15 Compartmental Population Balances by Means of Monte Carlo Methods
547
33. Wu, C.-Y., Biswas, P.: Study of numerical diffusion in a discrete-sectional model and its
application to aerosol dynamics simulation. Aerosol Sci. Technol. 29(5), 359–378 (1998)
34. Kumar, S., Ramkrishna, D.: On the solution of population balance equations by discretization
– III. Nucleation, growth and aggregation of particles. Chem. Eng. Sci. 52(24), 4659–4679
(1997)
35. Wyslouzil, B.E., Wölk, J.: Overview: homogeneous nucleation from the vapor phase−the
experimental science. J. Chem. Phys. 145(21) (2016)
36. Girshick, S.L., Chiu, C.-P.: Kinetic nucleation theory: a new expression for the rate of homogeneous nucleation from an ideal supersaturated vapor. J. Chem. Phys. 93(2), 1273–1277
(1990)
37. Lide, D.R. (ed.): CRC Handbook of Chemistry and Physics: A Ready-Reference Book of
Chemical and Physical Data, 85th edn. CRC Press, Boca Raton (2004)
38. Egry, I., Ricci, E., Novakovic, R., Ozawa, S.: Surface tension of liquid metals and alloys-recent
developments. Adv. Coll. Interface. Sci. 159(2), 198–212 (2010)
39. Mishra, B.K.: Monte Carlo simulation of particle breakage process during grinding. Powder
Technol. 110(3), 246–252 (2000)
40. Lee, K., Matsoukas, T.: Simultaneous coagulation and break-up using constant-N Monte Carlo.
Powder Technol. 110(1–2), 82–89 (2000)
41. Lee, K.F., Patterson, R.I.A., Wagner, W., Kraft, M.: Stochastic weighted particle methods for
population balance equations with coagulation, fragmentation and spatial inhomogeneity. J.
Comput. Phys. 303, 1–18 (2015)
42. Zhao, H., Zheng, C., Xu, M.: Multi-Monte Carlo approach for general dynamic equation
considering simultaneous particle coagulation and breakage. Powder Technol. 154(2–3), 164–
178 (2005)
43. Kotalczyk, G., Devi, J., Kruis, F.E.: A time-driven constant-number Monte Carlo method for the
GPU-simulation of particle breakage based on weighted simulation particles. Powder Technol.
317, 417–429 (2017)
44. Devi, J., Kotalczyk, G., Kruis, F.E.: Accuracy control in Monte Carlo simulations of particle
breakage. Int. J. Model. Ident. Control 31(3), 278–291 (2019)
45. Muscato, O., Di Stefano, V., Wagner, W.: A variance-reduced electrothermal Monte Carlo
method for semiconductor device simulation. Comput. Math Appl. 65(3), 520–527 (2013)
46. Ziff, R.M., McGrady, E.D.: The kinetics of cluster fragmentation and depolymerisation. J.
Phys. A: Math. Gen. 18(15), 3027–3037 (1985)
47. Celnik, M., Patterson, R.I.A., Kraft, M., Wagner, W.: Coupling a stochastic soot population
balance to gas-phase chemistry using operator splitting. Combust. Flame 148(3), 158–176
(2007)
48. Liffman, K.: A direct simulation Monte-Carlo method for cluster coagulation. J. Comput. Phys.
100(1), 116–127 (1992)
49. Zhao, H., Maisels, A., Matsoukas, T., Zheng, C.: Analysis of four Monte Carlo methods for the
solution of population balances in dispersed systems. Powder Technol. 173(1), 38–50 (2007)
50. Wei, J.: A parallel Monte Carlo method for population balance modeling of particulate processes
using bookkeeping strategy. Physica A 402, 186–197 (2014)
51. Kotalczyk, G., Kruis, F.E.: Fractional Monte Carlo time steps for the simulation of coagulation
for parallelized flowsheet simulations. Chem. Eng. Res. Des. 136, 71–82 (2018)
52. Gelbard, F., Tambour, Y., Seinfeld, J.H.: Sectional representations for simulating aerosol
dynamics. J. Colloid Interface Sci. 76(2), 541–556 (1980)
53. Landgrebe, J.D., Pratsinis, S.E.: A discrete-sectional model for particulate production by gasphase chemical reaction and aerosol coagulation in the free-molecular regime. J. Colloid
Interface Sci. 139(1), 63–86 (1990)
54. Marshall, C.L., Rajniak, P., Matsoukas, T.: Multi-component population balance modeling of
granulation with continuous addition of binder. Powder. Technol. 236, 211–220 (2013)
55. Khalili, S., Lin, Y., Armaou, A., Matsoukas, T.: Constant number Monte Carlo simulation of
population balances with multiple growth mechanisms. AIChE J. 56(12), 3137–3145 (2010)
547
33. Wu, C.-Y., Biswas, P.: Study of numerical diffusion in a discrete-sectional model and its
application to aerosol dynamics simulation. Aerosol Sci. Technol. 29(5), 359–378 (1998)
34. Kumar, S., Ramkrishna, D.: On the solution of population balance equations by discretization
– III. Nucleation, growth and aggregation of particles. Chem. Eng. Sci. 52(24), 4659–4679
(1997)
35. Wyslouzil, B.E., Wölk, J.: Overview: homogeneous nucleation from the vapor phase−the
experimental science. J. Chem. Phys. 145(21) (2016)
36. Girshick, S.L., Chiu, C.-P.: Kinetic nucleation theory: a new expression for the rate of homogeneous nucleation from an ideal supersaturated vapor. J. Chem. Phys. 93(2), 1273–1277
(1990)
37. Lide, D.R. (ed.): CRC Handbook of Chemistry and Physics: A Ready-Reference Book of
Chemical and Physical Data, 85th edn. CRC Press, Boca Raton (2004)
38. Egry, I., Ricci, E., Novakovic, R., Ozawa, S.: Surface tension of liquid metals and alloys-recent
developments. Adv. Coll. Interface. Sci. 159(2), 198–212 (2010)
39. Mishra, B.K.: Monte Carlo simulation of particle breakage process during grinding. Powder
Technol. 110(3), 246–252 (2000)
40. Lee, K., Matsoukas, T.: Simultaneous coagulation and break-up using constant-N Monte Carlo.
Powder Technol. 110(1–2), 82–89 (2000)
41. Lee, K.F., Patterson, R.I.A., Wagner, W., Kraft, M.: Stochastic weighted particle methods for
population balance equations with coagulation, fragmentation and spatial inhomogeneity. J.
Comput. Phys. 303, 1–18 (2015)
42. Zhao, H., Zheng, C., Xu, M.: Multi-Monte Carlo approach for general dynamic equation
considering simultaneous particle coagulation and breakage. Powder Technol. 154(2–3), 164–
178 (2005)
43. Kotalczyk, G., Devi, J., Kruis, F.E.: A time-driven constant-number Monte Carlo method for the
GPU-simulation of particle breakage based on weighted simulation particles. Powder Technol.
317, 417–429 (2017)
44. Devi, J., Kotalczyk, G., Kruis, F.E.: Accuracy control in Monte Carlo simulations of particle
breakage. Int. J. Model. Ident. Control 31(3), 278–291 (2019)
45. Muscato, O., Di Stefano, V., Wagner, W.: A variance-reduced electrothermal Monte Carlo
method for semiconductor device simulation. Comput. Math Appl. 65(3), 520–527 (2013)
46. Ziff, R.M., McGrady, E.D.: The kinetics of cluster fragmentation and depolymerisation. J.
Phys. A: Math. Gen. 18(15), 3027–3037 (1985)
47. Celnik, M., Patterson, R.I.A., Kraft, M., Wagner, W.: Coupling a stochastic soot population
balance to gas-phase chemistry using operator splitting. Combust. Flame 148(3), 158–176
(2007)
48. Liffman, K.: A direct simulation Monte-Carlo method for cluster coagulation. J. Comput. Phys.
100(1), 116–127 (1992)
49. Zhao, H., Maisels, A., Matsoukas, T., Zheng, C.: Analysis of four Monte Carlo methods for the
solution of population balances in dispersed systems. Powder Technol. 173(1), 38–50 (2007)
50. Wei, J.: A parallel Monte Carlo method for population balance modeling of particulate processes
using bookkeeping strategy. Physica A 402, 186–197 (2014)
51. Kotalczyk, G., Kruis, F.E.: Fractional Monte Carlo time steps for the simulation of coagulation
for parallelized flowsheet simulations. Chem. Eng. Res. Des. 136, 71–82 (2018)
52. Gelbard, F., Tambour, Y., Seinfeld, J.H.: Sectional representations for simulating aerosol
dynamics. J. Colloid Interface Sci. 76(2), 541–556 (1980)
53. Landgrebe, J.D., Pratsinis, S.E.: A discrete-sectional model for particulate production by gasphase chemical reaction and aerosol coagulation in the free-molecular regime. J. Colloid
Interface Sci. 139(1), 63–86 (1990)
54. Marshall, C.L., Rajniak, P., Matsoukas, T.: Multi-component population balance modeling of
granulation with continuous addition of binder. Powder. Technol. 236, 211–220 (2013)
55. Khalili, S., Lin, Y., Armaou, A., Matsoukas, T.: Constant number Monte Carlo simulation of
population balances with multiple growth mechanisms. AIChE J. 56(12), 3137–3145 (2010)