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@article{stokes1851,
author = {{Stokes}, G.~G.},
title = "{On the Effect of the Internal Friction of Fluids on the Motion of Pendulums}",
journal = {Transactions of the Cambridge Philosophical Society},
year = 1851,
month = jan,
volume = {9},
pages = {8}
}
@book{kundu2015fluid,
title={Fluid Mechanics},
author={Kundu, P.K. and Cohen, I.M. and Dowling, D.R.},
isbn={9780124071513},
url={https://books.google.no/books?id=EehDBAAAQBAJ},
year={2015},
publisher={Academic Press}
}
@book{happel2012low,
title={Low Reynolds number hydrodynamics: with special applications to particulate
media},
author={Happel, J. and Brenner, H.},
isbn={9789400983526},
series={Mechanics of Fluids and Transport Processes},
url={https://books.google.no/books?id=u-ptCQAAQBAJ},
year={2012},
publisher={Springer Netherlands}
}
@article{laurez2025bridging,
title = {Numerical investigation and stochastic modeling of particle bridging under various
flow, pore, and particle properties},
journal = {Advances in Water Resources},
volume = {206},
pages = {105158},
year = {2025},
issn = {0309-1708},
doi = {https://doi.org/10.1016/j.advwatres.2025.105158},
url = {https://www.sciencedirect.com/science/article/pii/S0309170825002726},
author = {Laurez {Fogouang Maya} and Laurent André and Cyprien Soulaine},
keywords = {Pore-clogging, Particle transport, Bridging, CFD-DEM, Computational
microfluidics, Discrete stochastic},
abstract = {A complex interplay of fluid, particle, and pore properties influences the
stochastic nature of particle bridging in confined channels. This study investigates the role
of constriction angle, particle Reynolds number, particle concentration, particle-to
constriction size ratio, and constriction smoothness in clogging behavior within semidilute
suspensions. A coupled CFD-DEM approach was used to simulate particle transport through
a constricted channel, and a discrete stochastic model was developed to describe the
statistical nature of clogging events. The model characterizes clogging through the average
number of particles, or escapees, that pass through a constriction before a stable arch
forms. Results show that the number of escapees decreases with increasing constriction
angle and particle concentration, while remaining largely unaffected by injection flow rate
within the Stokes regime. The number of particles forming stable arches increases in
discrete steps, closely matching integer values of the particle-to-constriction size ratio.
Sharper constrictions were observed to promote more frequent and stable clogging
compared to smoother geometries. The stochastic model accurately captures these trends,
demonstrating its predictive capability across various conditions.}
}
@article{proudman_pearson_1957, title={Expansions at small Reynolds numbers for the
flow past a sphere and a circular cylinder}, volume={2}, DOI={10.1017
S0022112057000105}, number={3}, journal={Journal of Fluid Mechanics},
author={Proudman, Ian and Pearson, J. R. A.}, year={1957}, pages={237–262}}
@article{Kynch_1959, title={The slow motion of two or more spheres through a viscous
fluid}, volume={5}, DOI={10.1017/S0022112059000155}, number={2}, journal={Journal
of Fluid Mechanics}, author={Kynch, G. J.}, year={1959}, pages={193–208}}
@article{GOLDMAN1966,
title = {The slow motion of two identical arbitrarily oriented spheres through a viscous
fluid},
journal = {Chemical Engineering Science},
volume = {21},
number = {12},
pages = {1151-1170},
year = {1966},
issn = {0009-2509},
doi = {https://doi.org/10.1016/0009-2509(66)85036-4},
url = {https://www.sciencedirect.com/science/article/pii/0009250966850364},
author = {A.J. Goldman and R.G. Cox and H. Brenner},
abstract = {Bipolar coordinates are employed to determine the terminal settling motion of
two, identical, homogeneous, unconstrained spheres in an unbounded fluid at small
Reynolds numbers. Exact numerical values are obtained for the linear and angular velocities
of the spheres as a function of their relative separation and of the orientation of their line-of
centers relative to the direction of gravity. Comparison with published experimental data
indicates good agreement, especially when wall effects are taken into account.
Résumé
Les auteurs emploient les coordonnées bipolaires pour déterminer le mouvement résultant
de deux sphères identiques et homogènes libres, dans un fluide illimité, avec un faible
nombre de Reynolds. Des valeurs numériques exactes, sont obtenues pour des vitesses
linéaires et angulaires des sphères, en fonction de leur séparation relative et de l'orientation
de la ligne des centres par rapport à la direction de la pesanteur. Une comparaison avec les
résultats expérimentaux déjà publiés montre que ceux-ci sont en accord avec la théorie et
plus spécialement lorsqu'on tient compte des effets de paroi.
Zusammenfassung
Zur Bestimmung der Endabsetzbewegung zweier identischer, homogener, ungehemmter
Kugeln in einer unbegrenzten Flüssigkeit bei niedrigen Reynoldsschen Zahlen werden
Bipolarkoordinaten verwendet. Für die Linear- und Winkelgeschwindigkeiten der Kugeln, in
Abhängigkeit von ihrer gegenseitigen Trennung und der Ausrichtung ihrer Mittellinien in
Bezug auf die Richtung der Schwerkraft, werden genaue zahlenmässige Werte erhalten. Ein
Vergleich mit veröffentlichten Daten zeigt gute Überienstimmung, besonders wenn man die
Wandeffekte in Betracht zieht.}
}
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