Similar articles

Abstract: In this study, the permeability of structured porous media with the microfluidic model is experimentally and numerically determined, and compared with the classic Kozeny-Carman (KC) equation. The Reynolds number (Re) varies from 0.83 to 142.98. It is observed that the threshold of the Reynolds number is 1. When Re is below the threshold, the permeability is independent of the Reynolds number. When Re is over this threshold, the viscous force plays a dominant role and the permeability decreases with the Reynolds number increment. The permeability also rises with the diameter increment. With the same micropillar diameter, the microfluidic model with a triangular pillar arrangement yields 4.5%–7.4% lower permeability than that with a square pillar arrangement. The tortuosity obtained by numerical simulation in the triangular-arrangement model is 5.1%–7.9% higher than that in the square-arrangement model. Based on the arrangement of micropillars, a tortuosity model is proposed for quasi-two-dimensional microfluidic models. There is an inverse relationship between permeability and tortuosity. In addition, the permeability generated by numerical simulation is consistent with that obtained experimentally. However, the permeability estimated by the classic KC equation roughly agrees with experimental results when the porosity is between 0.50 and 0.60. A model proposed in this study is suitable for predicting the permeability of microfluidic models. Furthermore, anisotropy induced by the tilt angle (0°–90°) of a model rectangular micropillar arrangement causes preferential flow and decreases the effective porosity. When the tilt angle increases from 0° to 90°, the tortuosity declines from 2.04 to 1.03, causing the permeability to rise from 1.0×10-11 to 4.3×10-11 m2.

结构化多孔介质的渗透性：数值模拟和微流控模型

[1]AkbariM, SintonD, BahramiM, 2009. Pressure drop in rectangular microchannels as compared with theory based on arbitrary cross section. Journal of Fluids Engineering, 131(4):041202.

[2]AntoheBV, LageJL, PriceDC, et al., 1997. Experimental determination of permeability and inertia coefficients of mechanically compressed aluminum porous matrices. Journal of Fluids Engineering, 119(2):404-412.

[3]AusetM, KellerAA, 2004. Pore-scale processes that control dispersion of colloids in saturated porous media. Water Resources Research, 40(3):W03503.

[4]BahramiM, YovanovichMM, CulhamJR, 2007. A novel solution for pressure drop in singly connected microchannels of arbitrary cross-section. International Journal of Heat and Mass Transfer, 50(13-14):2492-2502.

[5]BateB, ChenC, LiuPF, et al., 2022. The migration and deposition behaviors of montmorillonite and kaolinite particles in a two-dimensional micromodel. Materials, 15(3):855.

[6]BazarinRLM, de LaiFC, NaaktgeborenC, et al., 2021. Boundary effects on the tortuosity and permeability of idealized porous media. Transport in Porous Media, 136(3):743-764.

[7]BazylakA, BerejnovV, MarkicevicB, et al., 2008. Numerical and microfluidic pore networks: towards designs for directed water transport in GDLs. Electrochimica Acta, 53(26):7630-7637.

[8]CaiJC, HuXY, StandnesDC, et al., 2012. An analytical model for spontaneous imbibition in fractal porous media including gravity. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 414:228-233.

[9]CaoSC, JungJ, RadonjicM, 2019. Application of microfluidic pore models for flow, transport, and reaction in geological porous media: from a single test bed to multifunction real-time analysis tool. Microsystem Technologies, 25(11):4035-4052.

[10]CardonaA, SantamarinaJC, 2020. Carbonate rocks: matrix permeability estimation. AAPG Bulletin, 103(1):131-144.

[11]CarmanPC, 1939. Permeability of saturated sands, soils and clays. The Journal of Agricultural Science, 29(2):262-273.

[12]CarmanPC, 1956. Flow of Gases Through Porous Media. Academic Press, New York, USA.

[13]Castillo-AraizaCO, Lopez-IsunzaF, 2008. Hydrodynamic models for packed beds with low tube-to-particle diameter ratio. International Journal of Chemical Reactor Engineering, 6(1):A1.

[14]ChenC, 2021. Study on Fine Particle Migration and Permeability Characteristics in Porous Media Based on Microfluidic Chips. MS Thesis, Zhejiang University, Hangzhou, China(in Chinese).

[15]ChenC, NieSK, LiuPF, et al., 2021. Permeability characteristics of porous media based on 2D microfluidic chips. Journal of Central South University (Science and Technology), 52(9):3295-3302(in Chinese).

[16]ChenKX, LiuPF, WangWY, et al., 2023. Effects of capillary and viscous forces on two-phase fluid displacement in the microfluidic model. Energy & Fuels, 37(22):17263-17276.

[17]CollinsRE, 1961. Flow of Fluids Through Porous Materials. Reinhold Publishing Corporation, New York, USA.

[18]ComitiJ, RenaudM, 1989. A new model for determining mean structure parameters of fixed beds from pressure drop measurements: application to beds packed with parallelepipedal particles. Chemical Engineering Science, 44(7):1539-1545.

[19]ConnCA, MaK, HirasakiGJ, et al., 2014. Visualizing oil displacement with foam in a microfluidic device with permeability contrast. Lab on a Chip, 14(20):3968-3977.

[20]DaigleH, DuganB, 2011. Permeability anisotropy and fabric development: a mechanistic explanation. Water Resources Research, 47(12):W12517.

[21]DeS, KrishnanP, van der SchaafJ, et al., 2018. Viscoelastic effects on residual oil distribution in flows through pillared microchannels. Journal of Colloid and Interface Science, 510:262-271.

[22]DybbsA, EdwardsRV, 1984. A new look at porous media fluid mechanics—Darcy to turbulent. In: Bear J, Corapcioglu MY (Eds.), Fundamentals of Transport Phenomena in Porous Media. Springer, Dordrecht, the Netherlands, p.199-256.

[23]FeranieS, LatiefFDE, 2013. Tortuosity-porosity relationship in two-dimensional fractal model of porous media. Fractals, 21(2):1350013.

[24]GundaNSK, JosephJ, TamayolA, et al., 2013. Measurement of pressure drop and flow resistance in microchannels with integrated micropillars. Microfluidics and Nanofluidics, 14(3):711-721.

[25]HappelJ, 1959. Viscous flow relative to arrays of cylinders. AIChE Journal, 5(2):174-177.

[26]HuR, WanJM, YangZB, et al., 2018. Wettability and flow rate impacts on immiscible displacement: a theoretical model. Geophysical Research Letters, 45(7):3077-3086.

[27]HuangYP, YaoF, ZhouB, et al., 2020. Numerical study on permeability characteristics of fractal porous media. Chinese Physics B, 29(5):054701.

[28]KavianyM, 1995. Principles of Heat Transfer in Porous Media. Springer, New York, USA.

[29]KawagoeY, OshimaT, TomarikawaK, et al., 2016. A study on pressure-driven gas transport in porous media: from nanoscale to microscale. Microfluidics and Nanofluidics, 20(12):162.

[30]KhabbaziAE, HinebaughJ, BazylakA, 2015. Analytical tortuosity‍–‍porosity correlations for Sierpinski carpet fractal geometries. Chaos, Solitons & Fractals, 78:124-133.

[31]KoponenA, KatajaM, TimonenJ, 1996. Tortuous flow in porous media. Physical Review E, 54(1):406-410.

[32]KoponenA, KatajaM, TimonenJ, 1997. Permeability and effective porosity of porous media. Physical Review E, 56(3):3319-3325.

[33]KoponenA, KandhaiD, HellénE, et al., 1998. Permeability of three-dimensional random fiber webs. Physical Review Letters, 80(4):716-719.

[34]KoponenA, EkmanA, MattilaK, et al., 2017. The effect of void structure on the permeability of fibrous networks. Transport in Porous Media, 117(2):247-259.

[35]KoşarA, MishraC, PelesY, 2005. Laminar flow across a bank of low aspect ratio micro pin fins. Journal of Fluids Engineering, 127(3):419-430.

[36]KruczekB, 2014. Carman‍–‍Kozeny equation. In: Drioli E, Giorno L (Eds.), Encyclopedia of Membranes. Springer, Berlin, Germany, p.1-3.

[37]KumarA, ReddyRG, 2003. Modeling of polymer electrolyte membrane fuel cell with metal foam in the flow-field of the bipolar/end plates. Journal of Power Sources, 114(1):54-62.

[38]LanfreyPY, KuzeljevicZV, DudukovicMP, 2010. Tortuosity model for fixed beds randomly packed with identical particles. Chemical Engineering Science, 65(5):1891-1896.

[39]LeeSL, YangJH, 1997. Modeling of Darcy-Forchheimer drag for fluid flow across a bank of circular cylinders. International Journal of Heat and Mass Transfer, 40(13):3149-3155.

[40]LefebvreLP, BanhartJ, DunandDC, 2008. Porous metals and metallic foams: current status and recent developments. Advanced Engineering Materials, 10(9):775-787.

[41]LiT, LiM, JingXQ, et al., 2019. Influence mechanism of pore-scale anisotropy and pore distribution heterogeneity on permeability of porous media. Petroleum Exploration and Development, 46(3):594-604.

[42]LiuDD, TranT, 2018. Microfluidic mixing using PDMS-based microporous structures. Microfluidics and Nanofluidics, 22(11):123.

[43]LockPA, JingXD, ZimmermanRW, et al., 2002. Predicting the permeability of sandstone from image analysis of pore structure. Journal of Applied Physics, 92(10):6311-6319.

[44]LoosveldtH, LafhajZ, SkoczylasF, 2002. Experimental study of gas and liquid permeability of a mortar. Cement and Concrete Research, 32(9):1357-1363.

[45]LuT, TangYM, TieYB, et al., 2023. Fractal analysis of small-micro pores and estimation of permeability of loess using mercury intrusion porosimetry. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 24(7):584-595.

[46]LuTJ, StoneHA, AshbyMF, 1998. Heat transfer in open-cell metal foams. Acta Materialia, 46(10):3619-3635.

[47]MathavanGN, ViraraghavanT, 1992. Coalescence/filtration of an oil-in-water emulsion in a peat bed. Water Research, 26(1):91-98.

[48]MiguelAF, 2012. Non-Darcy porous media flow in no-slip and slip regimes. Thermal Science, 16(1):167-176.

[49]NieSK, LiuPF, BaT, et al., 2023. Seepage experiment and numerical simulation based on microfluidic chip model. Journal of Zhejiang University (Engineering Science), 57(5):967-976(in Chinese).

[50]PozrikidisC, 1994. The motion of particles in the Hele-Shaw cell. Journal of Fluid Mechanics, 261:199-222.

[51]RaeesiB, PiriM, 2009. The effects of wettability and trapping on relationships between interfacial area, capillary pressure and saturation in porous media: a pore-scale network modeling approach. Journal of Hydrology, 376(3-4):337-352.

[52]SantamarinaJC, ChoGC, 2004. Soil behavior: the role of particle shape. Advances in Geotechnical Engineering: the Skempton Conference.

[53]SerrenhoA, MiguelAF, 2009. Simulation and characterization of high-porosity media for aerosol particle processing: a numerical study. Journal of Porous Media, 12(12):1129-1137.

[54]SerrenhoA, MiguelAF, 2011. Fluid flow and solid/fluid suspensions flow in 3-D packed beds of spheres: the effect of periodicity of fixed beds. Defect and Diffusion Forum, 312-315:871-876.

[55]SharmaS, GeyerTF, ArcondoulisEJG, 2023. On the influence of porous coating thickness and permeability on passive flow and noise control of cylinders. Journal of Sound and Vibration, 549:117563.

[56]ShenJT, ChenSY, 1989. The following behaviours of a spherical particle in fluid flow. Acta Aerodynamica Sinica, 7(1):50-58(in Chinese).

[57]StraughanB, HarfashAJ, 2013. Instability in Poiseuille flow in a porous medium with slip boundary conditions. Microfluidics and Nanofluidics, 15(1):109-115.

[58]TamayolA, BahramiM, 2011a. In-plane gas permeability of proton exchange membrane fuel cell gas diffusion layers. Journal of Power Sources, 196(7):3559-3564.

[59]TamayolA, BahramiM, 2011b. Transverse permeability of fibrous porous media. Physical Review E, 83(4):046314.

[60]TamayolA, BahramiM, 2011c. Water permeation through gas diffusion layers of proton exchange membrane fuel cells. Journal of Power Sources, 196(15):6356-6361.

[61]TamayolA, KhoslaA, GrayBL, et al., 2012a. Creeping flow through ordered arrays of micro-cylinders embedded in a rectangular minichannel. International Journal of Heat and Mass Transfer, 55(15-16):3900-3908.

[62]TamayolA, WongKW, BahramiM, 2012b. Effects of microstructure on flow properties of fibrous porous media at moderate Reynolds number. Physical Review E, 85(2):026318.

[63]TawfikH, HungY, MahajanD, 2007. Metal bipolar plates for PEM fuel cell—a review. Journal of Power Sources, 163(2):755-767.

[64]von RickenbachJ, LucciF, NarayananC, et al., 2014. Multi-scale modelling of mass transfer limited heterogeneous reactions in open cell foams. International Journal of Heat and Mass Transfer, 75:337-346.

[65]WagnerA, EggenweilerE, WeinhardtF, et al., 2021. Permeability estimation of regular porous structures: a benchmark for comparison of methods. Transport in Porous Media, 138(1):1-23.

[66]WanJM, WilsonJL, 1994. Colloid transport in unsaturated porous media. Water Resources Research, 30(4):857-864.

[67]WangP, 2014. Lattice Boltzmann simulation of permeability and tortuosity for flow through dense porous media. Mathematical Problems in Engineering, 2014:694350.

[68]WhiteFM, 1991. Viscous Fluid Flow. McGraw-Hill, New York, USA.

[69]YangJ, YinZY, LaouafaF, et al., 2019. Modeling coupled erosion and filtration of fine particles in granular media. Acta Geotechnica, 14(6):1615-1627.

[70]YangJ, YinZY, LaouafaF, et al., 2020a. Hydromechanical modeling of granular soils considering internal erosion. Canadian Geotechnical Journal, 57(2):157-172.

[71]YangJ, YinZY, LaouafaF, et al., 2020b. Three-dimensional hydromechanical modeling of internal erosion in dike-on-foundation. International Journal for Numerical and Analytical Methods in Geomechanics, 44(8):1200-1218.

[72]YangXH, SongSY, YangC, et al., 2017. Permeability model of micro-metal foam with surface micro-roughness. Microfluidics and Nanofluidics, 21(3):32.

[73]YangXH, WeldetsadikNT, HayatZ, et al., 2019. Pressure drop of single phase flow in microchannels and its application in characterizing the apparent rheological property of fluids. Microfluidics and Nanofluidics, 23(5):75.

[74]YazdchiK, SrivastavaS, LudingS, 2011. Microstructural effects on the permeability of periodic fibrous porous media. International Journal of Multiphase Flow, 37(8):956-966.

[75]YinZY, YangJ, LaouafaF, et al., 2023. A framework for coupled hydro-mechanical continuous modelling of gap-graded granular soils subjected to suffusion. European Journal of Environmental and Civil Engineering, 27(8):2678-2699.

[76]YovanovichMM, 1974. A general expression for predicting conduction shape factors. The 11th Aerospace Sciences Meeting.

[77]YuBM, LiJH, 2004. A geometry model for tortuosity of flow path in porous media. Chinese Physics Letters, 21(8):1569-1571.

[78]ZhangJF, 2011. Lattice Boltzmann method for microfluidics: models and applications. Microfluidics and Nanofluidics, 10(1):1-28.

[79]ZhangS, YanH, TengJD, et al., 2020. A mathematical model of tortuosity in soil considering particle arrangement. Vadose Zone Journal, 19(1):e20004.

[80]ZhouC, WangWY, ChenKX, et al., 2022. Influence of wettability in immiscible displacements with lattice Boltzmann method. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 23(9):704-720.