Drag coefficient and relative velocity in bubbly, droplet or particulate flows
Abstract
Abstract Drag coefficient and relative motion correlations for dispersed two‐phase flows of bubbles, drops, and particles were developed from simple similarity criteria and a mixture viscosity model. The results are compared with a number of experimental data, and satisfactory agreements are obtained at wide ranges of the particle concentration and Reynolds number. Characteristics differences between fluid particle systems and solid particle systems at higher Reynolds numbers or at higher concentration regimes were successfully predicted by the model. Results showed that the drag law in various dispersed two‐phase flows could be put on a general and unified base by the present method.
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?
Ishii and Zuber [258] considered the dense particle effect in the computation of the drag coefficient utilizing a mixture viscosity, and the drag coefficient assumes different forms depending on the flow regimes (viscous, distorted particle, churn turbulent).
“Ishii and Zuber [258] considered the dense particle effect in the computation of the drag coefficient utilizing of a mixture viscosity. The drag coefficient assumes different forms depending on the flow regimes, i.e., the viscous CD ( sphere ) , the distorted particle CD ( ellipse ) , and the churn turbulent flow regime CD ( cap ) .”
From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [258]
Cites
One Dimensional Two-Phase Flow
Wallis, G. B. (1969) · CERN Document Server (European Organization for Nuclear Research) · Cited by 4,886 · see citing works
The Viscosity of Concentrated Suspensions and Solutions
Brinkman, H. (1952) · The Journal of Chemical Physics · doi:10.1063/1.1700493 · Cited by 4,628 · see citing works
Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes
Hinze, J. O. (1955) · AIChE Journal · doi:10.1002/aic.690010303 · Cited by 2,653 · see citing works
Average Volumetric Concentration in Two-Phase Flow Systems
Zuber, N., & Findlay, J. A. (1965) · ASME Journal of Heat and Mass Transfer · doi:10.1115/1.3689137 · Cited by 2,528 · see citing works
Self-citationWen, C. Y. (1966) · Medical Entomology and Zoology · Cited by 2,311 · see citing works
The viscosity of a fluid containing small drops of another fluid
Taylor, G. I. (1932) · Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical Character · doi:10.1098/rspa.1932.0169 · Cited by 1,971 · see citing works
Thermo-fluid dynamic theory of two-phase flow
(1976) · International Journal of Multiphase Flow · doi:10.1016/0301-9322(76)90008-2 · Cited by 1,551 · see citing works
Thomas, D. G. (1965) · Journal of Colloid Science · doi:10.1016/0095-8522(65)90016-4 · Cited by 1,158 · see citing works
The viscosity of suspensions of rigid spheres
Roscoe, R. (1952) · British Journal of Applied Physics · doi:10.1088/0508-3443/3/8/306 · Cited by 1,143 · see citing works
Viscous flow in multiparticle systems: Slow motion of fluids relative to beds of spherical particles
Happel, J. A. (1958) · AIChE Journal · doi:10.1002/aic.690040214 · Cited by 994 · see citing works
Ishii, M. (1977) · doi:10.2172/6871478 · Cited by 752 · see citing works
Self-citationOn the viscosity of a concentrated suspension of solid spheres
Frankel, N. A., & Acrivos, A. (1967) · Chemical Engineering Science · doi:10.1016/0009-2509(67)80149-0 · Cited by 731 · see citing works
Velocity of large drops and bubbles in media of infinite or restricted extent
Harmathy, T. Z. (1960) · AIChE Journal · doi:10.1002/aic.690060222 · Cited by 635 · see citing works
(1889) · Nature · doi:10.1038/040412a0 · Cited by 632 · see citing works
Die Viskosität von Emulsionen hochviskoser Stoffe als Funktion der Konzentration
Eilers, H. (1941) · Colloid & Polymer Science · doi:10.1007/bf01503023 · Cited by 543 · see citing works
Inception criteria for droplet entrainment in two‐phase concurrent film flow
Ishii, M., & Grolmes, M. A. (1975) · AIChE Journal · doi:10.1002/aic.690210212 · Cited by 483 · see citing works
Self-citationOn the dispersed two-phase flow in the laminar flow regime
Zuber, N. (1964) · Chemical Engineering Science · doi:10.1016/0009-2509(64)85067-3 · Cited by 452 · see citing works
Self-citationTchen, C. M. (1947) · Research Repository (Delft University of Technology) · Cited by 337 · see citing works
Convective boiling and condensation
Griffith, P. (1973) · International Journal of Heat and Mass Transfer · doi:10.1016/0017-9310(73)90198-1 · Cited by 323 · see citing works
Rate of sedimentation.Nonflocculated Suspensions of Uniform Spheres
Steinour, H. H. (1944) · Industrial & Engineering Chemistry · doi:10.1021/ie50415a005 · Cited by 264 · see citing works
CARRIER, G. F. (1958) · Journal of Fluid Mechanics · doi:10.1017/s0022112058000513 · Cited by 200 · see citing works
Performance of gas bubble columns: Volumetric liquid‐phase mass transfer coefficient and gas holdup
Yoshida, F., & Akita, K. (1965) · AIChE Journal · doi:10.1002/aic.690110106 · Cited by 161 · see citing works
The terminal speed of single drops or bubbles in an infinite medium
Wallis, G. B. (1974) · International Journal of Multiphase Flow · doi:10.1016/0301-9322(74)90003-2 · Cited by 156 · see citing works
Fluidization and fluid-particle systems
Botterill, J. S. M. (1961) · Combustion and Flame · doi:10.1016/0010-2180(61)90084-0 · Cited by 110 · see citing works
Miles, G. D., Shedlovsky, L., & Ross, J. (1945) · The Journal of Physical Chemistry · doi:10.1021/j150440a006 · Cited by 99 · see citing works
Spray liquid-liquid extraction columns :
Thornton, J. D. (1956) · Chemical Engineering Science · doi:10.1016/0009-2509(56)80031-6 · Cited by 85 · see citing works
Fluidization and sedimentation of spherical particles
Hanratty, T. J., & Bandukwala, A. (1957) · AIChE Journal · doi:10.1002/aic.690030230 · Cited by 71 · see citing works
Gasblasen in Flüssigkeiten. Teil II: Der Aufstieg von Gasblasen in Flüssigkeiten
Siemes, W. (1954) · Chemie Ingenieur Technik · doi:10.1002/cite.330261109 · Cited by 55 · see citing works
Particulate fluidization and sedimentation of spheres
Loeffler, A. L., & Rüth, B. (1959) · AIChE Journal · doi:10.1002/aic.690050312 · Cited by 53 · see citing works
The mechanics of vertical gas‐liquid fluidized system I: Countercurrent flow
Bridge, A. G., Lapidus, L., & Elgin, J. C. (1964) · AIChE Journal · doi:10.1002/aic.690100610 · Cited by 52 · see citing works
Constitutive equation for vapor drift velocity in two‐phase annular flow
Ishii, M., Chawla, T. C., & Zuber, N. (1976) · AIChE Journal · doi:10.1002/aic.690220210 · Cited by 50 · see citing works
Self-citation(1962) · Elsevier eBooks · doi:10.1016/b978-0-12-395556-2.x5001-5 · Cited by 43 · see citing works
Fluid-Dynamic Characteristics of Two-Phase Flow
Serizawa, A. (1974) · Institutional Repositories DataBase (IRDB) · doi:10.14989/doctor.k1513 · Cited by 38 · see citing works
The mechanics of a spray column
Letan, R., & Kehat, E. (1967) · AIChE Journal · doi:10.1002/aic.690130311 · Cited by 30 · see citing works
Weaver, R. E. C., Lapidus, L., & Elgin, J. C. (1959) · AIChE Journal · doi:10.1002/aic.690050423 · Cited by 28 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Large eddy simulation of the Gas–Liquid flow in a square cross-sectioned bubble column
Deen, N. G., Solberg, T., & Hjertager, B. H. (2001) · Chemical Engineering Science · doi:10.1016/s0009-2509(01)00249-4 · Cited by 341 · 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
Joshi, J. B., Nere, N. K., Rane, C. V., Murthy, B. N., Mathpati, C. S., Patwardhan, A. W., & Ranade, V. V. (2011) · The Canadian Journal of Chemical Engineering · doi:10.1002/cjce.20465 · Cited by 131 · see citing works
Gupta, A., & Roy, S. (2013) · Chemical Engineering Journal · doi:10.1016/j.cej.2012.11.012 · Cited by 125 · see citing works
Luo, H.-P., & Al-Dahhan, M. H. (2011) · Chemical Engineering Science · doi:10.1016/j.ces.2010.11.038 · Cited by 122 · see citing works
Flow Generated by an Aerated Rushton Impeller: Two-phase PIV Experiments and Numerical Simulations
Deen, N. G., Solberg, T., & Hjertager, B. H. (2002) · The Canadian Journal of Chemical Engineering · doi:10.1002/cjce.5450800406 · Cited by 112 · see citing works
Measurement of local flow characteristics in buoyancy-driven bubbly flow at high void fraction
Garnier, C., Lance, M., & Marié, J. L. (2002) · Experimental Thermal and Fluid Science · doi:10.1016/s0894-1777(02)00198-x · Cited by 111 · see citing works
Simulation of coalescence, break-up and mass transfer in a gas-liquid stirred tank with CQMOM
Petitti, M., Vanni, M., Marchisio, D. L., Buffo, A., & Podenzani, F. (2013) · Chemical Engineering Journal · doi:10.1016/j.cej.2013.05.047 · Cited by 90 · see citing works
Comparative study of wall-force models for the simulation of bubbly flows
Rzehak, R., Krepper, E., & Lifante, C. (2012) · Nuclear Engineering and Design · doi:10.1016/j.nucengdes.2012.07.009 · Cited by 66 · see citing works
Fluid dynamics in a bubble column: New experiments and simulations
Rzehak, R., Krauß, M., Kováts, P., & Zähringer, K. (2017) · International Journal of Multiphase Flow · doi:10.1016/j.ijmultiphaseflow.2016.09.024 · Cited by 61 · see citing works
Modelling of a RDC using a combined CFD-population balance approach
Vikhansky, A., & Kraft, M. (2004) · Chemical Engineering Science · doi:10.1016/j.ces.2004.02.016 · Cited by 59 · see citing works
Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review
Luzi, G., & McHardy, C. (2022) · Energies · doi:10.3390/en15113966 · Cited by 44 · see citing works
Luzi, G., McHardy, C., Lindenberger, C., Rauh, C., & Delgado, A. (2019) · Algal Research · doi:10.1016/j.algal.2018.101404 · Cited by 24 · see citing works
Coalescence and Break-Up in Bubble Columns: Euler-Lagrange Simulations Using a Stochastic Approach
Gruber, M. C., Radl, S., & Khinast, J. G. (2013) · Chemie Ingenieur Technik · doi:10.1002/cite.201300024 · Cited by 18 · see citing works
Numerical simulation of interfacial closures for 3D bubble column flows
Masood, R. M. A., Jovicic, V., & Delgado, A. (2015) · Chemical Engineering & Technology · doi:10.1002/ceat.201400182 · Cited by 4 · see citing works
- Authors
- Ishii, M., & Zuber, N.
- Affiliations
- Argonne National Laboratory (US)
- United States Nuclear Regulatory Commission (US)
- Corresponding author
- Ishii, Mamoru
- ORCID
- Ishii, Mamoru
- Venue
- AIChE Journal
- Publisher
- Wiley
- Published
- 1979-09
- Volume
- 25
- Issue
- 5
- Pages
- 843-855
- ISSN
- 0001-1541 (ISSN-L)
- 1547-5905
- OpenAlex
- W2153492345
- Cited by
- 2,031
- References
- 35
- Citations by year
- 2026: 109 · 2025: 107 · 2024: 117 · 2023: 108 · 2022: 124 · 2021: 119 · 2020: 111 · 2019: 88 · 2018: 102 · 2017: 113 · 2016: 77 · 2015: 69 · 2014: 67 · 2013: 61 · 2012: 54
- FWCI
- 3.79
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- AIChE Journal (publishedVersion)
- Funders
- U.S. Nuclear Regulatory Commission
- Topics
- Physical Sciences › Engineering › Ocean Engineering › Particle Dynamics in Fluid Flows
- Physical Sciences › Engineering › Biomedical Engineering › Fluid Dynamics and Mixing
- Physical Sciences › Engineering › Computational Mechanics › Fluid Dynamics and Heat Transfer
- Keywords
- drag coefficient, relative velocity, dispersed two-phase flow, bubbly flow, droplet flow, particulate flow, similarity criteria, particle concentration, Reynolds number, drag law
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