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
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“It has been shown that for population balance models for aggregation and breakage phenomena, a sectional method like fixed pivot techniques approximates the behavior of the system sufficiently accurate [24].”
BackgroundMethodLehnigk, R., Bainbridge, W., Liao, Y., Lucas, D., Niemi, T., Peltola, J., & Schlegel, F. (2021) · AIChE Journal · doi:10.1002/aic.17539 · Cited by 44
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“Kumar and Ramkrishna (1996) use pivotal points to ensure mass conservation in the system and Zhang and Li (2003) use the section approximation method.”
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“The fixed pivot (FP) technique is simple to implement and is computationally attractive [34].”
BackgroundAdvanced Polymer Flocculants for Solid–Liquid Separation in Oil Sands Tailings
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“Since pivots may naturally move away from the nuclei size, Kumar and Ramkrishna [23] proposed to frequently add a bin whose pivot is located at the nuclei size to the left of the leftmost bin.”
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“In this work we study the convergence of the fixed pivot techniques (Kumar and Ramkrishna, 1996, Chem.”
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“The fixed-pivot technique (Kumar and Ramkrishna, 1996; Nopens et al., 2005) was applied to an evenly distributed discretization grid with 166 pivots (in the range [m0, mf]¼ [0, 2000]).”
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On the attainment of steady state in turbulent pipe flow of dilute dispersions
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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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