@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.}
}

@book{krueger2017lbm,
  abstract = {

    A textbook that is strong on basics but also includes in-depth descriptions of the latest applications of LBM

    Thorough chapter summaries, example codes, and an FAQ make this book suitable as both textbook and handbook for practitioners

    The book webpage gives the full code corresponding to the examples presented in the text},
  added-at = {2023-05-15T08:32:39.000+0200},
  address = {Cham},
  author = {Krüger, Timm and Kusumaatmaja, Halim and Kuzmin, Alexandr and Shardt, Orest and Silva, Goncalo and Viggen, Erlend Magnus},
  biburl = {https://www.bibsonomy.org/bibtex/25bef572509fccea3046f021b802a8e80/gdmcbain},
  description = {The Lattice Boltzmann Method: Principles and Practice | SpringerLink},
  doi = {10.1007/978-3-319-44649-3},
  edition = {First},
  interhash = {fcc668c7b88b73034d2ef9949bd6eaef},
  intrahash = {5bef572509fccea3046f021b802a8e80},
  isbn = {978-3-319-83103-9},
  keywords = {76-02-fluid-mechanics-research-exposition 76m28-particle-methods-and-lattice-gas-methods-in-fluid-mechanics},
  publisher = {Springer},
  series = {Graduate Texts in Physics},
  timestamp = {2025-08-20T05:09:47.000+0200},
  title = {The Lattice Boltzmann Method},
  url = {https://link.springer.com/book/10.1007/978-3-319-44649-3},
  year = 2017
}

@article{KRAUSE2017HLBM,
title = {Particle flow simulations with homogenised lattice Boltzmann methods},
journal = {Particuology},
volume = {34},
pages = {1-13},
year = {2017},
issn = {1674-2001},
doi = {https://doi.org/10.1016/j.partic.2016.11.001},
url = {https://www.sciencedirect.com/science/article/pii/S167420011730041X},
author = {Mathias J. Krause and Fabian Klemens and Thomas Henn and Robin Trunk and
Hermann Nirschl},
keywords = {Particulate flow simulations, Arbitrarily shaped particles, Lattice Boltzmann
methods, Validation, Sedimentation processes},
abstract = {An alternative approach to simulating arbitrarily shaped particles submersed in
viscous fluid in two dimensions is proposed, obtained by adapting the velocity parameter of
the equilibrium distribution function of a standard lattice Boltzmann method (LBM).
Comparisons of exemplifying simulations to results in the literature validate the approach as
well as the convergence analysis. Pressure fluctuations occurring in Ladd’s approach are
greatly reduced. In comparison with the immersed boundary method, this approach does
not require cost intensive interpolations. The parallel efficiency of LBM is retained. An
intrinsic momentum transfer is observed during particle–particle collisions. To demonstrate
the capabilities of the approach, sedimentation of particles of several shapes is simulated
despite omitting an explicit particle collision model.}
}

@article{Peskin_2002, title={The immersed boundary method}, volume={11},
DOI={10.1017/S0962492902000077}, journal={Acta Numerica}, author={Peskin, Charles
S.}, year={2002}, pages={479–517}}

@article{MAYA2024,
title = {Particulate transport in porous media at pore-scale. Part 2: CFD-DEM and colloidal forces},
journal = {Journal of Computational Physics},
volume = {519},
pages = {113439},
year = {2024},
issn = {0021-9991},
doi = {https://doi.org/10.1016/j.jcp.2024.113439},
url = {https://www.sciencedirect.com/science/article/pii/S0021999124006879},
author = {Laurez {Maya Fogouang} and Laurent André and Philippe Leroy and Cyprien Soulaine},
keywords = {DLVO theory, JKR theory, Colloid deposition, Pore-scale modeling, CFD-DEM model, Pore-clogging},
abstract = {Pore-clogging by aggregation of fine particles is one of the key mechanisms in particulate transport in porous media. In this work, the unresolved-resolved four-way coupling CFD-DEM (Computational Fluid Dynamics - Discrete Element Method) proposed in Part 1 is coupled with colloidal forces (long-range interactions) to model the transport of charged particles and retention by aggregation at the pore-scale. The model includes hydro-mechanical interactions (e.g. collision, drag, buoyancy, gravity) and electrochemical interactions (e.g. Van der Waals attraction, electrostatic double layer repulsion) between the particles, the fluid, and the porous formation. An adhesive contact force based on the Johnson-Kendall-Roberts theory allows for realistic particle adhesion on the walls. The model robustness is verified using reference semi-analytical solutions of the particle dynamics including long-range interactions. Finally, our CFD-DEM for particulate transport including DLVO and JKR adhesive contact forces is used to investigate the effect of fluid salinity on pore-clogging and permeability reduction. Importantly and unlike other approaches, our CFD-DEM model is not constrained by the size of the particle relative to the cell size. Our pore-scale model offers new possibilities to explore the impact of various parameters including particle size distribution, particle concentration, flow rates, and pore geometry structure on the particulate transport and retention in porous media.}
}