The DOI matches its Crossref record; 11 of the 11 references it cites were found in a registry or an index.
Continuous flow systems. Distribution of residence times
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
“Accounting for deviations from perfect mixing and piston flow and assuming negligible transport lags in connecting lines, [26] the Danckwerts boundary conditions have become an inseparable part of modelling axial tubular reactors in the field of chemical engineering process control and dynamics.”
From Optimal control of axial dispersion tubular reactors with recycle: Addressing state‐delay through transport PDEs (2025) · cites this paper as [26]
Citations
Cites
Present, R. D. (1958) · McGraw-Hill eBooks · Cited by 1,995
Lapidus, L., & Amundson, N. R. (1952) · The Journal of Physical Chemistry · doi:10.1021/j150500a014 · Cited by 947
The definition and measurement of some characteristics of mixtures
Danckwerts, P. V. (1952) · Applied Scientific Research · doi:10.1007/bf03184936 · Cited by 898
Self-citationVelocities and Effective Thermal Conductivities in Packed Beds
Morales, M., Spinn, C. W., & Smith, J. M. (1951) · Industrial & Engineering Chemistry · doi:10.1021/ie50493a055 · Cited by 89
Gas and Solid Mixing in Fluidized Beds
Gilliland, E. R., & Mason, E. A. (1949) · Industrial & Engineering Chemistry · doi:10.1021/ie50474a013 · Cited by 83
GAS MIXING IN BEDS OF FLUIDIZED SOLIDS
Gilliland, E. R., & Mason, E. A. (1952) · Industrial & Engineering Chemistry · doi:10.1021/ie50505a060 · Cited by 79
C. Distribution of reaction times for laminar flow in cylindrical reactors
Bosworth, R. C. L. (1948) · The London Edinburgh and Dublin Philosophical Magazine and Journal of Science · doi:10.1080/14786444808521811 · Cited by 69
The kinetics of continuous reaction processes: Application to polymerization
Denbigh, K. G. (1951) · Journal of Applied Chemistry · doi:10.1002/jctb.5010010508 · Cited by 48
Radioactive Tracers to Mark Interfaces and Measure Intermixing in Pipelines
Hull, D. E., & Kent, J. W. (1952) · Industrial & Engineering Chemistry · doi:10.1021/ie50515a066 · Cited by 46
XXIX. Distribution of reaction times for turbulent flow in cylindrical reactors
Bosworth, R. C. L. (1949) · The London Edinburgh and Dublin Philosophical Magazine and Journal of Science · doi:10.1080/14786444908561253 · Cited by 28
Research works printed but not linked: 8
- Beaudry, 1948, Chem. Engng, 55, 112
- Danckwerts, 1951, Ind. Chemist, 27, 395
- Danckwerts, 1952, Coke and Gas, 14, 247
- Fowler, 1943, Trans. Amer. Inst. Chem. Engng, 39, 491
- Hull, 1949, World Oil, 129, 188
- Smith, 1948, Petroleum Engng, 19, 94
- Smith, 1948, Petroleum Engng, 20, 330
- Bernard, 1950, Chem. Engng. Prog., 46, 233
Cited by
Sorted by citations
A solution of the differential equation of longitudinal dispersion in porous media
Ogata, A., & Banks, R. B. (1961) · USGS professional paper · doi:10.3133/pp411a · Cited by 966
A review and evaluation of catchment transit time modeling
McGuire, K. J., & McDonnell, J. J. (2006) · Journal of Hydrology · doi:10.1016/j.jhydrol.2006.04.020 · Cited by 919
Developments in the theory of particle mixing
Lacey, P. (1954) · Journal of Applied Chemistry · doi:10.1002/jctb.5010040504 · Cited by 803
A critical review of dispersion in packed beds
Delgado, J. M. P. Q. (2005) · Heat and Mass Transfer · doi:10.1007/s00231-005-0019-0 · Cited by 491
Spatial variability of the leaching characteristics of a field soil
Biggar, J. W., & Nielsen, D. R. (1976) · Water Resources Research · doi:10.1029/wr012i001p00078 · Cited by 460
Metadata
- Authors
- Danckwerts, P. V.
- Affiliations
- University of Cambridge (GB)
- Corresponding author
- Danckwerts, P.V.
- Venue
- Chemical Engineering Science
- Publisher
- Elsevier BV
- Published
- 1995-12
- Volume
- 50
- Issue
- 24
- Pages
- 3857-3866
- ISSN
- 0009-2509 (ISSN-L)
- OpenAlex
- W2107475321
- Cited by
- 1,274
- References
- 11
- Citations by year
- 2026: 16 · 2025: 17 · 2024: 7 · 2023: 15 · 2022: 13 · 2021: 42 · 2020: 27 · 2019: 44 · 2018: 53 · 2017: 36 · 2016: 44 · 2015: 49 · 2014: 51 · 2013: 57 · 2012: 55
- FWCI
- 30.39
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Chemical Engineering Science (publishedVersion)
- Topics
- Physical Sciences › Chemical Engineering › Fluid Flow and Transfer Processes › Fluid Dynamics and Mixing
- Physical Sciences › Engineering › Computational Mechanics › Heat and Mass Transfer in Porous Media
- Physical Sciences › Chemical Engineering › Fluid Flow and Transfer Processes › Innovative Microfluidic and Catalytic Techniques Innovation
- Keywords
- residence time distribution, continuous flow system, open tube, reactor efficiency, non-ideal flow, plug flow, ideal mixing
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
