On the solution of population balance equations by discretization—I. A fixed pivot technique
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Kumar and Ramkrishna [292] presented a framework for discretization of PBEs where particle populations in discrete size ranges are concentrated only in representative volumes, and coarseness can be varied freely without a specific geometric type.
“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]
Kumar and Ramkrishna [292] technique applied to binary and multiple breakages, aggregation with constant, sum, and product kernels, and simultaneous breakage and aggregation; comparison between analytical and numerical results shows good agreement.
“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]
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 · see citing works
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 · see citing works
Self-citationSectional representations for simulating aerosol dynamics
Gelbard, F., Tambour, Y., & Seinfeld, J. H. (1980) · Journal of Colloid and Interface Science · doi:10.1016/0021-9797(80)90394-x · Cited by 607 · see citing works
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 · see citing works
The Status of Population Balances
Ramkrishna, D. (1985) · Reviews in Chemical Engineering · doi:10.1515/revce.1985.3.1.49 · Cited by 393 · see citing works
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 · see citing works
Marchal, P., David, R., Klein, J. P., & Villermaux, J. (1988) · Chemical Engineering Science · doi:10.1016/0009-2509(88)87126-4 · Cited by 257 · see citing works
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 · see citing works
The general dynamic equation for aerosols. Theory and application to aerosol formation and growth
Gelbard, F., & Seinfeld, J. H. (1979) · Journal of Colloid and Interface Science · doi:10.1016/0021-9797(79)90289-3 · Cited by 170 · see citing works
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 · see citing works
Scaling solutions of Smoluchowski's coagulation equation
van Dongen, P. G. J., & Ernst, M. H. (1988) · Journal of Statistical Physics · doi:10.1007/bf01022996 · Cited by 167 · see citing works
On the theory of the coagulation of noninteracting particles in brownian motion
Hidy, G. M. (1965) · Journal of Colloid Science · doi:10.1016/0095-8522(65)90003-6 · Cited by 146 · see citing works
Analysis of drop size distributions in lean liquid‐liquid dispersions
Narsimhan, G., Ramkrishna, D., & Gupta, J. P. (1980) · AIChE Journal · doi:10.1002/aic.690260614 · Cited by 136 · see citing works
Self-citationA fast, approximative method for integrating the stochastic coalescence equation
Bleck, R. (1970) · Journal of Geophysical Research Atmospheres · doi:10.1029/jc075i027p05165 · Cited by 108 · see citing works
Evaluation of Zero Order Methods for Simulating Particle Coagulation
Kostoglou, M., & Karabelas, A. J. (1994) · Journal of Colloid and Interface Science · doi:10.1006/jcis.1994.1121 · Cited by 80 · see citing works
A new model for the breakage frequency of drops in turbulent stirred dispersions
Nambiar, D. K. R., Kumari, R., Das, T. R., & Gandhi, K. S. (1992) · Chemical Engineering Science · doi:10.1016/0009-2509(92)87001-7 · Cited by 76 · see citing works
PELLETIZING KINETICS AND SIMULATION OF FULL SCALE BALLING CIRCUITS.
Batterham, R., Hall, J., & Barton, G. J. (1981) · Cited by 74 · see citing works
Simulation of particle size distribution in an aggregation-breakup process
Chen, W., Fischer, R. R., & Berg, J. C. (1990) · Chemical Engineering Science · doi:10.1016/0009-2509(90)80201-o · Cited by 55 · see citing works
Discretization procedure for the coalescence equation of particulate processes
Sastry, K. V. S., & Gaschignard, P. (1981) · Industrial & Engineering Chemistry Fundamentals · doi:10.1021/i100004a010 · Cited by 34 · see citing works
Modelling shear-flocculation by population balances
Koh, P. T. L., Andrews, J. R. G., & Uhlherr, P. H. T. (1987) · Chemical Engineering Science · doi:10.1016/0009-2509(87)85065-0 · Cited by 34 · see citing works
Analytic Studies of Cloud Droplet Coalescence I
Scott, W. T. (1968) · Journal of the Atmospheric Sciences · doi:10.1175/1520-0469(1968)025
Flagged first, then by citations
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 · see citing works
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 · see citing works
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 · see citing works
Self-citationKumar, S., & Ramkrishna, D. (1997) · Chemical Engineering Science · doi:10.1016/s0009-2509(97)00307-2 · Cited by 350 · see citing works
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 · see citing works
Numerical 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 293 · see citing works
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 268 · see citing works
Self-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 · see citing works
Advanced control of crystallization processes
Braatz, R. D. (2002) · Annual Reviews in Control · doi:10.1016/s1367-5788(02)80016-5 · Cited by 239 · see citing works
Multiphase Porous Electrode Theory
Smith, R. B., & Bazant, M. Z. (2017) · Journal of The Electrochemical Society · doi:10.1149/2.0171711jes · Cited by 230 · see citing works
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 · see citing works
Jacobson, M. Z. (2002) · Journal of Geophysical Research Atmospheres · doi:10.1029/2001jd002044 · Cited by 227 · see citing works
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 · see citing works
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 203 · see citing works
Self-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 201 · see citing works
Alopaeus, V., Koskinen, J., & Keskinen, K. I. (1999) · Chemical Engineering Science · doi:10.1016/s0009-2509(99)00170-0 · Cited by 201 · see citing works
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 198 · see citing works
Tyagi, H., Kushwaha, A., Kumar, A., & Aslam, M. (2016) · Nanoscale Research Letters · doi:10.1186/s11671-016-1576-5 · Cited by 196 · see citing works
Population 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 194 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 159 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 140 · see citing works
Gan, Y., & Qiao, L. (2011) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2011.07.003 · Cited by 136 · see citing works
Nonlinear control of particulate processes
Chiu, T. Y., & Christofides, P. D. (1999) · AIChE Journal · doi:10.1002/aic.690450613 · Cited by 132 · see citing works
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 · see citing works
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 · see citing works
Sommer, M., Stenger, F., Peukert, W., & Wagner, N. J. (2005) · Chemical Engineering Science · doi:10.1016/j.ces.2004.12.057 · Cited by 123 · see citing works
Buffo, A., Vanni, M., & Marchisio, D. L. (2011) · Chemical Engineering Science · doi:10.1016/j.ces.2011.04.042 · Cited by 122 · see citing works
Kotoulas, C., & Kiparissides, C. A. (2005) · Chemical Engineering Science · doi:10.1016/j.ces.2005.07.013 · Cited by 121 · see citing works
Kumar, J., Peglow, M., Warnecke, G., & Heinrich, S. (2007) · Powder Technology · doi:10.1016/j.powtec.2007.05.028 · Cited by 121 · see citing works
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 · see citing works
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 · see citing works
Kiparissides, C. A. (2005) · Journal of Process Control · doi:10.1016/j.jprocont.2005.06.004 · Cited by 119 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 113 · see citing works
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 · see citing works
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 · see citing works
Immanuel, C. D., & Doyle, F. J. (2003) · Chemical Engineering Science · doi:10.1016/s0009-2509(03)00216-1 · Cited by 110 · see citing works
Zauner, R., & Jones, A. G. (2000) · Chemical Engineering Science · doi:10.1016/s0009-2509(00)00059-2 · Cited by 108 · see citing works
Li, G., Yang, X., & Dai, G. (2009) · Chemical Engineering Science · doi:10.1016/j.ces.2009.08.016 · Cited by 107 · see citing works
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 · see citing works
Bannari, R., Kerdouss, F., Selma, B., Bannari, A., & Proulx, P. (2008) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2008.05.016 · Cited by 106 · see citing works
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 · see citing works
Selma, B., Bannari, R., & Proulx, P. (2010) · Chemical Engineering Science · doi:10.1016/j.ces.2009.11.018 · Cited by 103 · see citing works
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 · see citing works
Netzell, K., Lehtiniemi, H., & Mauß, F. (2006) · Proceedings of the Combustion Institute · doi:10.1016/j.proci.2006.08.081 · Cited by 101 · see citing works
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 100 · see citing works
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 · see citing works
The 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 · see citing works
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 · see citing works
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 98 · see citing works
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 · see citing works
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 · see citing works
Attarakih, M. M., Bart, H.-J., & Faqir, N. M. (2004) · Chemical Engineering Science · doi:10.1016/j.ces.2004.03.005 · Cited by 93 · see citing works
Modeling 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 · see citing works
Attarakih, M. M., Bart, H., & Faqir, N. M. (2005) · Chemical Engineering Science · doi:10.1016/j.ces.2004.12.055 · Cited by 92 · see citing works
Babakhani, P. (2019) · Scientific Reports · doi:10.1038/s41598-019-50493-6 · Cited by 89 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 89 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
Singh, M., Shirazian, S., Ranade, V. V., Walker, G., & Kumar, A. (2022) · Powder Technology · doi:10.1016/j.powtec.2022.117380 · Cited by 90 · see citing works
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 86 · see citing works
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 · see citing works
Fundamental 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 86 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 83 · see citing works
Zauner, R., & Jones, A. G. (2002) · Chemical Engineering Science · doi:10.1016/s0009-2509(01)00417-1 · Cited by 82 · see citing works
Alexopoulos, A. H., Roussos, A. I., & Kiparissides, C. A. (2004) · Chemical Engineering Science · doi:10.1016/j.ces.2004.06.021 · Cited by 82 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
Šoóš, M., Šefčı́k, J., & Morbidelli, M. (2005) · Chemical Engineering Science · doi:10.1016/j.ces.2005.11.001 · Cited by 79 · see citing works
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 · see citing works
Monitoring 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 · see citing works
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 78 · see citing works
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 · see citing works
Meimaroglou, D., & Kiparissides, C. A. (2014) · Industrial & Engineering Chemistry Research · doi:10.1021/ie4033044 · Cited by 77 · see citing works
Crystallization: Key thermodynamic, kinetic and hydrodynamic aspects
Vedantam, S., & Ranade, V. V. (2013) · Sadhana · doi:10.1007/s12046-013-0195-4 · Cited by 76 · see citing works
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 74 · see citing works
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 · see citing works
Liu, Y., & Hinrichsen, O. (2014) · Computers & Fluids · doi:10.1016/j.compfluid.2014.09.023 · Cited by 73 · see citing works
- 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 › Engineering › Biomedical Engineering › 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 ›
Are you an author, or do you see a problem with this page? Request a review