The DOI matches its Crossref record; 21 of the 21 references it cites were found in a registry or an index.
On the solution of population balance equations by discretization—I. A fixed pivot technique
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“Kumar and Ramkrishna [292] presented a new framework for the discretization of PBEs, considering particle populations in discrete size ranges to be concentrated only in representative volumes. One of the main advantages of this approach is that the coarseness of the discretization can be varied freely, without any specific geometric type, thus having a general and flexible pattern.”
From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [292]
In the citing paper
“The technique has been applied to binary and multiple breakages with power-law breakage rates, aggregation with constant, sum, and product kernel, and simultaneous breakage and aggregation. Comparison between analytical [293-295] and numerical results show good agreement.”
From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [292]
Citations
Cites
A discretized population balance for nucleation, growth, and aggregation
Hounslow, M. J., Ryall, R. L., & Marshall, V. R. (1988) · AIChE Journal · doi:10.1002/aic.690341108 · Cited by 995
On the solution of population balance equations by discretization—II. A moving pivot technique
Kumar, S., & Ramkrishna, D. (1996) · Chemical Engineering Science · doi:10.1016/0009-2509(95)00355-x · Cited by 825
Self-citationSectional representations for simulating aerosol dynamics
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The kinetics of cluster fragmentation and depolymerisation
Ziff, R. M., & McGrady, E. D. (1985) · Journal of Physics A: Mathematical and General · doi:10.1088/0305-4470/18/15/026 · Cited by 397
The Status of Population Balances
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Self-citationLandgrebe, J. D., & Pratsinis, S. E. (1990) · Journal of Colloid and Interface Science · doi:10.1016/0021-9797(90)90445-t · Cited by 287
Marchal, P., David, R., Klein, J. P., & Villermaux, J. (1988) · Chemical Engineering Science · doi:10.1016/0009-2509(88)87126-4 · Cited by 257
New solutions to the fragmentation equation
Ziff, R. M. (1991) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/24/12/020 · Cited by 187
The general dynamic equation for aerosols. Theory and application to aerosol formation and growth
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Note on the Kinetics of Systems Manifesting Simultaneous Polymerization-Depolymerization Phenomena
Blatz, P. J., & Tobolsky, A. V. (1945) · The Journal of Physical Chemistry · doi:10.1021/j150440a004 · Cited by 169
Cited by
Sorted by citations
On the solution of population balance equations by discretization—II. A moving pivot technique
Kumar, S., & Ramkrishna, D. (1996) · Chemical Engineering Science · doi:10.1016/0009-2509(95)00355-x · Cited by 825
Self-citationQuadrature method of moments for population-balance equations
Marchisio, D. L., Pikturna, J. T., Fox, R. O., Vigil, R. D., & Barresi, A. A. (2003) · AIChE Journal · doi:10.1002/aic.690490517 · Cited by 461
Modeling of Formation of Gold Nanoparticles by Citrate Method
Kumar, S., Gandhi, K. S., & Kumar, R. (2006) · Industrial & Engineering Chemistry Research · doi:10.1021/ie060672j · Cited by 386
Self-citationKumar, S., & Ramkrishna, D. (1997) · Chemical Engineering Science · doi:10.1016/s0009-2509(97)00307-2 · Cited by 379
Self-citationHigh resolution algorithms for multidimensional population balance equations
Gunawan, R., Fusman, I., & Braatz, R. D. (2004) · AIChE Journal · doi:10.1002/aic.10228 · Cited by 324
“In the method of finite differences/discretized population balances, the population balance equation is approximated by a finite difference scheme (Kumar and Ramkrishna, 1996).”
MethodNumerical simulation of bubble columns flows: effect of different breakup and coalescence closures
Chen, P., Sanyal, J., & Duduković, M. P. (2004) · Chemical Engineering Science · doi:10.1016/j.ces.2004.09.070 · Cited by 296
Population Balance Modeling: Current Status and Future Prospects
Ramkrishna, D., & Singh, M. R. (2014) · Annual Review of Chemical and Biomolecular Engineering · doi:10.1146/annurev-chembioeng-060713-040241 · Cited by 278
“Bubble columns have been modeled (152) with discretization methods (153), but not without other compromising simplifying assumptions.”
MethodSelf-citationApproximate Population Balance Equations for Aggregation–Breakage Processes
Vanni, M. (2000) · Journal of Colloid and Interface Science · doi:10.1006/jcis.1999.6571 · Cited by 244
Advanced control of crystallization processes
Braatz, R. D. (2002) · Annual Reviews in Control · doi:10.1016/s1367-5788(02)80016-5 · Cited by 239
Multiphase Porous Electrode Theory
Smith, R. B., & Bazant, M. Z. (2017) · Journal of The Electrochemical Society · doi:10.1149/2.0171711jes · Cited by 238
Kumar, J., Peglow, M., Warnecke, G., Heinrich, S., & Mörl, L. (2006) · Chemical Engineering Science · doi:10.1016/j.ces.2005.12.014 · Cited by 230
Jacobson, M. Z. (2002) · Journal of Geophysical Research Atmospheres · doi:10.1029/2001jd002044 · Cited by 227
The strength of multi-scale modeling to unveil the complexity of radical polymerization
D’hooge, D., Steenberge, P. H. M. V., Reyniers, M., & Marin, G. B. (2016) · Progress in Polymer Science · doi:10.1016/j.progpolymsci.2016.04.002 · Cited by 212
CFD simulation of bubble columns incorporating population balance modeling
Bhole, M. R., Joshi, J. B., & Ramkrishna, D. (2008) · Chemical Engineering Science · doi:10.1016/j.ces.2008.01.013 · Cited by 206
“(8), the discrete equations in the domain of bubble volume, the fixed pivot technique of Kumar and Ramkrishna (1996) has been used.”
BackgroundMethodInfluentialSelf-citationA CFD–PBM coupled model for gas–liquid flows
Wang, T., Wang, J., & Jin, Y. J. (2005) · AIChE Journal · doi:10.1002/aic.10611 · Cited by 204
Alopaeus, V., Koskinen, J., & Keskinen, K. I. (1999) · Chemical Engineering Science · doi:10.1016/s0009-2509(99)00170-0 · Cited by 205
A transport equation for the interfacial area density applied to bubble columns
Lehr, F., & Mewes, D. (2001) · Chemical Engineering Science · doi:10.1016/s0009-2509(00)00335-3 · Cited by 200
Tyagi, H., Kushwaha, A., Kumar, A., & Aslam, M. (2016) · Nanoscale Research Letters · doi:10.1186/s11671-016-1576-5 · Cited by 200
“successfully takes into account these simultaneous processes and we used it to understand the nucleation and growth process of gold nanoparticles at room temperature [39, 40].”
MethodPopulation Balance Model for Gas−Liquid Flows: Influence of Bubble Coalescence and Breakup Models
Wang, T., Wang, J., & Jin, Y. J. (2005) · Industrial & Engineering Chemistry Research · doi:10.1021/ie0489002 · Cited by 195
Three‐dimensional simulation of bubble column flows with bubble coalescence and breakup
Chen, P., Duduković, M. P., & Sanyal, J. (2005) · AIChE Journal · doi:10.1002/aic.10381 · Cited by 193
Population balance modeling of flame synthesis of titania nanoparticles
Tsantilis, S., Kammler, H. K., & Pratsinis, S. E. (2002) · Chemical Engineering Science · doi:10.1016/s0009-2509(02)00107-0 · Cited by 184
A simple model for the structure of fractal aggregates
Lattuada, M., Wu, H., & Morbidelli, M. (2003) · Journal of Colloid and Interface Science · doi:10.1016/j.jcis.2003.07.027 · Cited by 172
Process systems modelling and applications in granulation: A review
Cameron, I. T., Wang, F. Y., Immanuel, C. D., & Stepanek, F. (2005) · Chemical Engineering Science · doi:10.1016/j.ces.2005.02.004 · Cited by 168
High-Resolution Simulation of Multidimensional Crystal Growth
Ma, D. L., Tafti, D. K., & Braatz, R. D. (2002) · Industrial & Engineering Chemistry Research · doi:10.1021/ie010680u · Cited by 160
Population balance modelling of polydispersed particles in reactive flows
Rigopoulos, S. (2010) · Progress in Energy and Combustion Science · doi:10.1016/j.pecs.2009.12.001 · Cited by 163
Efficient solution of population balance equations with discontinuities by finite elements
Mahoney, A. W., & Ramkrishna, D. (2002) · Chemical Engineering Science · doi:10.1016/s0009-2509(01)00427-4 · Cited by 150
Self-citationSelomulya, C., Bushell, G. C., Amal, R., & Waite, T. D. (2002) · Chemical Engineering Science · doi:10.1016/s0009-2509(02)00523-7 · Cited by 144
Theoretical prediction of flow regime transition in bubble columns by the population balance model
Wang, T., Wang, J., & Jin, Y. (2005) · Chemical Engineering Science · doi:10.1016/j.ces.2005.04.027 · Cited by 141
Dynamic simulation of emulsion formation in a high pressure homogenizer
Håkansson, A., Trägårdh, C., & Bergenståhl, B. (2009) · Chemical Engineering Science · doi:10.1016/j.ces.2009.03.034 · Cited by 141
Multiscale multiphase phenomena in bubble column reactors: A review
Shu, S., Vidal, D. J.-E., Bertrand, F., & Chaouki, J. (2019) · Renewable Energy · doi:10.1016/j.renene.2019.04.020 · Cited by 141
Gan, Y., & Qiao, L. (2011) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2011.07.003 · Cited by 136
Nonlinear control of particulate processes
Chiu, T. Y., & Christofides, P. D. (1999) · AIChE Journal · doi:10.1002/aic.690450613 · Cited by 132
Kumar, A., Gernaey, K. V., Beer, T. D., & Ingmar Nopens, A. (2013) · European Journal of Pharmaceutics and Biopharmaceutics · doi:10.1016/j.ejpb.2013.09.013 · Cited by 127
Modeling and simulation of crystallization processes using parsival
Wulkow, M., Gerstlauer, A., & Nieken, U. (2001) · Chemical Engineering Science · doi:10.1016/s0009-2509(00)00432-2 · Cited by 127
Sommer, M., Stenger, F., Peukert, W., & Wagner, N. J. (2005) · Chemical Engineering Science · doi:10.1016/j.ces.2004.12.057 · Cited by 123
Buffo, A., Vanni, M., & Marchisio, D. L. (2011) · Chemical Engineering Science · doi:10.1016/j.ces.2011.04.042 · Cited by 123
Kotoulas, C., & Kiparissides, C. A. (2005) · Chemical Engineering Science · doi:10.1016/j.ces.2005.07.013 · Cited by 121
Kumar, J., Peglow, M., Warnecke, G., & Heinrich, S. (2007) · Powder Technology · doi:10.1016/j.powtec.2007.05.028 · Cited by 121
Hydrodynamic radius of fractal clusters
Lattuada, M., Wu, H., & Morbidelli, M. (2003) · Journal of Colloid and Interface Science · doi:10.1016/j.jcis.2003.07.028 · Cited by 121
On the numerical study of isothermal vertical bubbly flow using two population balance approaches
Cheung, S. C. P., Yeoh, G. H., & Tu, J. Y. (2007) · Chemical Engineering Science · doi:10.1016/j.ces.2007.05.030 · Cited by 120
“Assuming each bubble class travel at the same mean algebraic velocity, individual number density of bubble class i based on Kumar and Ramkrishna (1996a) can be expressed as:”
BackgroundKiparissides, C. A. (2005) · Journal of Process Control · doi:10.1016/j.jprocont.2005.06.004 · Cited by 119
Finite‐element scheme for solution of the dynamic population balance equation
Rigopoulos, S., & Jones, A. G. (2003) · AIChE Journal · doi:10.1002/aic.690490507 · Cited by 116
Titania formation by TiCl4 gas phase oxidation, surface growth and coagulation
Spicer, P. T., Chaoul, O., Tsantilis, S., & Pratsinis, S. E. (2002) · Journal of Aerosol Science · doi:10.1016/s0021-8502(01)00069-6 · Cited by 115
Emulsification in turbulent flow
Vankova, N., Tcholakova, S. S., Denkov, N. D., Vulchev, V. D., & Danner, T. (2007) · Journal of Colloid and Interface Science · doi:10.1016/j.jcis.2007.04.064 · Cited by 113
A closer look at an aggregation model of the Stöber process
Lee, K., Sathyagal, A., & McCormick, A. V. (1998) · Colloids and Surfaces A Physicochemical and Engineering Aspects · doi:10.1016/s0927-7757(98)00566-4 · Cited by 125
Aggregation kinetics of polymer colloids in reaction limited regime: experiments and simulations
Lattuada, M., Sandkühler, P., Wu, H., Šefčı́k, J., & Morbidelli, M. (2003) · Advances in Colloid and Interface Science · doi:10.1016/s0001-8686(02)00082-9 · Cited by 111
Considerations on the crystallization modeling: Population balance solution
Costa, C. B. B., Maciel, M. R. W., & Filho, R. M. (2006) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2006.06.005 · Cited by 110
Immanuel, C. D., & Doyle, F. J. (2003) · Chemical Engineering Science · doi:10.1016/s0009-2509(03)00216-1 · Cited by 110
Zauner, R., & Jones, A. G. (2000) · Chemical Engineering Science · doi:10.1016/s0009-2509(00)00059-2 · Cited by 108
Li, G., Yang, X., & Dai, G. (2009) · Chemical Engineering Science · doi:10.1016/j.ces.2009.08.016 · Cited by 107
Heinrich, S., Peglow, M., Ihlow, M., Henneberg, M., & Mörl, L. (2002) · Chemical Engineering Science · doi:10.1016/s0009-2509(02)00352-4 · Cited by 107
Bannari, R., Kerdouss, F., Selma, B., Bannari, A., & Proulx, P. (2008) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2008.05.016 · Cited by 109
Evolution of Colloidal Nanocrystals: Theory and Modeling of their Nucleation and Growth
van Embden, J., Sader, J. E., Davidson, M. R., & Mulvaney, P. A. (2009) · The Journal of Physical Chemistry C · doi:10.1021/jp9027673 · Cited by 104
Selma, B., Bannari, R., & Proulx, P. (2010) · Chemical Engineering Science · doi:10.1016/j.ces.2009.11.018 · Cited by 103
Nguyen, T. T., Laurent, F., Fox, R. O., & Massot, M. (2016) · Journal of Computational Physics · doi:10.1016/j.jcp.2016.08.017 · Cited by 102
Netzell, K., Lehtiniemi, H., & Mauß, F. (2006) · Proceedings of the Combustion Institute · doi:10.1016/j.proci.2006.08.081 · Cited by 101
Crystal Population Balance Formulation and Solution Methods: A Review
Omar, H. M., & Rohani, S. (2017) · Crystal Growth & Design · doi:10.1021/acs.cgd.7b00645 · Cited by 107
Raikar, N. B., Bhatia, S. R., Malone, M. F., & Henson, M. A. (2009) · Chemical Engineering Science · doi:10.1016/j.ces.2009.01.062 · Cited by 100
“A variety of numerical techniques have been developed for solving PBE models of particulate processes (Kumar and Ramkrishna, 1996; Ramkrishna, 2000; Dorao and Jakobsen, 2006; Gavi et al., 2008).”
MethodThe effect of oil type on the aggregation stability of nanostructured lipid carriers
Yang, Y., Corona, A., Schubert, B. A., Reeder, R. C., & Henson, M. A. (2013) · Journal of Colloid and Interface Science · doi:10.1016/j.jcis.2013.12.024 · Cited by 99
A novel fixed-sectional model for the formation and growth of aerosol agglomerates
Park, S. H., & Rogak, S. N. (2004) · Journal of Aerosol Science · doi:10.1016/j.jaerosci.2004.05.010 · Cited by 99
Population Balance Modeling of Antibodies Aggregation Kinetics
Arosio, P., Rima, S., Lattuada, M., & Morbidelli, M. (2012) · The Journal of Physical Chemistry B · doi:10.1021/jp301091n · Cited by 95
Li, Z., Lu, P., Zhang, D., Chen, G., Zeng, S.-W., & He, Q. (2016) · Separation and Purification Technology · doi:10.1016/j.seppur.2016.02.011 · Cited by 96
Simulation of crystal size and shape by means of a reduced two-dimensional population balance model
Briesen, H. (2005) · Chemical Engineering Science · doi:10.1016/j.ces.2004.11.062 · Cited by 96
Attarakih, M. M., Bart, H.-J., & Faqir, N. M. (2004) · Chemical Engineering Science · doi:10.1016/j.ces.2004.03.005 · Cited by 93
“Among these methods, the >xed-pivot technique of Kumar and Ramkrishna (1996a), is the best candidate for this task.”
BackgroundMethodInfluentialModeling particle size distribution in emulsion polymerization reactors
Vale, H. M., & McKenna, T. F. L. (2005) · Progress in Polymer Science · doi:10.1016/j.progpolymsci.2005.06.006 · Cited by 92
“This method is also superior to the moving grid technique proposed by Kumar and Ramkrishna [143], as the latter is not well suited for problems involving nucleation.”
BackgroundMethodInfluentialAttarakih, M. M., Bart, H., & Faqir, N. M. (2005) · Chemical Engineering Science · doi:10.1016/j.ces.2004.12.055 · Cited by 92
Babakhani, P. (2019) · Scientific Reports · doi:10.1038/s41598-019-50493-6 · Cited by 89
Role of turbulent shear rate distribution in aggregation and breakage processes
Marchisio, D. L., Šoóš, M., Šefčı́k, J., & Morbidelli, M. (2005) · AIChE Journal · doi:10.1002/aic.10614 · Cited by 91
Further insights into the universality of colloidal aggregation
Sandkühler, P., Lattuada, M., Wu, H., Šefčı́k, J., & Morbidelli, M. (2005) · Advances in Colloid and Interface Science · doi:10.1016/j.cis.2004.12.001 · Cited by 91
Water Model and CFD-PBM Coupled Model of Gas-Liquid-Slag Three-Phase Flow in Ladle Metallurgy
Li, L., Liu, Z., Li, B., Matsuura, H., & Tsukihashi, F. (2015) · ISIJ International · doi:10.2355/isijinternational.55.1337 · Cited by 90
Modeling of bubble behaviors and size distribution in a slab continuous casting mold
Zhongqiu, L. I. U., Qi, F., Li, B. K., & Cheung, S. C. P. (2016) · International Journal of Multiphase Flow · doi:10.1016/j.ijmultiphaseflow.2015.07.009 · Cited by 90
An aerosol model to predict size and structure of soot particles
Park, S. H., Rogak, S. N., Bushe, W. K., Wen, J. Z., & Thomson, M. J. (2005) · Combustion Theory and Modelling · doi:10.1080/13647830500195005 · Cited by 89
Solution of population balance equations with a new combined Lax-Wendroff/Crank-Nicholson method
Bennett, M. K., & Rohani, S. (2001) · Chemical Engineering Science · doi:10.1016/s0009-2509(01)00314-1 · Cited by 87
Physics-informed machine learning for MPC: Application to a batch crystallization process
Wu, G., Tan, W. G. Y., Dang, K. L. N. Q., & Wu, Z. (2023) · Process Safety and Environmental Protection · doi:10.1016/j.cherd.2023.02.048 · Cited by 87
Singh, M., Shirazian, S., Ranade, V. V., Walker, G., & Kumar, A. (2022) · Powder Technology · doi:10.1016/j.powtec.2022.117380 · Cited by 90
Population balance modelling for bubbly flows with heat and mass transfer
Yeoh, G. H., & Tu, J. Y. (2004) · Chemical Engineering Science · doi:10.1016/j.ces.2004.04.023 · Cited by 85
COMPUTATIONAL MODELING OF GAS-LIQUID FLOW IN BUBBLE COLUMNS
Rafique, M., Chen, P., & Duduković, M. P. (2004) · Reviews in Chemical Engineering · doi:10.1515/revce.2004.20.3-4.225 · Cited by 86
“Saffman force As described by Lahey (1990) and Jakobsen (1993), a non rotating particle experiences a similar lateral force when placed in a shear flow field.”
BackgroundFundamental consideration of wall heat partition of vertical subcooled boiling flows
Yeoh, G. H., Cheung, S. C. P., Tu, J. Y., & Ho, M. K. M. (2008) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2007.11.047 · Cited by 87
Numerical Simulations of Inclusion Behavior in Gas-Stirred Ladles
Lou, W., & Zhu, M. (2013) · Metallurgical and Materials Transactions B · doi:10.1007/s11663-013-9802-3 · Cited by 86
Comparison of numerical methods for the simulation of dispersed phase systems
Motz, S., Mitrović, A., & Gilles, E. D. (2002) · Chemical Engineering Science · doi:10.1016/s0009-2509(02)00349-4 · Cited by 86
Evolution of primary and aggregate particle‐size distributions by coagulation and sintering
Tsantilis, S., & Pratsinis, S. E. (2000) · AIChE Journal · doi:10.1002/aic.690460218 · Cited by 86
Lim, Y. I., Lann, J.-M. L., Meyer, X.-M., Joulia, X., Lee, G., & Yoon, E. S. (2002) · Chemical Engineering Science · doi:10.1016/s0009-2509(02)00236-1 · Cited by 84
Bubble Sizes, Breakup, and Coalescence in Deepwater Gas/Oil Plumes
Bandara, U. C., & Yapa, P. D. (2011) · Journal of Hydraulic Engineering · doi:10.1061/(asce)hy.1943-7900.0000380 · Cited by 86
Zauner, R., & Jones, A. G. (2002) · Chemical Engineering Science · doi:10.1016/s0009-2509(01)00417-1 · Cited by 82
Alexopoulos, A. H., Roussos, A. I., & Kiparissides, C. A. (2004) · Chemical Engineering Science · doi:10.1016/j.ces.2004.06.021 · Cited by 82
Resolved simulations of single iron particle combustion and the release of nano-particles
Thijs, L. C., van Gool, C. E. A. G., Ramaekers, W. G., van Oijen, J. A., & de Goey, L. P. H. (2022) · Proceedings of the Combustion Institute · doi:10.1016/j.proci.2022.07.044 · Cited by 81
Solving population balance equations for two-component aggregation by a finite volume scheme
Qamar, S., & Warnecke, G. (2006) · Chemical Engineering Science · doi:10.1016/j.ces.2006.10.001 · Cited by 81
Mechanistic modelling of fluidized bed drying processes of wet porous granules: A review
Mortier, S. T. F. C., Beer, T. D., Gernaey, K. V., Remon, J. P., Vervaet, C., & Ingmar Nopens, A. (2011) · European Journal of Pharmaceutics and Biopharmaceutics · doi:10.1016/j.ejpb.2011.05.013 · Cited by 80
Liu, Z., Li, L., Qi, F., Li, B., Jiang, M., & Tsukihashi, F. (2014) · Metallurgical and Materials Transactions B · doi:10.1007/s11663-014-0192-y · Cited by 79
High-shear granulation modeling using a discrete element simulation approach
Gantt, J. A., & Gatzke, E. P. (2005) · Powder Technology · doi:10.1016/j.powtec.2005.04.012 · Cited by 79
Šoóš, M., Šefčı́k, J., & Morbidelli, M. (2005) · Chemical Engineering Science · doi:10.1016/j.ces.2005.11.001 · Cited by 79
Gao, Z., Li, D., Buffo, A., Podgórska, W., & Marchisio, D. L. (2015) · Chemical Engineering Science · doi:10.1016/j.ces.2015.11.040 · Cited by 79
“Many methods have been developed to solve the PBM, such as the classes method (CM) (Kumar and Ramkrishna, 1996), the Monte Carlo method (MCM)(Lin et al., 2002; Buffo et al., 2013b; Zhang and You, 2015; Hussain et al., 2015) and the method of moments (MOM) (Hulburt and Katz, 1964).”
MethodMonitoring polymer flocculation in oil sands tailings: A population balance model approach
Vajihinejad, V., & Soares, J. B. P. (2018) · Chemical Engineering Journal · doi:10.1016/j.cej.2018.04.039 · Cited by 78
Numerical simulation of micro-bubble drag reduction using population balance model
Mohanarangam, K., Cheung, S. C. P., Tu, J. Y., & Chen, L. (2009) · Ocean Engineering · doi:10.1016/j.oceaneng.2009.05.001 · Cited by 80
Robust control of particulate processes using uncertain population balances
Chiu, T. Y., & Christofides, P. D. (2000) · AIChE Journal · doi:10.1002/aic.690460207 · Cited by 77
Meimaroglou, D., & Kiparissides, C. A. (2014) · Industrial & Engineering Chemistry Research · doi:10.1021/ie4033044 · Cited by 77
Crystallization: Key thermodynamic, kinetic and hydrodynamic aspects
Vedantam, S., & Ranade, V. V. (2013) · Sadhana · doi:10.1007/s12046-013-0195-4 · Cited by 76
CFD modeling of the mixing of water in oil emulsions
Roudsari, S. F., Turcotte, G., Dhib, R., & Ein‐Mozaffari, F. (2012) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2012.06.013 · Cited by 77
Hanhoun, M., Montastruc, L., Azzaro‐Pantel, C., Biscans, B., Freche, M., & Pibouleau, L. G. (2012) · Chemical Engineering Journal · doi:10.1016/j.cej.2012.10.038 · Cited by 73
Liu, Y., & Hinrichsen, O. (2014) · Computers & Fluids · doi:10.1016/j.compfluid.2014.09.023 · Cited by 76
Metadata
- Authors
- Kumar, S., & Ramkrishna, D.
- Affiliations
- Purdue University West Lafayette (US)
- Corresponding author
- Ramkrishna, D.
- Venue
- Chemical Engineering Science
- Publisher
- Elsevier BV
- Published
- 1996-04
- Volume
- 51
- Issue
- 8
- Pages
- 1311-1332
- ISSN
- 0009-2509 (ISSN-L)
- OpenAlex
- W4249613604
- Cited by
- 1,109
- References
- 21
- Citations by year
- 2026: 55 · 2025: 50 · 2024: 36 · 2023: 48 · 2022: 47 · 2021: 61 · 2020: 52 · 2019: 67 · 2018: 51 · 2017: 48 · 2016: 44 · 2015: 43 · 2014: 55 · 2013: 57 · 2012: 29
- FWCI
- 7.75
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Chemical Engineering Science (publishedVersion)
- Topics
- Physical Sciences › Engineering › Computational Mechanics › Granular flow and fluidized beds
- Physical Sciences › Chemical Engineering › Fluid Flow and Transfer Processes › Fluid Dynamics and Mixing
- Physical Sciences › Engineering › Mechanical Engineering › Mineral Processing and Grinding
- Keywords
- population balance equation, discretization, aggregation, breakage, mesh refinement, representative volume element, aerosol dynamics
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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