References

Adamson, A. W. 1982 . Physical Chemistry of Surfaces . 4th ed. New York : John Wiley & Sons . Google Scholar

Ahmed, N. , and Sunada, D. K. 1969 . Nonlinear flow in porous media . J. Hydraulics Div. , 95 ( 6 ), 1847 – 1858 . CrossRefGoogle Scholar

Aker, E. , Måløy, K. J. , Hansen, A. , and Batrouni, G. G. 1998 . A two-dimensional network simulator for two-phase flow in porous media . Transp. Porous Med. , 32 , 163 – 186 . CrossRefGoogle Scholar

Ambegaokar, V. , Halperin, B. I. , and Langer, J. S. 1971 . Hopping conductivity in disordered systems . Phys. Rev. B , 4 ( 8 ), 2612 – 2620 . CrossRefGoogle Scholar

Anderson, P. W. 1972 . More is different . Science , 177 ( 4047 ), 393 – 396 . CrossRefGoogle ScholarPubMed

Archie, G. E. 1942 . The electrical resistivity log as an aid in determining some reservoir characteristics . Transactions of the AIME , 146 ( 1 ), 54 – 62 . CrossRefGoogle Scholar

Armstrong, R. T. , McClure, J. E. , Robins, V. , et al. 2018 . Porous media characterization using Minkowski functionals: Theories, applications and future directions . Transp. Porous Med. , 130 ( 1 ), 305 – 335 . CrossRefGoogle Scholar

Aronovici, V. S. , and Donnan, W. W. 1946 . Soil-permeability as a criterion for drainage-design . EOS, Trans. Amer. Geophys. Un. , 27 ( 1 ), 95 – 101 . CrossRefGoogle Scholar

Avraam, D. G. , and Payatakes, A. C. 1995 . Flow regimes and relative permeabilities during steady-state two-phase flow in porous media . J. Fluid. Mech. , 293 , 207 – 236 . CrossRefGoogle Scholar

Bak, P. , Tang, C. , and Wiesenfeld, K. 1987 . Self-organized criticality: An explanation of 1/ f noise . Phys. Rev. Lett. , 59 ( 4 ), 381 – 384 . CrossRefGoogle ScholarPubMed

Bakke, J. Ø. H. , and Hansen, A. 2007 . Accuracy of roughness exponent measurement methods . Phys. Rev. E , 76 ( 3 ), 031136 . CrossRefGoogle Scholar

Barabási, A. L. , and Stanley, H. E. 1995 . Fractal Concepts in Surface Growth . Cambridge : Cambridge University Press . CrossRefGoogle Scholar

Barabási, A. L. , and Vicsek, T. 1991 . Multifractality of self-affine fractals . Phys. Rev. A , 44 ( 4 ), 2730 – 2733 . CrossRefGoogle ScholarPubMed

Batchelor, G. K. 1967 . An Introduction to Fluid Dynamics . Cambridge : Cambridge University Press . Google Scholar

Batrouni, G. G. , Hansen, A. , and Larson, B. 1996 . Current distribution in the three-dimensional random resistor network at the percolation threshold . Phys. Rev. E , 53 , 2292 – 2297 . CrossRefGoogle ScholarPubMed

Bauer, D. , Talon, L. , Peysson, Y. , et al. 2019 . Experimental and numerical determination of Darcy's law for yield stress fluids in porous media . Phys. Rev. Fluids , 4 ( 6 ), 063301 . CrossRefGoogle Scholar

Bear, J. 1972 . Dynamics of Fluids in Porous Media . Amsterdam : Elsevier Publishing Co . Republished by Dover Publications Inc., New York, 1988. ISBN 9780486656755 . Google Scholar

Bear, J , and Bachmat, Y. 1990 . Introduction to Modeling of Transport Phenomena in Porous Media . Dordrecht : Springer . CrossRefGoogle Scholar

Bensimon, D. , Kadanoff, L. P. , Liang, S. , Shraiman, B. I. , and Tang, C. 1986 . Viscous flows in two dimensions . Rev. Mod. Phys. , 58 ( 4 ), 977 – 999 . CrossRefGoogle Scholar

Berendsen, H. J. C. 2007 . Simulating the Physical World: Hierarchical Modeling from Quantum Mechanics to Fluid Dynamics . Cambridge : Cambridge University Press . CrossRefGoogle Scholar

Berlekamp, E. R. , Conway, J. H. , and Guy, R. K. 1982 . Winning Ways for Your Mathematical Plays . New York : Academic Press . Google Scholar

Bernal, J. D. 1964 . The Bakerian Lecture, 1962 The structure of liquids . Proc. R. Soc. Lond. A , 280 ( 1382 ), 299 – 333 . Google Scholar

Bernal, J. D. 1965 . The geometry of the structure of liquids . Pages 25 – 50 of: Hughel, T. J. (ed), Liquids: Structure Properties, Solid Interactions . Amsterdam : Elsevier . Google Scholar

Bernal, J. D. , and Mason, J. 1960 . Packing of spheres: Co-ordination of randomly packed spheres . Nature , 188 ( 4754 ), 910 – 911 . CrossRefGoogle Scholar

Berryman, J. G. 1985 . Measurement of spatial correlation functions using image precessing techniques . J. Appl. Phys. , 57 ( 7 ), 2374 – 2384 . CrossRefGoogle Scholar

Berryman, J. G. , and Blair, S. C. 1986 . Use of digital image analysis to estimate fluid permeability of porous materials: Application of two-point correlation functions . J. Appl. Phys. , 60 ( 6 ), 1930 – 1938 . CrossRefGoogle Scholar

Bird, R. B. , Armstrong, R. C. , and Hassager, O. 1987 . Dynamics of Polymeric Liquids . New York : John Wiley & Sons . Google Scholar

Birovljev, A. , Furuberg, L. , Feder, J. , et al. 1991 . Gravity invasion percolation in two dimensions: Experiments and simulations . Phys. Rev. Lett. , 67 ( 5 ), 584 – 587 . CrossRefGoogle Scholar

Blake, F. C. 1922 . The resistance of packing to fluid flow . Trans. Amer. Inst. Chem. Engrs. , 14 , 415 – 421 . Google Scholar

Blunt, M. J. 2017 . Multiphase Flow in Permeable Media . Cambridge : Cambridge University Press . Google Scholar

Boger, F. , Feder, J. , Jøssang, T. , and Hilfer, R. 1992 . Microstructural sensitivity of local porosity distributions . Physica A , 187 ( 1–2 ), 55 – 70 . CrossRefGoogle Scholar

Bretherton, F. P. 1961 . The motion of long bubbles in tubes . J. Fluid Mech. , 10 ( 2 ), 166 – 188 . CrossRefGoogle Scholar

Brinkman, H.C͂. 1949 . A Calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles . Applied Scientific Research , 1 , 27 – 34 . Google Scholar

Broadbent, S. R. , and Hammersley, J. M. 1957 . Percolation processes I. Crystals and mazes . Math. Proc. Camb. Philos. Soc. , 53 ( 3 ), 629 – 641 . CrossRefGoogle Scholar

Brooks, R. H. , and Corey, A. T. 1966 . Properties of porous media affecting fluid flow . J. Irrig. Grain. Div. , 92 ( 2 ), 61 – 90 . CrossRefGoogle Scholar

Brown, R. L. , and Bolt, R. H. 1942 . The measurement of flow resistance of porous acoustic materials . J. Acous. Soc. Amer. , 13 ( 4 ), 337 – 344 . CrossRefGoogle Scholar

Buckley, S. E. , and Leverett, M. C. 1942 . Mechanism of fluid displacement in sands . Trans. Am. Inst. Min. Eng. , 146 ( 1 ), 107 – 116 . Google Scholar

Buldyrev, S. V. , Barabási, A. L. , Caserta, F. , et al. 1992 . Anomalous interface roughening in porous media: Experiment and model . Phys. Rev. A , 45 , R8313 – R8316 . CrossRefGoogle ScholarPubMed

Capuani, F. , Frenkel, D. , and Lowe, C. P. 2003 . Velocity fluctuations and dispersion in a simple porous medium . Phys. Rev. E , 67 ( 5 ), 056306 . CrossRefGoogle Scholar

Carman, P. C. 1937 . Fluid flow through granular beds . Trans. Inst. Chem. Eng. Lond. , 15 , 150 – 166 . Google Scholar

Carman, P. C. 1938 . Determination of the specific surface of powders I. Transactions . J. Soc. Chem. Ind. , 57 , 225 – 234 . Google Scholar

Chen, L. , De Luca, A. , Rosso, A. , and Talon, L. 2019 . Darcy's law for yield stress fluids . Phys. Rev. Lett. , 122 , 245502 . Google Scholar

Chen, S. , and Doolen, G. D. 1998 . Lattice Boltzmann method for fluid flows . Ann. Rev. Fluid Mech. , 30 ( 1 ), 329 – 364 . CrossRefGoogle Scholar

Chuoke, R. L. , van Meurs, P. , and van der Poel, C. 1959 . The instability of slow, immiscible, viscous liquid-liquid displacements in permeable media . Trans. Metall. Soc. AIME , 216 ( 1 ), 188 – 194 . CrossRefGoogle Scholar

Darcy, H. 1856 . Les Fontaines Publiques de la Ville de Dijon . Paris : Dalmont . Google Scholar

de Arcangelis, L. , Redner, S. , and Coniglio, A. 1985 . Anomalous voltage distribution of random resistor networks and a new model for the backbone at the percolation threshold . Phys. Rev. B , 31 , R4725 – R4727 . CrossRefGoogle Scholar

de Arcangelis, L. , Redner, S. , and Coniglio, A. 1997 . Multiscaling approach in random resistor and random superconducting networks . Phys. Rev. B , 34 , 4656 – 4673 . CrossRefGoogle Scholar

de Gennes, P. G. 1983 . Theory of slow biphasic flows in porous media . Physico-Chem. Hydrodyn. , 4 , 175 – 185 . Google Scholar

de Gennes, P. G. 1985 . Wetting: Statics and dynamics . Rev. Mod. Phys. , 57 ( 3 ), 827 – 863 . CrossRefGoogle Scholar

de Ligny, C. L. 1970 . Coupling between diffusion and convection in radial dispersion of matter by fluid flow through packed beds . Chem. Eng. Sci. , 25 ( 7 ), 1177 – 1181 . CrossRefGoogle Scholar

Debye, P. , and Bueche, A. M. 1949 . Scattering by an inhomogeneous solid . J. Appl. Phys. , 20 ( 6 ), 518 – 525 . CrossRefGoogle Scholar

Debye, P. , Anderson, H. R. , and Brumberger, H. 1957 . Scattering by an inhomogeneous solid. II. The correlation function and its application . J. Appl. Phys. , 28 ( 6 ), 679 – 683 . CrossRefGoogle Scholar

Devillard, P. 1993 . Directed polymer modeling in hydrodynamic dispersion and fracture . Phys. Rev. Lett. , 70 ( 8 ), 1124 – 1127 . CrossRefGoogle Scholar

d’Humières, D. , Lallemand, P. , and Frisch, U. 1986 . Lattice gas models for 3D hydrodynamics . EPL , 2 ( 4 ), 291 – 297 . CrossRefGoogle Scholar

Dowson, D. 1979 . History of Tribology . London and New York : Longman . Google Scholar

Dullien, F. A. L. 1992 . Porous Media: Fluid Transport and Pore Structure . 2nd ed. San Diego, CA 92101 : Academic Press . Google Scholar

Dupuit, A. J. E. J. 1854 . Traité Théoretique et Practique de la conduite et de la Distribution des Eaux . Paris : Dalmont . Google Scholar

Einstein, A. 1905 . Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen . Ann. Phys. , 322 ( 8 ), 549 – 560 . CrossRefGoogle Scholar

Einstein, A. 1906 . Eine neue Bestimmung der Moleküldimensionen . Ann. Phys. , 324 ( 2 ), 289 – 306 . CrossRefGoogle Scholar

Einstein, A. 1911 . Berichtigung zu meiner Arbeit: “Eine neue Bestimmung der Moleküldimensionen.” Ann. Phys. , 339 ( 3 ), 591 – 592 . CrossRefGoogle Scholar

Engelberts, W. F. , and Klinkenberg, L. J. 1951 . Laboratory experiments on the displacement of oil by water from packs of granular material . Pages 544 – 554 of: 3rd World Petroleum Congress, 28 May-6 June, The Hague, the Netherlands . World Petroleum Congress. Google Scholar

Fairbrother, F. , and Stubbs, A. E. 1935 . 119. Studies in electro-endosmosis. Part VI. The “bubble-tube” method of measurement . J. Chem. Soc. , 527 – 529 . CrossRefGoogle Scholar

Feder, Jens. 1988 . Fractals . New York : Springer . CrossRefGoogle Scholar

Fleischer, R. L. 1995 . Technological applications of ion tracks in insulators . MRS Bull. , 20 ( 12 ), 35 – 41 . CrossRefGoogle Scholar

Fleischer, R. L. , and Price, P. B. 1963 . Tracks of charged particles in high polymers . Science , 140 ( 3572 ), 1221 – 1222 . CrossRefGoogle ScholarPubMed

Fleischer, R. L. , Price, P. B. , and Symes, E. M. 1964 . Novel filter for biological materials . Science , 143 ( 3603 ), 249 – 250 . CrossRefGoogle ScholarPubMed

Flekkøy, E. G. 1993 . Lattice Bhatnagar-Gross-Krook models for miscible fluids . Phys. Rev. E , 47 ( 6 ), 4247 – 4257 . CrossRefGoogle ScholarPubMed

Flekkøy, E. G. , and Rothman, D. H. 1995 . Fluctuating fluid interfaces . Phys. Rev. Lett. , 75 ( 2 ), 260 – 263 . CrossRefGoogle ScholarPubMed

Flekkøy, E. G. , Oxaal, U. , Feder, J. , and Jøssang, T. 1995 . Hydrodynamic dispersion at stagnation points: Simulations and experiments . Phys. Rev. E , 52 ( 5 ), 4952 – 4962 . CrossRefGoogle ScholarPubMed

Flekkøy, E. G. , Rage, T. , Oxaal, U. , and Feder, J. 1996 . Hydrodynamic irreversibility in creeping flow . Phys. Rev. Lett. , 77 ( 20 ), 4170 – 4173 . CrossRefGoogle ScholarPubMed

Forchheimer, P. 1901 . Wasserbewegung durch Boden . Z. Ver. Deutsch. Ing. , 45 , 1781 – 1787 . Google Scholar

Frette, V. , Christensen, K. , Malthe-Sørenssen, A. , et al. 1996 . Avalanche dynamics in a pile of rice . Nature , 379 ( 6560 ), 49 – 52 . CrossRefGoogle Scholar

Frisch, U. , Hasslacher, B. , and Pomeau, Y. 1986 . Lattice-gas automata for the Navier–Stokes equation . Phys. Rev. Lett. , 56 ( 14 ), 1505 – 1508 . CrossRefGoogle ScholarPubMed

Frisch, U. , d’Humières, D. , Hasslacher, B. , et al. 1987 . Lattice gas hydrodynamics in two and three dimensions . Complex Syst. , 1 ( 4 ), 649 – 707 . Google Scholar

Furuberg, L. , Hansen, A. , Hinrichsen, E. , Feder, J. , and Jøssang, T. 1991 . Scaling of overhang distribution of invasion percolation fronts . Phys. Script. , T38 , 91 – 94 . CrossRefGoogle Scholar

Furuberg, L. , Måløy, K. J. , and Feder, J. 1996 . Imtermittent behavior in slow drainage . Phys. Rev. E , 53 ( 1 ), 966 – 977 . CrossRefGoogle Scholar

Grassberger, P. 1999 . Conductivity exponent and backbone dimension in 2-d percolation . Physica A , 262 , 251 – 263 . CrossRefGoogle Scholar

Gumbel, E. J. 2004 . Statistics of Extremes . New York : Dover . Google Scholar

Gunstensen, A. K. , and Rothman, D. H. 1993 . Lattice-Boltzmann studies of immiscible two-phase flow through porous media . J. Geophys. Res. , 98 ( B4 ), 6431 – 6441 . CrossRefGoogle Scholar

Gunstensen, A. K. , Rothman, D. H. , Zaleski, S. , and Zanetti, G. 1991 . Lattice-Boltzmann model of immiscible fluids . Phys. Rev. A. , 43 ( 8 ), 4320 – 4327 . CrossRefGoogle ScholarPubMed

Hagen, G. H. L. 1839 . Ueber die Bewegung des Wassers in engen cylindrischen Röhren . Ann. Phys. , 122 ( 3 ), 423 – 442 . CrossRefGoogle Scholar

Hales, T. C. 1994 . The status of the Kepler conjecture . Math. Intell. , 16 ( 3 ), 47 – 58 . CrossRefGoogle Scholar

Hales, T. C. 1998 . Sphere Packings I–V . His computer based proof is now found at github. Version 12/26/15. His site has many interesting historical notes and pointers to other sites . https://github.com/flyspeck/kepler98 . Google Scholar

Hansen, A. Hinrichsen, E.L͂. and Roux, S. 1991 . Scale-invariant disorder in fracture and related breakdown phenomena . Phys. Rev. B , 43 , 665 – 678 . CrossRefGoogle ScholarPubMed

Hansen, A. , Engøy, T. , and Måløy, K. J. 1994 . Measuring hurst exponents with the first return method . Fractals , 2 ( 4 ), 527 – 533 . CrossRefGoogle Scholar

Hansen, A. , Schmittbuhl, J. , and Batrouni, G. G. 2001 . Distinguishing fractional and white noise in one and two dimensions . Phys. Rev. E , 63 ( 6 ), 062102 . CrossRefGoogle ScholarPubMed

Hansen, A. , Batrouni, G. G. , Ramstad, T. , and Schmittbuhl, J. 2007 . Self-affinity in the gradient percolation problem . Phys. Rev. E , 75 ( 3 ), 030102 . CrossRefGoogle ScholarPubMed

Hansen, A. , Sinha, S. , Bedeaux, D. , et al. 2018 . Relations between seepage velocities in immiscible, incompressible two-phase flow in porous media . Transp. Porous Med. , 125 ( 3 ), 565 – 587 . CrossRefGoogle Scholar

Hardy, J. , de Pazzis, O. , and Pomeau, Y. 1976 . Molecular dynamics of a classical lattice gas: Transport properties and time correlation functions . Phys. Rev. A , 13 ( 5 ), 1949 – 1961 . CrossRefGoogle Scholar

Hele-Shaw, H. S. 1898 . The flow of water . Nature , 58 ( 1489 ), 34 – 36 . CrossRefGoogle Scholar

Hiby, J. W. 1962 . Longitudinal and transverse mixing during single-phase flow through granular beds . Pages 312 – 325 of: Rottenburg, P. A. & Sheperd, N. T. (eds), Symposium on the Interaction between Fluids and Particles . London : Inst. Chem. Engineers . Google Scholar

Higuera, F. J. , and Jiménez, J. 1989 . Boltzmann approach to lattice gas simulations . EPL , 9 ( 7 ), 663 – 668 . CrossRefGoogle Scholar

Higuera, F. J. , and Succi, S. 1989 . Simulating the flow around a circular cylinder with a lattice boltzmann equation . EPL , 8 ( 6 ), 517 – 521 . CrossRefGoogle Scholar

Higuera, F. J. , Succi, S. , and Benzi, R. 1989 . Lattice gas dynamics with enhanced collisions . EPL , 9 ( 4 ), 345 – 349 . CrossRefGoogle Scholar

Hilfer, R. 1991 . Geometric and dielectric characterization of porous media . Phys. Rev. B , 44 ( 1 ), 60 – 75 . CrossRefGoogle ScholarPubMed

Hinch, E. J. 1977 . An averaged-equation approach to particle interactions in a fluid suspension . J. Fluid Mech. , 83 ( 4 ), 695 – 720 . CrossRefGoogle Scholar

Honarpour, M. , Koederitz, L. , and Harvey, A. H. 1986 . Relative Permeability of Petroleum Reservoirs . Boca Raton, FL : CRC Press . Google Scholar

Hooke, R. 1661 . Pamphlet . Hooke's first publication was a pamphlet on capillary action . Google Scholar

Hsiang, W.-Y. 1993 . On the sphere packing problem and the proof of Kepler's conjecture . Int. J. Math. , 4 ( 5 ), 739 – 831 . CrossRefGoogle Scholar

Hsiang, W.-Y. 1995 . A rejoinder to Hales's article . Math. Intell. , 17 ( 1 ), 35 – 42 . CrossRefGoogle Scholar

Israelachivili, J. N. 1992 . Intermolecular and Surface Forces . 2nd ed. London : Academic Press . Google Scholar

Jaeger, H. M. , and Nagel, S. R. 1992 . Physics of the granular state . Science , 255 ( 5051 ), 1523 – 1531 . CrossRefGoogle ScholarPubMed

Jullien, R. , Pavlovitch, A. , and Meakin, P. 1992 a. Random packings of spheres built with sequential models . J. Phys. A , 25 ( 15 ), 4103 – 4113 . CrossRefGoogle Scholar

Jullien, R. , Meakin, P. , and Pavlovitch, A. 1992 b. Three-dimensional model for particle-size segregation by shaking . Phys. Rev. Lett. , 69 ( 4 ), 640 – 643 . CrossRefGoogle ScholarPubMed

Kalaydjian, F. 1990 . Origin and quantification of coupling between relative permeabilities for two-phase flows in porous media . Transp. Porous Med. , 5 ( 3 ), 215 – 229 . CrossRefGoogle Scholar

Katz, A. J. , and Thompson, A. H. 1986 . Quantitative prediction of permeability in porous rocks . Phys. Rev. B , 34 ( 11 ), 8179 – 8181 . CrossRefGoogle Scholar

Kepler, J. 1941 . Gesammelte Werke . Vol. 4 . München : C. H. Beck . Google Scholar

Kepler, J. 1966 . The Six-Cornered Snowflake . London : Oxford University Press . Edited by L. L. Whyte. The book contains Kepler's original (1611) text in latin with English translation by Colin Hardie. The book also contains comments by B. J. Mason: ‘On the shape of snow crystals’ , and by L. L. Whyte: ‘Kepler's unsolved problem and the Facultas Formatrix ’ . Google Scholar

Khanamiri, H. H. , Berg, C. F. , Slotte, P. A. , Sclüter, S. , and Torsæter, O. 2018 . description of free energy for immiscible two-fluid flow in porous media by integral geometry and thermodynamics . Water Resour. Res. , 54 ( 11 ), 9045 – 9059 . CrossRefGoogle Scholar

Kinzel, W. 1983 . Directed percolation . In: Deutscher, G. , Zallen, R. , and Adler, J. (eds), Percolation Structures and Processes . A. Hilger . Google Scholar

Kirkpatrick, S. 1971 . Classical transport in disordered media: Scaling and effective-medium theories . Phys. Rev. Lett. , 27 , 1722 – 1725 . CrossRefGoogle Scholar

Kirkpatrick, S. 1973 . Percolation and conduction . Rev. Mod. Phys , 45 ( 4 ), 574 – 588 . CrossRefGoogle Scholar

Kjelstrup, S. , Bedeaux, D. , Hansen, A. , Hafskjold, B. , and Galteland, O. 2019 . Non-isothermal transport of multi-phase fluids in porous media. Constitutive equations . Front. Phys. (Lausanne) , 6 , 150 . CrossRefGoogle Scholar

Klinkenberg, L. J. 1941 . The permeability of porous media to liquids and gases . Pages 200 – 213 of: Drilling and Production Practice . New York : American Petroleum Institute . Google Scholar

Koch, D. L. , and Brady, J. F. 1985 . Dispersion in fixed beds . J. Fluid Mech. , 154 , 399 – 427 . CrossRefGoogle Scholar

Kolmogorov, A. N. 1941 a. Dissipation of energy in locally isotropic turbulence . Dokl. Akad. Nauk SSSR , 32 , 16 – 18 . Republished: 1991. Proc. R. Soc. Lond. A , 434 (1890), 15–17. Google Scholar

Kolmogorov, A. N. 1941 b. The local structure of turbulence in incompressible viscous fluid with very large Reynolds’ numbers . Dokl. Akad. Nauk SSSR , 30 , 301 – 305 . Republished: 1991. Proc. R. Soc. Lond. A , 434 (1890), 9–13. Google Scholar

Kolmogorov, A. N. 1962 . A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number . J. Fluid Mech. , 13 ( 1 ), 82 – 85 . CrossRefGoogle Scholar

Koocheki, A. , Ghandi, A. , Razavi, S. M. A. , et al. 2009 . The rheological properties of ketchup as a function of differenthydrocolloids and temperature . Int. J. Food Sci. Tech. , 44 , 569 – 602 . CrossRefGoogle Scholar

Kozeny, J. 1927 . Über kapillare Leitung des Wassers im Boden (Aufstieg, Versickerung und Anwendung auf die Bewässerung) . Sitzungsber. Akad. Wiss. in Wien, Mathematisch-Naturwissenschaftliche Klasse, Abt. IIa , 136 ( 2a ), 271 – 306 . Google Scholar

Landau, L. D. , and Lifshitz, E. M. 1987 a. Fluid Mechanics . Oxford, New York : Pergamon Press . Google Scholar

Landau, L. D. , and Lifshitz, E. M. 1987 b. Statistical Mechanics . Oxford, New York : Pergamon Press . Google Scholar

Latva-Kokko, M. , and Rothman, D. H. 2005 . Diffusion properties of gradient-based lattice Boltzmann models of immiscible fluids . Phys. Rev. E , 71 ( 5 ), 056702 . CrossRefGoogle ScholarPubMed

Lavallee, P. , Boon, J. P. , and Noullez, A. 1991 . Boundaries in lattice gas flows . Physica D , 47 ( 1 ), 233 – 240 . CrossRefGoogle Scholar

Lenormand, R. , and Zarcone, C. 1985 . Invasion percolation in an etched network: measurement of a fractal dimension . Phys. Rev. Lett. , 54 ( 20 ), 2226 – 2229 . CrossRefGoogle Scholar

Leverett, M. C. 1941 . Capillary behavior in porous solids . Trans. AIME , 142 ( 1 ), 152 – 169 . CrossRefGoogle Scholar

Liu, C.-h. , Nagel, S. R. , Schecter, D. A. , et al. 1995 . Force fluctuations in bead packs . Science , 269 ( 5223 ), 513 – 515 . CrossRefGoogle ScholarPubMed

Locke, L. C. , and Bliss, J. E. 1950 . Core analysis technique for limestone and dolomite . World Oil , 131 ( 4 ), 206 – 207 . Google Scholar

Løvoll, G. , Méhuest, Y. , Toussaint, R. , Schmittbuhl, J. , and Måløy, K. J. 2004 . Growth activity during fingering in a porous Hele-Shaw cell . Phys. Rev. E , 70 ( 2 ), 026301 . CrossRefGoogle Scholar

Maher, J. V. 1985 . Development of viscous fingering patterns . Phys. Rev. Lett. , 54 ( 14 ), 1498 – 1501 . CrossRefGoogle ScholarPubMed

Måløy, K. J. , Feder, J. , and Jøssang, T. 1985 . Viscous fingering fractals in porous media . Phys. Rev. Lett. , 55 ( 24 ), 2688 – 2691 . CrossRefGoogle Scholar

Mandelbrot, B. B. 1982 . The Fractal Geometry of Nature . USA : W. H. Freeman and Co . Google Scholar

Maxwell, J. C. 1876 . Capillary action . In: Baynes, T. S. (ed), Encyclopædia Britannica , 9th ed. Encyclopædia Britannica, Inc . Reprinted in The Scientific Papers of James Clerk Maxwell , 2 , 541–591 (Cambridge University Press, 2011). Google Scholar

Mazur, P. , and Weisenborn, A. J. 1984 . The Ossen drag on a sphere and the method of induced forces . Physica A , 123 ( 1 ), 209 – 226 . CrossRefGoogle Scholar

McLaughlin, J. F. , and Goetz, W, H. 1955 . Permeability, void content, and durability of bitumious concrete . Highway Res. Board Proc. , 34 , 274 – 286 . Google Scholar

McLean, J. W. , and Saffman, P. G. 1981 . The effect of surface tension on the shape of fingers in a Hele-Shaw cell . J. Fluid Mech. , 102 , 455 – 469 . CrossRefGoogle Scholar

McNamara, G. R. , and Zanetti, G. 1988 . Use of the Boltzmann equation to simulate lattice-gas automata . Phys. Rev. Lett. , 61 ( 20 ), 2332 – 2335 . CrossRefGoogle ScholarPubMed

Mecke, K. , and Arns, C. H. 2005 . Fluids in porous media: A morphometric approach . J. Phys. Condens. Matter , 17 ( 9 ), S503 – S534 . CrossRefGoogle Scholar

Mecke, K. R. 2000 . Additivity, Convexity, and beyond: Applications of Minkowski functionals in statistical physics . Pages 111 – 184 of: Mecke, K. R. (ed), Statistical Physics and Spatial Statistics . Heidelberg : Springer . CrossRefGoogle Scholar

Méheust, Y. , Løvoll, G. , Måløy, K. J. , and Schmittbuhl, J. 2002 . Interface scaling in a two-dimensional porous medium under combined viscous, gravity, and capillary effects . Phys. Rev. A , 66 ( 5 ), 051603 . Google Scholar

Mehrabi, A. R. , Rassamdana, H. , and Sahimi, M. 1997 . Characterization of long-range correlations in complex distributions and profiles . Phys. Rev. E , 56 , 712 – 722 . CrossRefGoogle Scholar

Misner, C. W. , Thorne, K. S. , and Wheeler, J. A. 2017 . Gravitation . Princeton : Princeton University Press . Google Scholar

Mitchell, S. J. 2005 . Discontinuities in self-affine functions lead to multiaffinity . Phys. Rev. E , 72 ( 6 ), 065103(R) . CrossRefGoogle ScholarPubMed

Mitton, R. G. 1945 . The air pemeabilities of light leathers and their specific surfaces . J. Int. Soc. Leather Trades’ Chem. , 29 , 255 – 263 . Google Scholar

Moffatt, H. K. 1964 . Viscous and resistive eddies near a sharp corner . J. Fluid Mech. , 18 , 1 – 18 . CrossRefGoogle Scholar

Mott, R. A. 1951 . The laws of motion of particles in fluids and their application to the resistance of beds of solids to the passage of fluid . Pages 242 – 256 of: Lang, H. R. (ed), Some Aspects of Fluid Flow . London : Edward Arnold & Company, for The Institute of Physics . Google Scholar

Moura, M. , Fiorentino, E. A. , Maåløy, K. J. , Schäfer, G. , and Toussaint, R. 2015 . Impact of sample geometry on the measurement of pressure-saturation curves: Experiments and simulations . Water Resour. Res. , 51 ( 11 ), 8900 – 8926 . CrossRefGoogle Scholar

Moura, M. , Måløy, K. J. , Flekkøy, E. G. , and Toussaint, R. 2017 . Verification of a dynamic scaling for the pair correlation function during the slow drainage of a porous medium . Phys. Rev. Lett. , 119 ( 15 ), 154503 . CrossRefGoogle ScholarPubMed

Muskat, M. 1937 . The flow of Homogeneous Fluids through Porous Media . 1st ed. Ann Arbor : Edwards . 2nd printing, 1946. Google Scholar

Navier, C. L. M. H. 1822 . Mémoire sur les Lois du Mouvements des Fluides . Mémoires de l’Academie Royale des Sciences de l’Institut de France , VI . Chez Firmin Didot, père et fils, libraires , Paris 1827. Google Scholar

Newton, I. 1867 . Philosophiae Naturales Principia Mathematica . Berkeley and Los Angeles : Imprimatur S. Pepys. Re. Soc. Praeses . See A. Motte's and 1729. Revised and supplied with historical and explanatory appendix by F. Cajori, Edited by R. T. Crawford (1934) and published by University of California Press, Berkeley and Los Angeles (1966). Google Scholar

Nosé, S. 1984 . A unified formulation of the constant temperature molecular-dynamics methods . J. Chem. Phys. , 81 , 511 – 519 . CrossRefGoogle Scholar

Nutting, P. G. 1930 . Physical analysis of oil sands . Bull. Amer. Ass. Petr. Geol. , 14 , 1337 – 1349 . Google Scholar

Oak, M. J. , Baker, L. E. , and Thomas, D. C. 1990 . Three-phase relative permeability of Berea sandstone . J. Petr. Tech. , 42 ( 8 ), 1054 – 1061 . CrossRefGoogle Scholar

Olafuyi, O. A. , Cinar, Y. , Knackstedt, M. A. , and Pinczewski, W. V. 2008 . Capillary pressure and relative permeability of small cores . In: SPE Symposium on Improved Oil Recovery, 20–23 April 2008, Tulsa, Oklahoma, USA . Society of Petroleum Engineers . Google Scholar

Onoda, G. Y. , and Liniger, E. G. 1990 . Random loose packings of uniform spheres and the dilatancy onset . Phys. Rev. Lett. , 64 ( 22 ), 2727 – 2730 . CrossRefGoogle ScholarPubMed

Oseen, C. W. 1910 . Über die Stokes'sche Formel und über eine verwandte Aufgabe in der Hydrodynamik . Arkiv för matematik, ast. och fysik , 6 , 1 – 20 . Google Scholar

Oseen, C. W. 1913 . Über den Gültigkeitsbereich der Stokesschen Wiederstandsformel . Arkiv för matematik, ast. och fysik , 9 . Google Scholar

Oseen, C. W. 1945 . Neuere Methoden und Ergebnisse der Hydordynamik . Akademische Verlagsgesellschaft m.b.h.; Leipzig , 1 , 325 . Google Scholar

Oxaal, U. , Flekkøy, E. G. , and Feder, J. 1994 . Irreversible dispersion at a stagnation point: Experiments and lattice Boltzmann simulations . Phys. Rev. Lett. , 72 ( 22 ), 3514 – 3517 . CrossRefGoogle Scholar

Pallmann, H. , and Deuel, H. 1945 . Über die Wasserdurchlässigkeit von Hydrogelen . Experientia , 1 ( 9 ), 325 – 326 . CrossRefGoogle Scholar

Pitts, E. 1980 . Penetration of a fluid into a Hele-Shaw cell: The Saffman-Taylor experiment . J. Fluid Mech. , 97 , 53 – 64 . CrossRefGoogle Scholar

Poiseuille, J. L. M. 1840 . Recherches expérimentales sur le mouvement des liquides dans les tubes de très petits diamètres; I: Influence de la pression sur la quantitté de liquide qui travese les tubes de très petits diamètres . C. R. Acas. Sci. , 11 , 1041 – 1048 . Google Scholar

Porto, M. , Bunde, A. , Havlin, S. , and Roman, H. E. 1997 . Structural and dynamical properties of the percolation backbone in two and three dimensions . Phys. Rev. E , 56 , 1667 – 1675 . CrossRefGoogle Scholar

Press, W. H. , Teukolsky, S. A. , Vetterling, W. T. , and Flannery, B. P. 2007 . Numerical Recipes: The Art of Scientific Computing . 3rd ed. Cambridge : Cambridge University Press . Google Scholar

Proudman, I. , and Pearson, J. R. A. 1957 . Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder . J. Fluid Mech. , 2 ( 3 ), 237 – 262 . CrossRefGoogle Scholar

Qian, Y. H. , d‘Humières, D. , and Lallemand, P. 1992 . Lattice BGK models for Navier-Stokes equation . EPL , 17 ( 6 ), 479 – 484 . CrossRefGoogle Scholar

Reynolds, O. 1886 . IV. On the theory of lubrication and its application to Mr. Beauchamp tower's experiments, including an experimental determination of the viscosity of olive oil . Philosophical Transactions of the Royal Society of London , 177 , 157 – 234 . Google Scholar

Riguidel, F.-X. , Hansen, A. , and Bideau, D. 1994 . Gravity driven motion of a particle on an inclined plane with controlled roughness . EPL , 28 ( 1 ), 13 – 18 . CrossRefGoogle Scholar

Rivet, J.-P. , and Boon, J. P. 2001 . Lattice Gas Hydrodynamics . Cambridge : Cambridge University Press . CrossRefGoogle Scholar

Rothman, D. H. , and Keller, J. M. 1988 . Immiscible cellular-automaton fluids . J. Stat. Phys. , 52 ( 3–4 ), 1119 – 1127 . CrossRefGoogle Scholar

Rothman, D. H. , and Zaleski, S. 1994 . Lattice-gas models of phase separation: Interfaces, phase transitions, and multiphase flow . Rev. Mod. Phys. , 66 ( 4 ), 1417 – 1479 . CrossRefGoogle Scholar

Roux, S. , and Hansen, A. 1987 . Application of ‘logical transport’ to determine the directed and isotropic percolation thresholds . J. Phys. A: Math. Gen. , 20 , L873 – L878 . Google Scholar

Rowlinson, J. S. , and Widom, B. 1982 . Molecular Theory of Capillarity . Oxford : Oxford University Press . Google Scholar

Roy, S. , Hansen, A. , and Sinha, S. 2019 a. Effective rheology of two-phase flow in capillary fiber bundles . Front. Phys. (Lausanne) , 7 , 92 . CrossRefGoogle Scholar

Roy, S. , Pedersen, H. , Sinha, S. , and Hansen, A. 2021 . The co-moving velocity in immiscible two-phase flow in porous media . arXiv:2108.10187 . CrossRefGoogle Scholar

Roy, S. , Sinha, S. , and Hansen., A. 2019 b. Immiscible two-phase flow in porous media: Effective rheology in the continuum limit . arXiv:1912.05248 . CrossRefGoogle Scholar

Rumpf, H. C. H. , and Gupte, A. R. 1971 . Einflüsse der Porosität und Korngrössenverteilung im Wiederstandsgesetz der Porenströmung . Chem. Ing. Tech. , 43 ( 6 ), 367 – 375 . CrossRefGoogle Scholar

Saffman, P. G. , and Taylor, G. I. 1958 . The penetration of a fluid into a medium or Hele-Shaw cell containing a more viscous liquid . Proc. R. Soc. Lond. A , 245 ( 1242 ), 312 – 329 . Google Scholar

Scheidegger, A. E. 1953 . Theoretical models of porous matter . Producers Monthly , 17 , 17. Scheidegger, A. E. 1958. The physics of flow through porous media. Soil Sci. , 86, 355 . Google Scholar

Scheidegger, A. E. 1974 . The Physics of Flow through Porous Media . Toronto : University of Toronto Press . Google Scholar

Schick, M. 1990 . Introduction to wetting phenomena . Pages 417 – 497 of: Charvolin, J. , Joanny, J. F. , and Zinn-Justin, J. (eds), Liquids at Interfaces . Amsterdam : Elsevier Science Publishers B.V. Les Houches , Session XLVIII, 1988. Google Scholar

Schmittbuhl, J. , Vilotte, J.-P. , and Roux, S. 1995 . Reliability of self-affine measurements . Phys. Rev. E , 51 ( 1 ), 131 – 147 . CrossRefGoogle ScholarPubMed

Schriever, W. 1930 . Law of flow for the passage of a gas-free liquid through a spherical-grain sand . Trans. Amer. Inst. Min. Metall. Engrs., Pet. Div. , 86 ( 1 ), 329 – 336 . Google Scholar

Schweber, S. S. 1993 . Physics, community and the crisis in physical theory . Phys. Today , 46 ( 11 ), 34 – 40 . CrossRefGoogle Scholar

Scott, G. D. 1960 . Packing of spheres: Packing of equal spheres . Nature , 188 , 908 – 909 . CrossRefGoogle Scholar

Scott, G. D. , and Kilgour, D. M. 1969 . The density of random close packing of spheres . J. Phys. D: Appl. Phys. , 2 ( 6 ), 863 – 866 . CrossRefGoogle Scholar

Simonsen, I. , and Hansen, A. 2002 . Fast algorithm for generating long self-affine profiles . Phys. Rev. E , 65 ( 3 ), 037701 . CrossRefGoogle ScholarPubMed

Simonsen, I. , Hansen, A. , and Nes, O. M. 1998 . Determination of the Hurst exponent by use of wavelet transforms . Phys. Rev. E , 58 ( 3 ), 2779 – 2787 . CrossRefGoogle Scholar

Sinha, S. , and Hansen, A. 2012 . Effective rheology of immiscible two-phase flow in porous media . EPL , 99 ( 4 ), 44004 . CrossRefGoogle Scholar

Sinha, S. , Hansen, A. , Bedeaux, D. , and Kjelstrup, S. 2013 . Effective rheology of bubbles moving in a capillary tube . Phys. Rev. E , 87 ( 2 ), 025001 . CrossRefGoogle Scholar

Sinha, S. , Gjennestad, M. Aa. , Vassvik, M. , et al. 2019 . Rheology of high-capillary number two-phase flow in porous media . Front. Phys. (Lausanne) , 7 , 65 . CrossRefGoogle Scholar

Sinha, S. , Gjennestad, M. A. , Vassvik, M. , and Hansen, A. 2021 . Fluid meniscus algorithms for dynamic pore-network modeling of immiscible two-phase flow in porous media . Front. Phys. , 8 , 548497 . CrossRefGoogle Scholar

Slichter, C. S. 1899 . Theoretical investigations of the motions of ground waters . Pages 295 – 384 of: Nineteenth Annual Report of the U. S. Geological Survey, Pt. 2 . Google Scholar

Stanton, T. E. , and Pannell, J. R. 1914 . V. Similarity of motion in relation to the surface friction of fluids . Philos. Trans. R. Soc. A , 214 ( 513 ), 199 – 224 . Google Scholar

Stauffer, D. , and Aharony, A. 1992 . Introduction To Percolation Theory . 2nd ed. London : Taylor & Francis . Google Scholar

Stewart, I. 1991 . How to succeed in stacking . New Scientist , 131 , 29 – 32 . Google Scholar

Stokes, G. G. 1845 . On the theories of the internal friction of fluids in motion, and of the equilibrium and motion of elastic solids . Trans. Cambr. Phil. Soc. , 8 , 287 – 319 . Google Scholar

Strieder, W. , and Aris, R. 1973 . Variational Methods Applied to Problems of Diffusion and Reaction . Heidelberg : Springer-Verlag . CrossRefGoogle Scholar

Strogatz, S. H. 1994 . Non-Linear Dynamics and Chaos . Cambridge : Perseus Press . Google Scholar

Stull, R. T. , and Johnson, P. V. 1940 . Some properties of the pore system in bricks and their relation to frost action . J. Res. Natl. Bur. Stand. , 25 ( 6 ), 711 – 730 . CrossRefGoogle Scholar

Tallakstad, K. T. , Løvoll, G. , Knudsen, H. A. , Flekkøy, E. G. , and Måløy, K. J. 2009 . Steady-state, simultaneous two-phase flow in porous media: An experimental study . Phys. Rev. E , 80 ( 3 ), 036308 . CrossRefGoogle ScholarPubMed

Talon, L. , and Bauer, D. 2013 . On the determination of a generalized Darcy equation for yield-stress fluid in porous media using a lattice-Boltzmann TRT scheme . Eur. Phys. J. E , 36 ( 12 ), 139 . CrossRefGoogle ScholarPubMed

Talon, L. , Auradou, H. , Pessel, M. , and Hansen, A. 2013 . Geometry of optimal path hierarchies . EPL , 103 ( 3 ), 30003 . CrossRefGoogle Scholar

Taneda, S. 1956 . Experimental Investigation of the Wake behind a sphere at low Reynolds numbers . J. Phys. Soc. Jpn. , 11 ( 10 ), 1104 – 1108 . CrossRefGoogle Scholar

Taylor, G. I. 1953 . Dispersion of soluble matter in solvent flowing slowly through a tube . Proc. R. Soc. Lond. A , 219 ( 1137 ), 186 – 203 . Google Scholar

Taylor, T. D. , and Acrivos, A. 1964 . On the deformation and drag of a falling viscous drop at low Reynolds number . J. Fluid Mech. , 18 ( 3 ), 466 – 476 . CrossRefGoogle Scholar

Toussaint, R. , Løvoll, G. , Méheust, Y. , Måløy, K. J. , and Schmittbuhl, J. 2005 . Influence of pore-scale disorder on viscous fingering during drainage . EPL , 71 ( 4 ), 583 – 589 . CrossRefGoogle Scholar

Tritton, D. J. 1977 . Physical Fluid Dynamics . Wokingham : Van Nostrand Reinhold Co. Ltd . CrossRefGoogle Scholar

Tryggvason, G. , and Aref, H. 1983 . Numerical experiments on Hele Shaw flow with a sharp interface . J. Fluid Mech. , 136 , 1 – 30 . CrossRefGoogle Scholar

van Genabeek, O. , and Rothman, D. H. 1996 . Macroscopic manifestations of microscopic flows through porous media: Phenomenology from simulation . Annu. Rev. Earth Planet. Sci. , 24 ( 1 ), 63 – 87 . CrossRefGoogle Scholar

van Genuchten, M. T. 1980 . A closed-form equation for predicting the hydraulic conductivity of unsaturated soils . Soil Sci. Soc. Am. J. , 44 ( 5 ), 892 – 898 . CrossRefGoogle Scholar

van Kampen, N. G. 2007 . Stochastic Processes in Physics and Chemistry . 3rd ed. Amsterdam : North Holland . Google Scholar

Vergeles, M. , Keblinski, P. , Koplik, J. , and Banavar, J. R. 1995 . Stokes drag at the molecular level . Phys. Rev. Lett. , 75 ( 2 ), 232 – 235 . CrossRefGoogle ScholarPubMed

Washburn, E. W. 1921 . The dynamics of capillary flow . Phys. Rev. , 17 ( 3 ), 273 – 283 . CrossRefGoogle Scholar

Weissberg, H. L. 1963 . Effective diffusion coefficient in porous media . J. Appl. Phys. , 34 , 2636 . CrossRefGoogle Scholar

Whitaker, S. 1986 . Flow in porous media I: A theoretical derivation of Darcy's law . Transp. Porous Media , 1 ( 1 ), 3 – 25 . CrossRefGoogle Scholar

Wiggins, E. J. , Campbell, W. B. , and Maass, O. 1939 . Determination of the specific surface of fibrous materials . Can. J. Res. , 17b ( 10 ), 318 – 324 . CrossRefGoogle Scholar

Wilkinson, D. , and Willemsen, J. F. 1983 . Invasion percolation: A new form of percolation theory . J. Phys. A , 16 ( 14 ), 3365 – 3376 . CrossRefGoogle Scholar

Wold, I. , and Hafskjold, B. 1999 . Nonequilibrium molecular dynamics simulations of coupled heat and mass transport in binary fluid mixtures in pores . Int. J. Thermophys. , 20 ( 3 ), 847 – 856 . CrossRefGoogle Scholar

Wu, C. , Xu, X. , and Qian, T. 2013 . Molecular dynamics simulations for the motion of evaporative droplets driven by thermal gradients along nanochannels . J. Phys. Condens. Matter , 25 ( 19 ), 195103 . CrossRefGoogle ScholarPubMed

Wu, X-l. , Måløy, K. J. , Hansen, A. , Ammi, M. , and Bideau, D. 1993 . Why hour glasses tick . Phys. Rev. Lett. , 71 ( 9 ), 1363 – 1366 . CrossRefGoogle ScholarPubMed

Wyckoff, R. D. , and Botset, H. G. 1936 . The flow of gas-liquid mixtures through unconsolidated sands . Physics , 7 ( 9 ), 325 – 345 . CrossRefGoogle Scholar

Wyckoff, R. D. , Botset, H. G. , Muskat, M. , and Reed, D. W. 1933 . The measurement of the permeability of porous media for homogeneous fluids . Rev. Sci. Instrum. , 4 ( 7 ), 394 – 405 . CrossRefGoogle Scholar

Young, T. 1805 . III. An essay on the cohesion of fluids . Philos. Trans. Royal Soc. , 95 , 65 – 87 . Google Scholar

Zallen, R. 1983 . The Physics of Amorphous Solids . New York : John Wiley & Sons . CrossRefGoogle Scholar

Zhao, B. , MacMinn, C. W. , Primkulov, B., K. , et al. 2019 . Comprehensive comparison of pore-scale models for multiphase flow in porous media . Proc. Nat. Acad. Sci. , 116 , 13799 – 13806 . CrossRefGoogle ScholarPubMed

Zick, A. A. , and Homsy, G. M. 1982 . Stokes flow through periodic arrays of spheres . J. Fluid. Mech. , 115 , 13 – 26 . CrossRefGoogle Scholar