. Numerical Methods for Conservation Laws, Birkhuser-Verlag.
    • (1990)
    • Leveque, R.J.1
  • 36
    • 0037073056 scopus 로고    scopus 로고
    • On the solution of population balance equations (pbe) with accurate front tracking methods in practical crystallization processes
    • Lim, Y., Lann, J., Meyer, X., Joulia, X., Lee, G., Yoon, E., 2002. On the solution of population balance equations (pbe) with accurate front tracking methods in practical crystallization processes. Chemical Engineering Science 57:3715-3732.
    • (2002) Chemical Engineering Science , vol.57 , pp. 3715-3732
    • Lim, Y.1    Lann, J.2    Meyer, X.3    Joulia, X.4    Lee, G.5    Yoon, E.6
  • 37
    • 0029270768 scopus 로고
    • Adjustable discretized population balance for growth and aggregation
    • Litster, J.D., Smit, D.J., Hounslow, M.J., 1995. Adjustable discretized population balance for growth and aggregation. AIChE Journal 41:591-603.
    • (1995) AIChE Journal , vol.41 , pp. 591-603
    • Litster, J.D.1    Smit, D.J.2    Hounslow, M.J.3
  • 39
    • 0006145306 scopus 로고    scopus 로고
    • On the mass distribution of planetesimals in the early runaway stage
    • Makino, J., Fukushige, T., Funato, Y., Kokubo, E., 1998. On the mass distribution of planetesimals in the early runaway stage. New Astronomy 3:411-417.
    • (1998) New Astronomy , vol.3 , pp. 411-417
    • Makino, J.1    Fukushige, T.2    Funato, Y.3    Kokubo, E.4
  • 40
    • 0034641113 scopus 로고    scopus 로고
    • Monte Carlo simulation of particle breakage process during grinding
    • Mishra, B.K., 2000. Monte Carlo simulation of particle breakage process during grinding. Powder Technology 110:246-252.
    • (2000) Powder Technology , vol.110 , pp. 246-252
    • Mishra, B.K.1
  • 41
    • 7644223441 scopus 로고    scopus 로고
    • A novel fixed-sectional model for the formation and growth of aerosol agglomerates
    • Park, S.H., Rogak, S.N., 2004. A novel fixed-sectional model for the formation and growth of aerosol agglomerates. Journal of Aerosol Science 35:185-199.
    • (2004) Journal of Aerosol Science , vol.35 , pp. 185-199
    • Park, S.H.1    Rogak, S.N.2
  • 42
    • 0032004981 scopus 로고    scopus 로고
    • An analytical solution to continuous population balance model describing floc coalescence and breakage-a special case
    • Patil, D.P., Andrews, J.R.G., 1998. An analytical solution to continuous population balance model describing floc coalescence and breakage-a special case. Chemical Engineering Science 53:599-601.
    • (1998) Chemical Engineering Science , vol.53 , pp. 599-601
    • Patil, D.P.1    Andrews, J.R.G.2
  • 45
    • 0003689221 scopus 로고    scopus 로고
    • Population Balances
    • Academic Press, New York
    • Ramkrishna, D., 2000. Population Balances, Academic Press, New York.
    • (2000)
    • Ramkrishna, D.1
  • 46
    • 0003440119 scopus 로고
    • The Theory of Particulate Processes
    • Academic Press, New York
    • Randolph, A.D., Larson, M.A., 1978. The Theory of Particulate Processes, Academic Press, New York.
    • (1978)
    • Randolph, A.D.1    Larson, M.A.2
  • 49
    • 4143151696 scopus 로고    scopus 로고
    • Kinetics of fluidised bed melt granulation IV. Selecting the breakage model
    • 65-83
    • Tan, H.S., Salman, A.D., Hounslow, M.J., 2004. Kinetics of fluidised bed melt granulation IV. Selecting the breakage model. Powder Technology 143-144: 65-83.
    • (2004) Powder Technology , pp. 143-144
    • Tan, H.S.1    Salman, A.D.2    Hounslow, M.J.3
  • 50
    • 0030268411 scopus 로고    scopus 로고
    • Steady-state size distribution for the selfsimilar collision cascade
    • Tanaka, H., Inaba, S., Nakaza, K., 1996. Steady-state size distribution for the selfsimilar collision cascade. Icarus 123:450-455.
    • (1996) Icarus , vol.123 , pp. 450-455
    • Tanaka, H.1    Inaba, S.2    Nakaza, K.3
  • 51
    • 0033137031 scopus 로고    scopus 로고
    • A fast and efficient modified sectional method for simulating multicomponent collisional kinetics
    • Trautmann, T., Wanner, C., 1999. A fast and efficient modified sectional method for simulating multicomponent collisional kinetics. Atmospheric Environment 33:1631-1640.
    • (1999) Atmospheric Environment , vol.33 , pp. 1631-1640
    • Trautmann, T.1    Wanner, C.2
  • 52
    • 0036600595 scopus 로고    scopus 로고
    • Population balance modeling of flame synthesis of titania nanoparticles
    • Tsantilis, S., Kammler, H.K., Pratsinis, S.E., 2002. Population balance modeling of flame synthesis of titania nanoparticles. Chemical Engineering Science 57:2139-2156.
    • (2002) Chemical Engineering Science , vol.57 , pp. 2139-2156
    • Tsantilis, S.1    Kammler, H.K.2    Pratsinis, S.E.3
  • 53
    • 1442274763 scopus 로고    scopus 로고
    • Narrowing the size distribution of aerosolmade titania by surface growth and coagulation
    • Tsantilis, S., Pratsinis, S.E., 2004. Narrowing the size distribution of aerosolmade titania by surface growth and coagulation. Journal of Aerosol Science 35:405-420.
    • (2004) Journal of Aerosol Science , vol.35 , pp. 405-420
    • Tsantilis, S.1    Pratsinis, S.E.2
  • 54
    • 0033119084 scopus 로고    scopus 로고
    • Discretization procedure for the breakage equation
    • Vanni, M., 1999. Discretization procedure for the breakage equation. AIChE Journal 45:916-919.
    • (1999) AIChE Journal , vol.45 , pp. 916-919
    • Vanni, M.1
  • 55
    • 0034650756 scopus 로고    scopus 로고
    • Approximate population balance equations for aggregationbreakage processes
    • Vanni, M., 2000. Approximate population balance equations for aggregationbreakage processes. Journal of Colloid and Interface Science 221:143-160.
    • (2000) Journal of Colloid and Interface Science , vol.221 , pp. 143-160
    • Vanni, M.1
  • 57
    • 0030195436 scopus 로고    scopus 로고
    • Improved accuracy and convergence of discretized population balance of Lister et al.
    • Wynn, E.J.W., 1996. Improved accuracy and convergence of discretized population balance of Lister et al. AIChE Journal 22:2048-2086.
    • (1996) AIChE Journal , vol.22 , pp. 2048-2086
    • Wynn, E.J.W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.