Hostname: page-component-848d4c4894-m9kch Total loading time: 0 Render date: 2024-06-03T16:11:40.830Z Has data issue: false hasContentIssue false

Pore-scale modelling of particle transport in a porous bed

Published online by Cambridge University Press:  11 January 2024

Randall Storm
Affiliation:
Department of Mechanical Engineering, The University of Vermont, Burlington, VT 05405, USA
Jeffrey S. Marshall*
Affiliation:
Department of Mechanical Engineering, The University of Vermont, Burlington, VT 05405, USA
*
Email address for correspondence: jeffm@cems.uvm.edu

Abstract

A computational study was performed of the transport of both non-adhesive and adhesive particles in a porous bed with a body-centred cubic (BCC) structure. Pore-scale simulation of the flow within the porous bed was achieved through combining the immersed boundary method and the lattice Boltzmann method. Particle transport is computed using an adhesive discrete-element method based on a multi-time-scale soft-sphere model. The fluid flow results are validated by comparison with experimental data for dimensionless permeability of flow in a porous bed of spheres. For computations with non-adhesive particles, the particles are observed to drift to the centre of ‘channels’ in the BCC array, within which most of the fluid flow occurs. The mechanism of this inward drift was found to be related to the phenomenon of oscillatory clustering, which is an inertial drift mechanism observed for particles in a corrugated channel. A measure for particle drift into these channels was developed, and the time rate of change of this measure was found to compare closely with an approximate theoretical prediction based on oscillatory clustering theory. The drift measure was observed to be limited at long time by hold-up of outlier particles caught in long-duration collisions with the fixed bed particles in regions of low fluid velocity magnitude. Simulations with adhesive particles exhibited marked increase in collision duration, as well as inhibition of the tendency to drift toward the flow channels due to adhesive hold-up.

Type
JFM Papers
Copyright
© The Author(s), 2024. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abelhamid, Y. & El Shamy, U. 2016 Pore-scale modeling of fine-particle migration in granular filters. Intl J. Geomech. 16 (3), 04015086.CrossRefGoogle Scholar
Apte, S.V., Oujia, T., Matsuda, K., Kadoch, B., He, X. & Schneider, K. 2022 Clustering of inertial particles in turbulent flow through a porous unit cell. J. Fluid Mech. 937, A9.CrossRefGoogle Scholar
Babakhani, P., Bridge, J., Doong, R.A. & Phenrat, T. 2017 Continuum-based models and concepts for the transport of nanoparticles in saturated porous media: a state-of-the-science review. Adv. Colloid Interface Sci. 246, 75104.CrossRefGoogle ScholarPubMed
Bagi, K. & Kuhn, M.R. 2004 A definition of particle rolling in a granular assembly in terms of particle translations and rotations. J. Appl. Mech. 71, 493501.CrossRefGoogle Scholar
Bahrami, B., Hojjat-Farsangi, M., Mohammadi, H., Anvari, E., Ghalamfarsa, G., Yousefi, M. & Jadidi-Niaragh, F. 2017 Nanoparticles and targeted drug delivery in cancer therapy. Immunol. Lett. 190, 6483.CrossRefGoogle ScholarPubMed
Benamar, A., Ahfir, N.D., Wang, H.Q. & Alem, A. 2007 Particle transport in a saturated porous medium: pore structure effects. C. R. Geosci. 339, 674681.CrossRefGoogle Scholar
Bizmark, N., Schneider, J., Priestley, R.D. & Datta, S. 2020 Multiscale dynamics of colloidal deposition and erosion in porous media. Sci. Adv. 6, eabc2530.CrossRefGoogle ScholarPubMed
Blazejewski, R. & Murat-Blazejewski, S. 2014 Resistance to creeping flow and permeability of stacked spheres. J. Porous Media 17, 731740.CrossRefGoogle Scholar
Boccardo, G., Tosco, T., Fujisaki, A., Messina, F., Raoof, A., Aguilera, D.R., Crevacore, E., Marchisio, D.L. & Sethi, R. 2020 A review of transport of nanoparticles in porous media: from pore- to macroscale using computational methods. In Nanomaterials for the Detection and Removal of Wastewater Pollutants (eds. Bonelli, B. Frayria, F.S. Rossetti, I. & Sethi, R), pp. 351381. Elsevier.CrossRefGoogle Scholar
Boudina, M., Gosselin, F.P. & Étienne, S. 2020 Direct interception or inertial impaction? A theoretical derivation of the efficiency power law for a simple and practical definition of capture modes. Phys. Fluids 32, 123603.CrossRefGoogle Scholar
Bradford, S., Simunek, J., Bettahar, M., van Genuchten, M.T. & Yates, S.R. 2006 Significance of straining in colloid deposition: evidence and implications. Water Resour. Res. 42, W12S15.CrossRefGoogle Scholar
Bradford, S., Yates, S.R., Bettahar, M. & Simunek, J. 2002 Physical factors affecting the transport and fate of colloids in saturated porous media. Water Resour. Res. 38 (12), 1327.CrossRefGoogle Scholar
Chen, X., Zhang, X. & Wu, Z. 2019 Analytical solution for one-dimensional transport of particles considering dispersion in deposition kinetics. Geofluids 2019, 1941426.CrossRefGoogle Scholar
Chokshi, A., Tielens, A.G.G.M. & Hollenbach, D. 1993 Dust coagulation. Astrophys. J. 407, 806819.CrossRefGoogle Scholar
Chu, X., Li, T., Yan, A. & Shen, C. 2019 Transport of microplastic particles in saturated porous media. Water 11 (12), 2474.CrossRefGoogle Scholar
Crowe, C.T., Schwarzkopf, J.D., Sommerfeld, M. & Tsuji, Y. 2012 Multiphase Flows with Droplets and Particles, 2nd ed. CRC Press.Google Scholar
Deng, S., Li, H., Ma, G., Huang, H. & Li, X. 2014 Simulation of shale-proppant interaction in hydraulic fracturing by the discrete element method. Intl J. Rock Mech. Mining Sci. 70, 219228.CrossRefGoogle Scholar
Derjaguin, B.V. & Landau, L. 1941 Theory of the stability of strongly charged lyophobic sols and of the adhesion of strongly charged particles in solutions of electrolytes. Acta Physicochim. USSR 14, 633662.Google Scholar
Derjaguin, B.V., Muller, V.M. & Toporov, Y.P. 1975 Effect of contact deformations on the adhesion of particles. J. Colloid Interface Sci. 53 (2), 314326.CrossRefGoogle Scholar
Dominik, C. & Tielens, A.G.G.M. 1995 Resistance to rolling in the adhesive contact of two elastic spheres. Phil. Mag. A 92 (3), 783803.CrossRefGoogle Scholar
Druzhinin, O.A. & Ostrovsky, L.A. 1994 The influence of Basset force on particle dynamics in two-dimensional flows. Physica D 76, 3443.CrossRefGoogle Scholar
Elrahmani, A., Al-Raoush, R.I., Abugazia, H. & Seers, T. 2022 Pore-scale simulation of fine particles migration in porous media using coupled CFD-DEM. Powder Technol. 398, 117130.CrossRefGoogle Scholar
Endo Kokubun, M.A., Muntean, A., Radu, F.A., Kumar, K., Pop, I.S., Keilegavlen, E. & Spildo, K. 2019 A pore-scale study of transport of inertial particles by water in porous media. Chem. Engng Sci. 207, 397409.CrossRefGoogle Scholar
Ferry, J., Rani, S.L. & Balachandar, S. 2003 A locally implicit improvement of the equilibrium Eulerian method. Intl J. Multiphase Flow 29, 869891.CrossRefGoogle Scholar
Forier, K., Raemdonck, K., De Smedt, S.C., Demeester, J., Coenye, T. & Braeckmans, K. 2014 Lipid and polymer nanoparticles for drug delivery to bacterial biofilms. J. Control. Release 190, 607623.CrossRefGoogle ScholarPubMed
Franzen, P. 1979 Zum Einfluß der Porengeometrie auf den Druckverlust bei der Durchströmung von Porensystemen. Rheol. Acta 18, 518536.CrossRefGoogle Scholar
Fu, W., Min, J., Jiang, W., Li, Y. & Zhang, W. 2020 Separation, characterization and identification of microplastics and nanoplastics in the environment. Sci. Total Environ. 721, 137561.CrossRefGoogle ScholarPubMed
Galindo-Torres, S.A. 2013 A coupled discrete element lattice Boltzmann method for the simulation of fluid-solid interaction with particles of general shapes. Comput. Meth. Appl. Mech. Engng 265, 107119.CrossRefGoogle Scholar
Han, C.D., Romero, N., Fischer, S., Dookran, J., Berger, A. & Doiron, A.L. 2017 Recent developments in the use of nanoparticles for treatment of biofilms. Nanotechnol. Rev. 6, 383404.CrossRefGoogle Scholar
Hertz, H. 1882 Über die Berührung fester elastische Körper. J. Reine Angew. Math. 92, 156171.CrossRefGoogle Scholar
Hewitt, G.F. & Marshall, J.S. 2010 Particle focusing in suspension flow through a corrugated tube. J. Fluid Mech. 660, 258281.CrossRefGoogle Scholar
Heyman, J., Lester, D.R., Turuban, R., Méheust, Y. & Le Borgne, T. 2020 Stretching and folding sustain microscale chemical gradients in porous media. Proc. Natl Acad. Sci. 117 (24), 1335913365.CrossRefGoogle ScholarPubMed
Hill, R.J., Koch, D.L. & Ladd, A.J. 2001 Moderate Reynolds number flows in ordered and random arrays of spheres. J. Fluid Mech. 448, 243278.CrossRefGoogle Scholar
Iwashita, K. & Oda, M. 1998 Rolling resistance at contacts in simulation of shear band development by DEM. J. Engng Mech. 124 (3), 285292.Google Scholar
Jaganathan, D., Prasath, S.G., Govindarajan, R. & Vasan, V. 2023 The Basset-Boussinesq history force: its neglect, validity, and recent numerical developments. Front. Phys. 11, 1167338.CrossRefGoogle Scholar
Johnson, K.L. & Greenwood, J.A. 1997 An adhesion map for the contact of elastic spheres. J. Colloid Interface Sci. 192, 326333.CrossRefGoogle ScholarPubMed
Johnson, K.L., Kendall, K. & Roberts, A.D. 1971 Surface energy and the contact of elastic solids. Proc. R. Soc. Lond. A 324, 301313.Google Scholar
Joseph, G.G., Zenit, R., Hunt, M.R. & Rosenwinkel, A.M. 2001 Particle-wall collisions in a viscous fluid. J. Fluid Mech. 433, 329346.CrossRefGoogle Scholar
Kampel, G., Goldsztein, G.H. & Santamarina, J.C. 2009 Particle transport in porous media: the role of inertial effects and path tortuosity in the velocity of particles. Appl. Phys. Lett. 95, 194103.CrossRefGoogle Scholar
Kermani, M.S., Jafari, S., Rahnama, M. & Raoof, A. 2020 Direct pore scale numerical simulation of colloid transport and retention. Part I. Fluid flow velocity, colloid size, and pore structure effects. Adv. Water Resour. 144, 103694.CrossRefGoogle Scholar
Krüger, T., Kusumaatmaja, H., Kuzmin, A., Shardt, O., Silva, G. & Viggen, E.M. 2017 The Lattice Boltzmann Method: Principles and Practice, chapter 7. Springer.CrossRefGoogle Scholar
Li, J., Nickel, R., Wu, J., Lin, F., van Lierop, J. & Liu, S. 2019 A new tool to attack biofilms: driving magnetic iron-oxide nanoparticles to disrupt the matrix. Nanoscale 11 (14), 69056915.CrossRefGoogle ScholarPubMed
Li, S., Yu, H.H. & Fan, J. 2021 Modeling transport of soft particles in porous media. Phys. Rev. E 104, 025112.CrossRefGoogle ScholarPubMed
Liang, F., Sayed, M., Al-Muntasheri, G.A., Chang, F.F. & Li, L. 2016 A comprehensive review on proppant technologies. Petroleum 2, 2639.CrossRefGoogle Scholar
Ma, D., Green, A.M., Willsey, G.G., Marshall, J.S., Wargo, M.J. & Wu, J.R. 2015 Effects of acoustic streaming from moderate-intensity pulsed ultrasound for enhancing biofilm mitigation effectiveness of drug-loaded liposomes. J. Acoust. Soc. Am. 138 (2), 10431051.CrossRefGoogle ScholarPubMed
Maier, R. & Bernard, R.S. 2010 Lattice-Boltzmann accuracy in pore-scale flow simulation. J. Comput. Phys. 229, 233255.CrossRefGoogle Scholar
Maier, R., Kroll, D.M., Davis, H.T. & Bernard, R. 1998 Simulation of flow in bead packs using the lattice-Boltzmann method. Phys. Fluids 10 (1), 6074.CrossRefGoogle Scholar
Marshall, J.S. 2009 a Discrete-element modeling of particulate aerosol flows. J. Comput. Phys. 228, 15411561.CrossRefGoogle Scholar
Marshall, J.S. 2009 b Particle clustering in periodically-forced straining flows. J. Fluid Mech. 624, 69100.CrossRefGoogle Scholar
Marshall, J.S. & Li, S. 2014 Adhesive Particle Flow – A Discrete-Element Approach, pp. 58, 146. Cambridge University Press.CrossRefGoogle Scholar
McDowell-Boyer, L.M., Hunt, J.R. & Sitar, N. 1986 Particle transport through porous media. Water Resour. Res. 22 (13), 19011921.CrossRefGoogle Scholar
Millenbaugh, N.J., Baskin, J.B., DeSilva, M.N., Elliot, W.R. & Glickman, R.D. 2015 Photothermal killing of Staphylococcus aureus using antibody-targeted gold nanoparticles. Intl J. Nanomed. 10, 19531960.CrossRefGoogle ScholarPubMed
Mitchell, M.J., Billingsley, M.M., Haley, R.M., Wechsler, M.E., Peppas, N.A. & Langer, R. 2021 Engineering precision nanoparticles for drug delivery. Nat. Rev. 20, 101124.Google ScholarPubMed
Molnar, I.L., Johnson, W.P., Gerhard, J.I., Willson, C.S. & O'Carroll, D.M. 2015 Predicting colloid transport through saturated porous media: a critical review. Water Resour. Res. 51 (9), 68046845.CrossRefGoogle Scholar
Narayan, R., Coury, J.R., Masliyah, J.H. & Gray, M.R. 1997 Particle capture and plugging in packed-bed reactors. Ind. Engng Chem. Res. 36 (11), 46204627.CrossRefGoogle Scholar
Noble, D. & Torczzynski, J. 1998 A Lattice-Boltzmann method for partially saturated computational cells. Intl J. Mod. Phys. C 9 (8), 11891201.CrossRefGoogle Scholar
Oda, M., Konishi, J. & Nemat-Nasser, S. 1982 Experimental micromechanical evaluation of strength of granular materials: effects of particle rolling. Mech. Mater. 1 (4), 269283.CrossRefGoogle Scholar
Owen, D., Leonardi, C. & Feng, Y. 2010 An efficient framework for fluid–structure interaction using the lattice boltzmann method and immersed moving boundaries. Intl J. Numer. Meth. Engng 87 (1–5), 6695.CrossRefGoogle Scholar
Patra, J.K., et al. 2018 Nano based drug delivery systems: recent developments and future prospects. J. Nanobiotechnol. 16, 71.CrossRefGoogle ScholarPubMed
Peulen, T.-O. & Wilkinson, K.J. 2011 Diffusion of nanoparticles in a biofilm. Environ. Sci. Technol. 45, 33673373.CrossRefGoogle Scholar
Porubcan, A.A. & Xu, S. 2011 Colloid straining within saturated heterogeneous porous media. Water Res. 45, 17961806.CrossRefGoogle ScholarPubMed
Quan, K., Zhang, Z., Ren, Y., Busscher, H.J., van der Mei, H.C. & Peterson, B.W. 2020 Homogeneous distribution of magnetic, antimicrobial-carrying nanoparticles through an infectious biofilm enhances biofilm-killing efficacy. Biomater. Sci. Engng 6, 205212.CrossRefGoogle ScholarPubMed
Rasmuson, A., Pazmino, E., Assemi, S. & Johnson, W.P. 2017 Contribution of nano- to microscale roughness to heterogeneity: closing the gap between unfavorable and favorable colloid attachment conditions. Environ. Sci. Technol. 51, 21512160.CrossRefGoogle Scholar
Richardson, J.F. & Zaki, W.N. 1954 Sedimentation and fluidization. Part I. Trans. Inst. Chem. Engrs 32, 3553 (1954).Google Scholar
Rubinow, S.I. & Keller, J.B. 1961 The transverse force on a spinning sphere moving in a viscous fluid. J. Fluid Mech. 11, 447459.CrossRefGoogle Scholar
Sadeghnejad, S., Enzmann, F. & Kersten, M. 2022 Numerical study of particle retention mechanisms at the sub-pore scale. Transport in Porous Media 145 (7), 127151.CrossRefGoogle Scholar
Saffman, P.G. 1965 The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22, 385400.CrossRefGoogle Scholar
Saffman, P.G. 1968 Corrigendum to ‘The lift force on a small sphere in a slow shear flow’. J. Fluid Mech. 31, 624.Google Scholar
Sanematsu, P.C., Thompson, K.E. & Willson, C.S. 2019 Pore-scale modeling of nanoparticle transport and retention in real porous materials. Comput. Geosci. 127, 6574.CrossRefGoogle Scholar
Shen, C., Huang, Y., Li, B. & Jin, Y. 2010 Predicting attachment efficiency of colloid deposition under unfavorable attachment conditions. Water Resour. Res. 46, W11526.CrossRefGoogle Scholar
Shen, C., Jin, Y., Zhuang, J., Li, T. & Xing, B. 2020 Role and importance of surface heterogeneities in transport of particles in saturated porous media. Crit. Rev. Environ. Sci. Technol. 50 (3), 244329.CrossRefGoogle Scholar
Siddique, M.H., et al. 2020 Effect of silver nanoparticles on biofilm formation and EPS production of multidrug-resistant Klebsiella pneumoniae. BioMed Res. Intl 2020, 6398165.CrossRefGoogle ScholarPubMed
Su, J., Chai, G., Wang, L., Cao, W., Gu, Z., Chen, C. & Xu, X.Y. 2019 Pore-scale direct numerical simulation of particle transport in porous media. Chem. Engng Sci. 199, 613627.CrossRefGoogle Scholar
Thornton, C. 1991 Interparticle sliding in the presence of adhesion. J. Phys. D: Appl. Phys. 24, 19421946.CrossRefGoogle Scholar
Thornton, C. & Yin, K.K. 1991 Impact of elastic spheres with and without adhesion. Powder Technol. 65, 153166.CrossRefGoogle Scholar
Torkzaban, S., Bradford, S.A. & Walker, S.L. 2007 Resolving the coupled effects of hydrodynamics and DLVO forces on colloid attachment in porous media. Langmuir 23, 96529660.CrossRefGoogle ScholarPubMed
Tsuji, Y., Tanaka, T. & Ishida, T. 1992 Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe. Powder Technol. 71, 239250.CrossRefGoogle Scholar
Turuban, R., Lester, D.R., Heyman, J., Le Borgne, T. & Méheust, Y. 2019 Chaotic mixing in crystalline granular media. J. Fluid Mech. 871, 562594.CrossRefGoogle Scholar
Van der Hoef, M.A., Beetstra, R. & Kuipers, J.A.M. 2005 Lattice-Boltzmann simulations of low-Reynolds-number flow past mono- and bidisperse arrays of spheres: results for the permeability and drag force. J. Fluid Mech. 528, 233254.CrossRefGoogle Scholar
Verwey, E.J.W. & Overbeek, J.T.G. 1948 Theory of the Stability of Lyophobic Colloids. Elsevier.Google Scholar
Waldschläger, K., Lechthaler, S., Stauch, G. & Schüttrumpf, H. 2020 The way of microplastic through the environment -- application of the source-pathway-receptor model. Sci. Total Environ. 713, 136584.CrossRefGoogle ScholarPubMed
Yao, Y., Zhou, Y., Liu, L., Xu, Y., Chen, Q., Wang, Y., Wu, S., Deng, Y., Zhang, J. & Shao, A. 2020 Nanoparticle-based drug delivery in cancer therapy and its role in overcoming drug resistance. Front. Mol. Biosci. 7, 193.CrossRefGoogle ScholarPubMed
Zhou, Y., Chen, L., Gong, Y. & Wang, S. 2021 Pore-scale simulations of particles migration and deposition in porous media using LBM-DEM coupling method. Processes 9 (3), 465.CrossRefGoogle Scholar