Abstract
Particulate flows occur in various natural and technological settings. Understanding what influences the flow characteristics and how they can be manipulated is significant from scientific and engineering perspectives. In this paper, we review the lattice Boltzmann method combined with the smoothed profile method (LBM–SPM), one of the promising simulation methods for studying particle-containing systems. We present the background theory and numerical schemes of the LBM–SPM, then review several applications of this method for particulate flows; suspension rheology, deposition and clogging of particles within the flow, and the dynamics of particles in non-Newtonian media and at the fluid interface. Finally, we confirmed the versatility and feasibility of LBM–SPM for investigating particulate flows.
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References
Wagner NJ, Brady JF (2009) Shear thickening in colloidal dispersions. Phys Today 62(10):27–32
Mewis J, Wagner NJ (2012) Colloidal suspension rheology. Cambridge University Press
Crawford NC et al (2012) Shear thickening of chemical mechanical polishing slurries under high shear. Rheol Acta 51:637–647
Crawford NC et al (2013) Shear thickening and defect formation of fumed silica CMP slurries. Colloids Surf, A 436:87–96
Bauer W, Nötzel D (2014) Rheological properties and stability of NMP based cathode slurries for lithium ion batteries. Ceram Int 40(3):4591–4598
Bitsch B et al (2014) A novel slurry concept for the fabrication of lithium-ion battery electrodes with beneficial properties. J Power Sources 265:81–90
Bossis G, Brady JF (1989) The rheology of Brownian suspensions. J Chem Phys 91(3):1866–1874
Foss DR, Brady JF (2000) Structure, diffusion and rheology of Brownian suspensions by Stokesian dynamics simulation. J Fluid Mech 407:167–200
Santos P, Campanella O, Carignano M (2010) Brownian dynamics study of gel-forming colloidal particles. J Phys Chem B 114(41):13052–13058
Jung SY, Ahn KH (2019) Transport and deposition of colloidal particles on a patterned membrane surface: effect of cross-flow velocity and the size ratio of particle to surface pattern. J Membr Sci 572:309–319
Boek E et al (1997) Simulating the rheology of dense colloidal suspensions using dissipative particle dynamics. Phys Rev E 55(3):3124
Jamali S et al (2015) Microstructure and rheology of soft to rigid shear-thickening colloidal suspensions. J Rheol 59(6):1377–1395
Moghadam MGE, Shahmardan MM, Norouzi M (2022) Dissipative particle dynamics modeling of MR fluid flow in a novel magnetically optimized mini-MR damper. Korea-Aust Rheol J 34(4):291–315
Vázquez-Quesada A, Ellero M (2023) Numerical simulations of Brownian suspensions using smoothed dissipative particle dynamics: diffusion, rheology and microstructure. J Nonnewton Fluid Mech 317:105044
Gompper G et al (2009) Multi-particle collision dynamics: A particle-based mesoscale simulation approach to the hydrodynamics of complex fluids. Adv Comput Simul Approaches Soft Matter Sci III:1–87
Dickinson E (2013) Structure and rheology of colloidal particle gels: Insight from computer simulation. Adv Coll Interface Sci 199:114–127
Howard MP, Nikoubashman A, Palmer JC (2019) Modeling hydrodynamic interactions in soft materials with multiparticle collision dynamics. Curr Opin Chem Eng 23:34–43
Lee YK et al (2020) Hydrodynamic and frictional modulation of deformations in switchable colloidal crystallites. Proc Natl Acad Sci 117(23):12700–12706
Ladd AJ (1994) Numerical simulations of particulate suspensions via a discretized Boltzmann equation. part 1 theoretical foundation. J fluid mech 271:285–309
Ladd AJ (1994) Numerical simulations of particulate suspensions via a discretized Boltzmann equation. part 2. numerical results. J Fluid Mech 271:311–339
Shakib-Manesh A et al (2002) Shear stress in a Couette flow of liquid-particle suspensions. J Stat Phys 107(1–2):67–84
Aidun CK, Clausen JR (2010) Lattice-Boltzmann method for complex flows. Annu Rev Fluid Mech 42:439–472
Krüger T (2016) Effect of tube diameter and capillary number on platelet margination and near-wall dynamics. Rheol Acta 55(6):511–526
Jafari S, Yamamoto R, Rahnama M (2011) Lattice-Boltzmann method combined with smoothed-profile method for particulate suspensions. Phys Rev E 83(2):026702
Lee YK et al (2015) Rheology and microstructure of non-Brownian suspensions in the liquid and crystal coexistence region: strain stiffening in large amplitude oscillatory shear. Soft Matter 11(20):4061–4074
Mino Y et al (2017) Effect of internal mass in the lattice Boltzmann simulation of moving solid bodies by the smoothed-profile method. Phys Rev E 95(4):043309
Succi S (2001) The lattice Boltzmann equation: for fluid dynamics and beyond. Oxford university press
Guo Z, Zhao T (2002) Lattice Boltzmann model for incompressible flows through porous media. Phys Rev E 66(3):036304
Pan C, Luo L-S, Miller CT (2006) An evaluation of lattice Boltzmann schemes for porous medium flow simulation. Comput Fluids 35(8–9):898–909
Ginzburg I, Silva G, Talon L (2015) Analysis and improvement of Brinkman lattice Boltzmann schemes: Bulk, boundary, interface Similarity and distinctness with finite elements in heterogeneous porous media. Phys Rev E 91(2):023307
Kromkamp J et al (2006) Lattice Boltzmann simulation of 2D and 3D non-Brownian suspensions in Couette flow. Chem Eng Sci 61(2):858–873
Lorenz E, Hoekstra AG, Caiazzo A (2009) Lees-Edwards boundary conditions for lattice Boltzmann suspension simulations. Phys Rev E 79(3):036706
Denniston C, Orlandini E, Yeomans J (2001) Lattice Boltzmann simulations of liquid crystal hydrodynamics. Phys Rev E 63(5):056702
Marenduzzo D et al (2007) Steady-state hydrodynamic instabilities of active liquid crystals: hybrid lattice Boltzmann simulations. Phys Rev E 76(3):031921
Onishi J, Chen Y, Ohashi H (2005) A lattice Boltzmann model for polymeric liquids. Prog Comput Fluid Dyn Int J 5(1–2):75–84
Malaspinas O, Fiétier N, Deville M (2010) Lattice Boltzmann method for the simulation of viscoelastic fluid flows. J Nonnewton Fluid Mech 165(23):1637–1653
He X, Luo L-S (1997) Lattice Boltzmann model for the incompressible Navier-Stokes equation. J Stat Phys 88(3–4):927–944
Qian Y-H, d’Humières D, Lallemand P (1992) Lattice BGK models for Navier-Stokes equation. EPL (Europhysics Letters) 17(6):479
Lallemand P, Luo L-S (2000) Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance, and stability. Phys Rev E 61(6):6546
d’Humieres D (2002) Multiple–relaxation–time lattice Boltzmann models in three dimensions. Philos Trans Royal Soc London Ser A Math Phys Eng Sci 360(1792):437–451
Lallemand P, Luo L-S (2003) Theory of the lattice Boltzmann method: acoustic and thermal properties in two and three dimensions. Phys Rev E 68(3):036706
Luo L-S et al (2011) Numerics of the lattice Boltzmann method: effects of collision models on the lattice Boltzmann simulations. Phys Rev E 83(5):056710
Ginzburg I (2005) Equilibrium-type and link-type lattice Boltzmann models for generic advection and anisotropic-dispersion equation. Adv Water Resour 28(11):1171–1195
Ginzburg I, Verhaeghe F, d’Humieres D (2008) Two-relaxation-time lattice Boltzmann scheme: About parametrization, velocity, pressure and mixed boundary conditions. Commun Comput Phys 3(2):427–478
d’Humières D, Ginzburg I (2009) Viscosity independent numerical errors for Lattice Boltzmann models: from recurrence equations to “magic” collision numbers. Comput Math Appl 58(5):823–840
Lee YK (2023) Comparative study of two-relaxation time lattice Boltzmann and finite element methods for a planar 4: 1 contraction flow: a Newtonian fluid at finite Reynolds numbers. Korea-Aust Rheol J 35(1):47–54
Guo Z, Zheng C, Shi B (2002) Discrete lattice effects on the forcing term in the lattice Boltzmann method. Phys Rev E 65(4):046308
Nakayama Y, Yamamoto R (2005) Simulation method to resolve hydrodynamic interactions in colloidal dispersions. Phys Rev E 71(3):036707
Kim K, Nakayama Y, Yamamoto R (2006) Direct numerical simulations of electrophoresis of charged colloids. Phys Rev Lett 96(20):208302
Molina JJ et al (2016) Rheological evaluation of colloidal dispersions using the smoothed profile method: formulation and applications. J Fluid Mech 792:590–619
Lee YK, Ahn KH, Lee SJ (2014) Local shear stress and its correlation with local volume fraction in concentrated non-Brownian suspensions: lattice Boltzmann simulation. Phys Rev E 90(6):062317
Nguyen N-Q, Ladd A (2002) Lubrication corrections for lattice-Boltzmann simulations of particle suspensions. Phys Rev E 66(4):046708
Jahanshahi Javaran E, Rahnama M, Jafari S (2013) Investigating the applicability of combined lattice Boltzmann-smoothed profile methods in particulate systems. Part Sci Technol 31(6):643–652
Lees A, Edwards S (1972) The computer study of transport processes under extreme conditions. J Phys C: Solid State Phys 5(15):1921
Wagner AJ, Pagonabarraga I (2002) Lees-Edwards boundary conditions for lattice Boltzmann. J Stat Phys 107:521–537
Javaran EJ, Rahnama M, Jafari S (2013) Combining Lees-Edwards boundary conditions with smoothed profile-lattice Boltzmann methods to introduce shear into particle suspensions. Adv Powder Technol 24(6):1109–1118
Todd B, Evans DJ, Daivis PJ (1995) Pressure tensor for inhomogeneous fluids. Phys Rev E 52(2):1627
Krüger T, Varnik F, Raabe D (1945) Particle stress in suspensions of soft objects. Philos Trans R Soc A: Math Phys Eng Sci 2011(369):2414–2421
Raiskinmäki P et al (2003) Clustering and viscosity in a shear flow of a particulate suspension. Phys Rev E 68(6):061403
Kulkarni PM, Morris JF (2008) Suspension properties at finite Reynolds number from simulated shear flow. Phys Fluids 20(4):040602
Nam JG et al (2011) Strain stiffening of non-colloidal hard sphere suspensions dispersed in Newtonian fluid near liquid-and-crystal coexistence region. Rheol Acta 50(11–12):925–936
d’Haene P, Mewis J, Fuller G (1993) Scattering dichroism measurements of flow-induced structure of a shear thickening suspension. J Colloid Interface Sci 156(2):350–358
Hoffman RL (1998) Explanations for the cause of shear thickening in concentrated colloidal suspensions. J Rheol 42(1):111–123
Maranzano BJ, Wagner NJ (2002) Flow-small angle neutron scattering measurements of colloidal dispersion microstructure evolution through the shear thickening transition. J Chem Phys 117(22):10291–10302
Sierou A, Brady J (2002) Rheology and microstructure in concentrated noncolloidal suspensions. J Rheol 46(5):1031–1056
Lee YK, Hyun K, Ahn KH (2020) The first normal stress difference of non-Brownian hard-sphere suspensions in the oscillatory shear flow near the liquid and crystal coexistence region. Soft Matter 16(43):9864–9875
Chen V et al (1997) Particle deposition during membrane filtration of colloids: transition between concentration polarization and cake formation. J Membr Sci 125(1):109–122
Wyss HM et al (2006) Mechanism for clogging of microchannels. Phys Rev E 74(6):061402
Elimelech M, Gregory J, Jia X (2013) Particle deposition and aggregation: measurement, modelling and simulation. Butterworth-Heinemann.
Riley DJ, Carbonell RG (1993) Mechanisms of particle deposition from ultrapure chemicals onto semiconductor wafers: deposition from bulk liquid during wafer submersion. J Colloid Interface Sci 158(2):259–273
Bryers JD (1987) Biologically active surfaces: processes governing the formation and persistence of biofilms. Biotechnol Prog 3(2):57–68
Vrijenhoek EM, Hong S, Elimelech M (2001) Influence of membrane surface properties on initial rate of colloidal fouling of reverse osmosis and nanofiltration membranes. J Membr Sci 188(1):115–128
Lee YK et al (2018) Deposition of sticky spheres in channel flow: Modeling of surface coverage evolution requires accurate sphere-sphere collision hydrodynamics. J Colloid Interface Sci 530:383–393
Nishitani J, Mino Y, Matsuyama H (2019) Numerical simulation of particulate cake formation in cross-flow microfiltration: effects of attractive forces. Adv Powder Technol 30(8):1592–1599
Cundall PA, Strack OD (1979) A discrete numerical model for granular assemblies. Geotechnique 29(1):47–65
Mino Y, Sakai S, Matsuyama H (2018) Simulations of particulate flow passing through membrane pore under dead-end and constant-pressure filtration condition. Chem Eng Sci 190:68–76
Kawashima K et al (2022) Numerical modeling for particulate flow through realistic microporous structure of microfiltration membrane: Direct numerical simulation coordinated with focused ion beam scanning electron microscopy. Powder Technol 410:117872
Whitesides GM (2006) The origins and the future of microfluidics. Nature 442(7101):368–373
Jain R, Lee L (2012) Fiber reinforced polymer (FRP) composites for infrastructure applications: focusing on innovation, technology implementation and sustainability. Springer
Kim B, Kim JM (2016) Elasto-inertial particle focusing under the viscoelastic flow of DNA solution in a square channel. Biomicrofluidics. https://doi.org/10.1063/1.4944628
Song HY et al (2016) Relationship between particle focusing and dimensionless numbers in elasto-inertial focusing. Rheol Acta 55:889–900
Hwang WR, Hulsen MA, Meijer HE (2004) Direct simulations of particle suspensions in a viscoelastic fluid in sliding bi-periodic frames. J Nonnewton Fluid Mech 121(1):15–33
Hao J et al (2009) A fictitious domain/distributed Lagrange multiplier method for the particulate flow of Oldroyd-B fluids: a positive definiteness preserving approach. J Nonnewton Fluid Mech 156(1–2):95–111
Ji S et al (2011) Mesoscale hydrodynamic modeling of a colloid in shear-thinning viscoelastic fluids under shear flow. J Chem Phys. https://doi.org/10.1063/1.3646307
D’Avino G et al (2013) Rheology of viscoelastic suspensions of spheres under small and large amplitude oscillatory shear by numerical simulations. J Rheol 57(3):813–839
Yang M, Krishnan S, Shaqfeh ES (2016) Numerical simulations of the rheology of suspensions of rigid spheres at low volume fraction in a viscoelastic fluid under shear. J Nonnewton Fluid Mech 233:181–197
Vázquez-Quesada A et al (2019) Shear thickening of a non-colloidal suspension with a viscoelastic matrix. J Fluid Mech 880:1070–1094
Chen J, Hwang WR (2021) Shear rheology of circular particle suspensions in a Bingham fluid using numerical simulations. Korea-Aust Rheol J 33(3):273–282
Sobhani S, Bazargan S, Sadeghy K (2019) Sedimentation of an elliptic rigid particle in a yield-stress fluid: a lattice-Boltzmann simulation. Phys Fluids. https://doi.org/10.1063/1.5111633
Tazangi HR, Goharrizi AS, Javaran EJ (2021) Simulation of particles settling in power-law fluids by combined lattice Boltzmann-smoothed profile methods. Int J Sedim Res 36(5):637–655
Tazangi HR, Goharrizi AS, Javaran EJ (2021) Comparison of the rheological behavior of particulate suspensions in power-law and Newtonian fluids by combined improved smoothed profile-lattice Boltzmann methods. Korea-Aust Rheol J 33(3):293–306
Lee YK, Ahn KH (2017) A novel lattice Boltzmann method for the dynamics of rigid particles suspended in a viscoelastic medium. J Nonnewton Fluid Mech 244:75–84
Alves M, Pinho F, Oliveira P (2001) The flow of viscoelastic fluids past a cylinder: finite-volume high-resolution methods. J Nonnewton Fluid Mech 97(2–3):207–232
Hulsen MA, Fattal R, Kupferman R (2005) Flow of viscoelastic fluids past a cylinder at high Weissenberg number: stabilized simulations using matrix logarithms. J Nonnewton Fluid Mech 127(1):27–39
Coronado OM et al (2006) Four-field Galerkin/least-squares formulation for viscoelastic fluids. J Nonnewton Fluid Mech 140(1–3):132–144
Ribeiro V et al (2012) Three-dimensional effects in laminar flow past a confined cylinder. Chem Eng Sci 84:155–169
Zahn K, Maret G (2000) Dynamic criteria for melting in two dimensions. Phys Rev Lett 85(17):3656
Bausch A et al (2003) Grain boundary scars and spherical crystallography. Science 299(5613):1716–1718
Fendler JH (1996) Nanoparticles at air/water interfaces. Curr Opin Colloid Interface Sci 2(1):202–207
Swift MR et al (1996) Lattice Boltzmann simulations of liquid-gas and binary fluid systems. Phys Rev E 54(5):5041
Mino Y et al (2022) Lattice Boltzmann model for capillary interactions between particles at a liquid-vapor interface under gravity. Phys Rev E 105(4):045316
Mino Y, Shinto H (2020) Lattice Boltzmann method for simulation of wettable particles at a fluid-fluid interface under gravity. Phys Rev E 101(3):033304
Mino Y et al (2022) Numerical simulation of a drying colloidal suspension on a wettable substrate using the lattice Boltzmann method. Chem Eng Sci 263:118050
Lee YK, Ahn KH (2020) Particle dynamics at fluid interfaces studied by the color gradient lattice Boltzmann method coupled with the smoothed profile method. Phys Rev E 101(5):053302
Leclaire S, Reggio M, Trépanier J-Y (2013) Progress and investigation on lattice Boltzmann modeling of multiple immiscible fluids or components with variable density and viscosity ratios. J Comput Phys 246:318–342
Kralchevsky PA, Nagayama K (1994) Capillary forces between colloidal particles. Langmuir 10(1):23–36
Danov KD, Pouligny B, Kralchevsky PA (2001) Capillary forces between colloidal particles confined in a liquid film: the finite-meniscus problem. Langmuir 17(21):6599–6609
Danov KD, Kralchevsky PA (2010) Capillary forces between particles at a liquid interface: general theoretical approach and interactions between capillary multipoles. Adv Coll Interface Sci 154(1):91–103
Onishi J et al (2008) Lattice Boltzmann simulation of capillary interactions among colloidal particles. Comput Math Appl 55(7):1541–1553
Joshi AS, Sun Y (2009) Multiphase lattice Boltzmann method for particle suspensions. Phys Rev E 79(6):066703
Stratford K et al (2005) Colloidal jamming at interfaces: a route to fluid-bicontinuous gels. Science 309(5744):2198–2201
Koos E, Willenbacher N (2011) Capillary forces in suspension rheology. Science 331(6019):897–900
Acknowledgements
This work was supported by National Research Foundation of Korea (NRF) grants funded by the Korean government (MSIT) (NRF-2018R1A5A1024127 and RS-2022-00166649).
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Lee, Y.K. Applications of lattice Boltzmann method combined with smoothed profile method for particulate flows: a brief review. Korea-Aust. Rheol. J. 35, 213–228 (2023). https://doi.org/10.1007/s13367-023-00077-8
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DOI: https://doi.org/10.1007/s13367-023-00077-8