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
Overview
Integrity signals
Registry
Cites
Statistics
Verification
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?
In the citing paper
“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
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
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
Ramkrishna, D. (1985) · Reviews in Chemical Engineering · doi:10.1515/revce.1985.3.1.49 · Cited by 393
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
Gelbard, F., & Seinfeld, J. H. (1979) · Journal of Colloid and Interface Science · doi:10.1016/0021-9797(79)90289-3 · Cited by 170
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).”
Method
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 ›
Are you an author, or do you see a problem with this page? Request a review
