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1

Jaakko, Miettinen, and Ilvonen Mikko. "ICONE15-10291 SOLVING POROUS MEDIA FLOW FOR LWR COMPONENTS." Proceedings of the International Conference on Nuclear Engineering (ICONE) 2007.15 (2007): _ICONE1510. http://dx.doi.org/10.1299/jsmeicone.2007.15._icone1510_146.

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2

Blokhra, R. L., and J. Joshi. "Flow through Porous Media." Journal of Colloid and Interface Science 160, no. 1 (October 1993): 260–61. http://dx.doi.org/10.1006/jcis.1993.1393.

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3

Whitaker, Stephen. "Flow in porous media III: Deformable media." Transport in Porous Media 1, no. 2 (1986): 127–54. http://dx.doi.org/10.1007/bf00714689.

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4

STANLEY, H. E., A. D. ARAÚJO, U. M. S. COSTA, and J. S. ANDRADE. "FLUID FLOW THROUGH DISORDERED POROUS MEDIA." Fractals 11, supp01 (February 2003): 301–12. http://dx.doi.org/10.1142/s0218348x03001963.

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This talk briefly reviews the subject of fluid flow through disordered media. First, we use two-dimensional percolation networks as a simple model for porous media to investigate the dynamics of viscous penetration when the ratio between the viscosities of displaced and injected fluids is very large. The results indicate the possibility that viscous displacement through critical percolation networks constitutes a single universality class, independent of the viscosity ratio. We also focus on the sorts of considerations that may be necessary to move statistical physics from the description of idealized flows in the limit of zero Reynolds number to more realistic flows of real fluids moving at a nonzero velocity, when inertia effects may become relevant. We discuss several intriguing features, such as the surprisingly change in behavior from a "localized" to a "delocalized" flow structure (distribution of flow velocities) that seems to occur at a critical value of Re which is significantly smaller than the critical value of Re where turbulence sets in.
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5

Higdon, J. J. L. "Multiphase flow in porous media." Journal of Fluid Mechanics 730 (July 30, 2013): 1–4. http://dx.doi.org/10.1017/jfm.2013.296.

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AbstractMultiphase flows in porous media represent fluid dynamics problems of great complexity involving a wide range of physical phenomena. These flows have attracted the attention of an impressive group of renowned researchers and have spawned a number of classic problems in fluid dynamics. These multiphase flows are perhaps best known for their importance in oil recovery from petroleum reservoirs, but they also find application in novel areas such as hydrofracturing for natural gas recovery. In a recent article, Zinchenko & Davis (J. Fluid Mech. 2013, vol. 725, pp. 611–663) present computational simulations that break new ground in the study of emulsions flowing through porous media. These simulations provide sufficient scale to capture the disordered motion and complex break-up patterns of individual droplets while providing sufficient statistical samples for estimating meaningful macroscopic properties of technical interest.
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6

Paillat, T., E. Moreau, and G. Touchard. "Flow electrification through porous media." Journal of Loss Prevention in the Process Industries 14, no. 2 (March 2001): 91–93. http://dx.doi.org/10.1016/s0950-4230(00)00031-0.

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7

Geindreau, Christian, and Jean-Louis Auriault. "Magnetohydrodynamic flow through porous media." Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics 329, no. 6 (June 2001): 445–50. http://dx.doi.org/10.1016/s1620-7742(01)01354-x.

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8

Chan, Derek Y. C., Barry D. Hughes, Lincoln Paterson, and Christina Sirakoff. "Simulating flow in porous media." Physical Review A 38, no. 8 (October 1, 1988): 4106–20. http://dx.doi.org/10.1103/physreva.38.4106.

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9

Feder, Jens, and Torstein Jøssang. "Fractal Flow in Porous Media." Physica Scripta T29 (January 1, 1989): 200–205. http://dx.doi.org/10.1088/0031-8949/1989/t29/037.

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10

Adler, P. M., and H. Brenner. "Multiphase Flow in Porous Media." Annual Review of Fluid Mechanics 20, no. 1 (January 1988): 35–59. http://dx.doi.org/10.1146/annurev.fl.20.010188.000343.

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11

Koponen, A., M. Kataja, and J. Timonen. "Tortuous flow in porous media." Physical Review E 54, no. 1 (July 1, 1996): 406–10. http://dx.doi.org/10.1103/physreve.54.406.

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12

Rojas, Sergio, and Joel Koplik. "Nonlinear flow in porous media." Physical Review E 58, no. 4 (October 1, 1998): 4776–82. http://dx.doi.org/10.1103/physreve.58.4776.

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13

Barr, Douglas W. "Turbulent Flow Through Porous Media." Ground Water 39, no. 5 (September 2001): 646–50. http://dx.doi.org/10.1111/j.1745-6584.2001.tb02353.x.

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14

Adler, P. M., C. G. Jacquin, and J. A. Quiblier. "Flow in simulated porous media." International Journal of Multiphase Flow 16, no. 4 (July 1990): 691–712. http://dx.doi.org/10.1016/0301-9322(90)90025-e.

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15

Nazari Moghaddam, Rasoul, and Mahmoud Jamiolahmady. "Slip flow in porous media." Fuel 173 (June 2016): 298–310. http://dx.doi.org/10.1016/j.fuel.2016.01.057.

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16

Layton, William J., Friedhelm Schieweck, and Ivan Yotov. "Coupling Fluid Flow with Porous Media Flow." SIAM Journal on Numerical Analysis 40, no. 6 (January 2002): 2195–218. http://dx.doi.org/10.1137/s0036142901392766.

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17

Gruais, Isabelle, and Dan Poliševski. "Thermal flows in fractured porous media." ESAIM: Mathematical Modelling and Numerical Analysis 55, no. 3 (May 2021): 789–805. http://dx.doi.org/10.1051/m2an/2020087.

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We consider the thermal flow problem occuring in a fractured porous medium. The incompressible filtration flow in the porous matrix and the viscous flow in the fractures obey the Boussinesq approximation of Darcy-Forchheimer law and respectively, the Stokes system. They are coupled by the Saffman’s variant of the Beavers–Joseph condition. Existence and uniqueness properties are presented. The use of the energy norm in describing the Darcy-Forchheimer law proves to be appropriate. In the ε-periodic framework, we find the two-scale homogenized system which governs their asymptotic behaviours when ε → 0 and the Forchheimer effect vanishes. The limit problem is mainly a model of two coupled thermal flows, neither of them being incompressible.
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18

NAKAI, Hirotaka, Nobuhiro KIMURA, Masahide MURAKAMI, Tomiyoshi HARUYAMA, and Akira YAMAMOTO. "Superfluid Helium Flow through Porous Media." TEION KOGAKU (Journal of Cryogenics and Superconductivity Society of Japan) 31, no. 9 (1996): 474–80. http://dx.doi.org/10.2221/jcsj.31.474.

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19

Nakai, H., N. Kimura, M. Murakami, T. Haruyama, and A. Yamamoto. "Superfluid helium flow through porous media." Cryogenics 36, no. 9 (September 1996): 667–73. http://dx.doi.org/10.1016/0011-2275(96)00030-6.

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20

Dodson, C. T. J., and W. W. Sampson. "Flow Simulation in Stochastic Porous Media." SIMULATION 74, no. 6 (June 2000): 351–58. http://dx.doi.org/10.1177/003754970007400604.

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21

Watson, A. Ted, Raghavendra Kulkarni, Jan-Erik Nordtvedt, Andre Sylte, and Hege Urkedal. "Estimation of porous media flow functions." Measurement Science and Technology 9, no. 6 (June 1, 1998): 898–905. http://dx.doi.org/10.1088/0957-0233/9/6/006.

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22

Kordulová, P. "Hysteresis in flow through porous media." Journal of Physics: Conference Series 268 (January 1, 2011): 012014. http://dx.doi.org/10.1088/1742-6596/268/1/012014.

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23

Sochi, Taha. "Non-Newtonian flow in porous media." Polymer 51, no. 22 (October 2010): 5007–23. http://dx.doi.org/10.1016/j.polymer.2010.07.047.

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24

Winter, C. L., and Daniel M. Tartakovsky. "Mean Flow in composite porous media." Geophysical Research Letters 27, no. 12 (June 15, 2000): 1759–62. http://dx.doi.org/10.1029/1999gl011030.

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25

DENTZ, M., D. M. TARTAKOVSKY, E. ABARCA, A. GUADAGNINI, X. SANCHEZ-VILA, and J. CARRERA. "Variable-density flow in porous media." Journal of Fluid Mechanics 561 (August 2006): 209. http://dx.doi.org/10.1017/s0022112006000668.

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26

LIU, SHIJIE, and JACOB H. MASLIYAH. "SINGLE FLUID FLOW IN POROUS MEDIA." Chemical Engineering Communications 148-150, no. 1 (June 1996): 653–732. http://dx.doi.org/10.1080/00986449608936537.

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27

FABRIE, PIERRE, and THIERRY GALLOUËT. "MODELING WELLS IN POROUS MEDIA FLOW." Mathematical Models and Methods in Applied Sciences 10, no. 05 (July 2000): 673–709. http://dx.doi.org/10.1142/s0218202500000367.

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In this paper, we prove the existence of weak solutions for mathematical models of miscible and immiscible flow through porous medium. An important difficulty comes from the modelization of the wells, which does not allow us to use classical variational formulations of the equations.
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28

Moura, M., K. J. Måløy, and R. Toussaint. "Critical behavior in porous media flow." EPL (Europhysics Letters) 118, no. 1 (April 1, 2017): 14004. http://dx.doi.org/10.1209/0295-5075/118/14004.

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29

Dejam, Morteza, Hassan Hassanzadeh, and Zhangxin Chen. "Pre-Darcy Flow in Porous Media." Water Resources Research 53, no. 10 (October 2017): 8187–210. http://dx.doi.org/10.1002/2017wr021257.

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30

Farinato, Raymond S., and Wei S. Yen. "Polymer degradation in porous media flow." Journal of Applied Polymer Science 33, no. 7 (May 20, 1987): 2353–68. http://dx.doi.org/10.1002/app.1987.070330708.

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31

Dullien, Francis A. L. "Two-phase flow in porous media." Chemical Engineering & Technology - CET 11, no. 1 (1988): 407–24. http://dx.doi.org/10.1002/ceat.270110153.

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32

Massmann, Joel, and Lisa Johnson. "Exercises Illustrating Flow in Porous Media." Ground Water 39, no. 4 (July 2001): 499–503. http://dx.doi.org/10.1111/j.1745-6584.2001.tb02338.x.

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33

Reinson, Jeff R., Delwyn G. Fredlund, and G. Ward Wilson. "Unsaturated flow in coarse porous media." Canadian Geotechnical Journal 42, no. 1 (February 1, 2005): 252–62. http://dx.doi.org/10.1139/t04-070.

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Design of effective capillary barrier systems requires a thorough understanding of the soil–water interactions that take place in both coarse- and fine-grained unsaturated soils. Experimental observations of water flow through coarse porous media are presented to gain greater understanding of the processes and mechanisms that contribute to the movement and retention of water in coarse-grained unsaturated soils. The use of pendular ring theory to describe how water is held within a porous material with relatively low volumetric water contents is explored. Experimental measurements of seepage velocity and volumetric water content were obtained for columns of 12 mm glass beads using digital videography to capture the movement of a dye tracer front at several infiltration rates. An estimated curve for hydraulic conductivity versus matric suction is shown and compared to a theoretical curve. The method is shown to provide a reasonable predictive tool.Key words: soil-water characteristic curve, hydraulic conductivity curve, water permeability function, capillary barrier, matric suction.
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34

Entov, V. M. "Micromechanics of flow through porous media." Fluid Dynamics 27, no. 6 (1993): 824–33. http://dx.doi.org/10.1007/bf01051359.

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35

Hamdan, M. H., and K. D. Sawalha. "Dusty gas flow through porous media." Applied Mathematics and Computation 75, no. 1 (March 1996): 59–73. http://dx.doi.org/10.1016/0096-3003(95)00104-2.

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36

Gun, Wei Jin, and Alexander F. Routh. "Microcapsule flow behaviour in porous media." Chemical Engineering Science 102 (October 2013): 309–14. http://dx.doi.org/10.1016/j.ces.2013.08.028.

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37

Adler, Pierre M. "Multiphase flow in porous media ? Preface." Transport in Porous Media 20, no. 1-2 (August 1995): 1. http://dx.doi.org/10.1007/bf00616922.

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38

Zhu, Tao, and Michael Manhart. "Oscillatory Darcy Flow in Porous Media." Transport in Porous Media 111, no. 2 (December 14, 2015): 521–39. http://dx.doi.org/10.1007/s11242-015-0609-3.

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39

El Tawil, M. A., and M. H. Kamel. "MHD flow under stochastic porous media." Energy Conversion and Management 35, no. 11 (November 1994): 991–97. http://dx.doi.org/10.1016/0196-8904(94)90030-2.

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40

Du Plessis, J. Prieur, and Jacob H. Masliyah. "Flow through isotropic granular porous media." Transport in Porous Media 6, no. 3 (June 1991): 207–21. http://dx.doi.org/10.1007/bf00208950.

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41

Sauveplane, Claude M. "Flow in porous or fractured media." Journal of Hydrology 97, no. 3-4 (February 1988): 353–55. http://dx.doi.org/10.1016/0022-1694(88)90125-4.

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42

Buyevich, Yu A., and V. S. Nustrov. "Nonlinear flow in fractured porous media." Transport in Porous Media 12, no. 1 (July 1993): 1–17. http://dx.doi.org/10.1007/bf00616358.

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43

Mahadevan, Jagannathan, Mukul M. Sharma, and Yannis C. Yortsos. "Flow-through drying of porous media." AIChE Journal 52, no. 7 (2006): 2367–80. http://dx.doi.org/10.1002/aic.10859.

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44

Gayubov, A. T. "Non-Darcy Flow Through Porous Media." Proceedings of Gubkin Russian State University of Oil and Gas, no. 1 (2021): 19–28. http://dx.doi.org/10.33285/2073-9028-2021-1(302)-19-28.

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45

Liu, Hai Long, Junfeng Wang, and Wook Ryol Hwang. "Flow resistance of viscoelastic flows in fibrous porous media." Journal of Non-Newtonian Fluid Mechanics 246 (August 2017): 21–30. http://dx.doi.org/10.1016/j.jnnfm.2017.05.004.

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46

GRAHAM, D. R., and J. J. L. HIGDON. "Oscillatory forcing of flow through porous media. Part 1. Steady flow." Journal of Fluid Mechanics 465 (August 25, 2002): 213–35. http://dx.doi.org/10.1017/s0022112002001155.

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Oscillatory forcing of a porous medium may have a dramatic effect on the mean flow rate produced by a steady applied pressure gradient. The oscillatory forcing may excite nonlinear inertial effects leading to either enhancement or retardation of the mean flow. Here, in Part 1, we consider the effects of non-zero inertial forces on steady flows in porous media, and investigate the changes in the flow character arising from changes in both the strength of the inertial terms and the geometry of the medium. The steady-state Navier–Stokes equations are solved via a Galerkin finite element method to determine the velocity fields for simple two-dimensional models of porous media. Two geometric models are considered based on constricted channels and periodic arrays of circular cylinders. For both geometries, we observe solution multiplicity yielding both symmetric and asymmetric flow patterns. For the cylinder arrays, we demonstrate that inertial effects lead to anisotropy in the effective permeability, with the direction of minimum resistance dependent on the solid volume fraction. We identify nonlinear flow phenomena which might be exploited by oscillatory forcing to yield a net increase in the mean flow rate. In Part 2, we take up the subject of unsteady flows governed by the full time-dependent Navier–Stokes equations.
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47

Christie, M. A. "Flow in porous media — scale up of multiphase flow." Current Opinion in Colloid & Interface Science 6, no. 3 (June 2001): 236–41. http://dx.doi.org/10.1016/s1359-0294(01)00087-5.

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48

Kawale, Durgesh, Gelmer Bouwman, Shaurya Sachdev, Pacelli L. J. Zitha, Michiel T. Kreutzer, William R. Rossen, and Pouyan E. Boukany. "Polymer conformation during flow in porous media." Soft Matter 13, no. 46 (2017): 8745–55. http://dx.doi.org/10.1039/c7sm00817a.

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49

Sakamoto, H., and F. A. Kulacki. "Buoyancy Driven Flow in Saturated Porous Media." Journal of Heat Transfer 129, no. 6 (September 24, 2006): 727–34. http://dx.doi.org/10.1115/1.2717937.

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Measurements are reported of heat transfer coefficients in steady natural convection on a vertical constant flux plate embedded in a saturated porous medium. Results show that heat transfer coefficients can be adequately determined via a Darcy-based model, and our results confirm a correlation proposed by Bejan [Int. J. Heat Mass Transfer. 26(9), 1339–1346 (1983)]. It is speculated that the reason that the Darcy model works well in the present case is that the porous medium has a lower effective Prandtl number near the wall than in the bulk medium. The factors that contribute to this effect include the thinning of the boundary layer near the wall and an increase of effective thermal conductivity.
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50

Haward, Simon J., Cameron C. Hopkins, and Amy Q. Shen. "Stagnation points control chaotic fluctuations in viscoelastic porous media flow." Proceedings of the National Academy of Sciences 118, no. 38 (September 14, 2021): e2111651118. http://dx.doi.org/10.1073/pnas.2111651118.

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Viscoelastic flows through porous media become unstable and chaotic beyond critical flow conditions, impacting widespread industrial and biological processes such as enhanced oil recovery and drug delivery. Understanding the influence of the pore structure or geometry on the onset of flow instability can lead to fundamental insights into these processes and, potentially, to their optimization. Recently, for viscoelastic flows through porous media modeled by arrays of microscopic posts, Walkama et al. [D. M. Walkama, N. Waisbord, J. S. Guasto, Phys. Rev. Lett. 124, 164501 (2020)] demonstrated that geometric disorder greatly suppressed the strength of the chaotic fluctuations that arose as the flow rate was increased. However, in that work, disorder was only applied to one originally ordered configuration of posts. Here, we demonstrate experimentally that, given a slightly modified ordered array of posts, introducing disorder can also promote chaotic fluctuations. We provide a unifying explanation for these contrasting results by considering the effect of disorder on the occurrence of stagnation points exposed to the flow field, which depends on the nature of the originally ordered post array. This work provides a general understanding of how pore geometry affects the stability of viscoelastic porous media flows.
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