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Interaction of fluid interfaces with immersed solid particles using the lattice Boltzmann method for liquid-gas-particle systems. (English) Zbl 1351.76232

Summary: Due to their finite size and wetting properties, particles deform an interface locally, which can lead to capillary interactions that dramatically alter the behavior of the system, relative to the particle-free case. Many existing multi-component solvers suffer from spurious currents and the inability to employ components with sufficiently large density differences due to stability issues. We developed a liquid-gas-particle (LGP) lattice Boltzmann method (LBM) algorithm from existing multi-component and particle dynamics algorithms that is capable of suppressing spurious currents when geometry is fixed while simulating components with liquid-gas properties. This paper presents the LGP algorithm, with several code validations. It discusses numerical issues raised by the results and the conditions under which the algorithm is most useful. The previously existing particle dynamics algorithm was augmented to capture surface tension forces arising from the interface, which was validated for the case of a 2D capillary tube. Using the full algorithm, a particle situated in a region of bulk fluid in an otherwise quiescent situation remained in its original location, indicating that spurious currents were suppressed. A particle brought into the interface of a drop (without gravity) achieved its expected depth of immersion into the drop, demonstrating that all aspects of the code work together to produce the correct equilibrium state when a particle is in the interface. As in an experiment, two particles on a flat interface approached each other due to capillary effects. The simulation approach velocity was faster than that of the experiment, but agreed qualitatively, achieving the same equilibrium state. Given the validations and the favorable, though imperfect, experimental comparison, this algorithm can be a useful tool for simulating LGP systems. The motion of particles normal to the interface can be considered reliable, and the motion tangent to the interface can be considered qualitatively accurate, leading to the correct equilibrium state.

MSC:

76M28 Particle methods and lattice-gas methods
82C40 Kinetic theory of gases in time-dependent statistical mechanics
76Txx Multiphase and multicomponent flows
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[1] Tekin, E.; Smith, P. J.; Schubert, U. S., Inkjet printing as a deposition and patterning tool for polymers and inorganic particles, Soft Matter, 4, 703-713 (2008)
[2] Dickinson, E., Food emulsions and foams: stabilization by particles, Curr. Opin. Colloid Interface Sci., 15, 40-49 (2010)
[3] Hunter, T. N.; Pugh, R. J.; Franks, G. V.; Jameson, G. J., The role of particles in stabilising foams and emulsions, Adv. Colloid Interface Sci., 137, 57-81 (2008)
[4] Tambe, D. E.; Sharma, M. M., Factors controlling the stability of colloid-stabilized emulsions I. An experimental investigation, J. Colloid Interface Sci., 157, 244-253 (1993)
[5] Frankel, N. A.; Acrivos, A., On the viscosity of a concentrated suspension of solid spheres, Chem. Eng. Sci., 22, 6, 847-853 (1967)
[6] Binks, B. P., Particles as surfactants - similarities and differences, Curr. Opin. Colloid Interface Sci., 7, 21-41 (2002)
[7] Aveyard, R.; Binks, B. P.; Clint, J. H., Emulsions stabilised solely by colloidal particles, Adv. Colloid Interface Sci., 100-102, 503-546 (2003)
[8] Cates, M. E.; Adhikari, R.; Stratford, K., Colloidal arrest by capillary forces, J. Phys. Condens. Matter, 17, S2771-S2778 (2005)
[9] Kralchevsky, P. A.; Nagayama, K., Capillary interactions between particles bound to interfaces, liquid films, and biomembranes, Adv. Colloid Interface Sci., 85, 145-192 (2000)
[10] Yue, P.; Zhou, C.; Feng, J. J., Sharp-interface limit of the Cahn-Hilliard model for moving contact lines, J. Fluid Mech., 645, 279-294 (2010) · Zbl 1189.76074
[11] Kralchevsky, P. A.; Nagayama, K., Capillary forces between colloidal particles, Langmuir, 10, 23-36 (1994)
[12] Velev, O. D.; Denkov, N. D.; Paunov, V. N.; Kralchevsky, P. A.; Nagayama, K., Direct measurement of lateral capillary forces, Langmuir, 9, 3702-3709 (1993)
[13] Singh, P.; Joseph, D. D., Fluid dynamics of floating particles, J. Fluid Mech., 530, 31-80 (2005) · Zbl 1071.76059
[14] Bowden, N.; Terfort, A.; Carbeck, J.; Whitesides, G. M., Self-assembly of mesoscopic objects into ordered two-dimensional arrays, Science, 11, 233-235 (1997)
[15] Vella, D.; Mahadevan, L., The Cheerios effect, Am. J. Phys., 73, 9, 817-825 (2005)
[16] Dinsmore, A. D.; Hsu, M. F.; Nikolaides, M. G.; Marquez, M.; Bausch, A. R.; Weitz, D. A., Colloidosomes: selectively permeable capsules composed of colloidal particles, Science, 298, 1006-1009 (2002)
[17] Schaefer, D. W.; Martin, J. E., Fractal geometry of colloidal aggregates, Phys. Rev. Lett., 52, 26, 2371-2374 (1984)
[18] Forrest, S. R.; Witten, T. A., Long-range correlations in smoke-particle aggregates, J. Phys. A, Math. Gen., 12, 5, L109-L117 (1979)
[19] Nicolson, M. M., The interaction between floating particles, Proc. Cambridge Philos. Soc., 45, 02, 288-295 (1949) · Zbl 0033.04701
[20] Vella, D.; Metcalfe, P. D.; Whitaker, R. J., Equilibrium conditions for the floating of multiple interfacial objects, J. Fluid Mech., 549, 215-224 (2006)
[21] Cavallaro, M.; Botto, L.; Lewandowski, E.; Wang, M.; Stebe, K. J., Curvature-driven capillary migration and assembly of rod-like particles, Proc. Natl. Acad. Sci., 20923-20928 (2011)
[22] Botto, L.; Lewandowski, E. P.; Cavallaro, M.; Stebe, K. J., Capillary interactions between anisotropic particles, Soft Matter, 8, 9957-9971 (2012)
[23] Johnson, A. A.; Tezduyar, T. E., Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interface, Comput. Methods Appl. Mech. Eng., 119, 73-94 (1994) · Zbl 0848.76036
[24] Feng, Z.-G.; Michaelides, E. E., The immersed boundary-lattice Boltzmann method for solving fluid-particles interaction problems, J. Comput. Phys., 195, 602-628 (2004) · Zbl 1115.76395
[25] Tryggvason, G.; Bunner, B.; Esmaeeli, A.; Juric, D.; Al-Rawahi, N.; Tauber, W.; Han, J.; Nas, S.; Jan, Y. J., A front-tracking method for the computations of multiphase flow, J. Comput. Phys., 169, 708-759 (2001) · Zbl 1047.76574
[26] Hu, H. H.; Joseph, D. D.; Crochet, M. J., Direct simulation of fluid particle motions, Theor. Comput. Fluid Dyn., 3, 285-306 (1992) · Zbl 0754.76054
[27] Ladd, A. J.C., Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2. Numerical results, J. Fluid Mech., 271, 311-339 (1994) · Zbl 0815.76085
[28] Ladd, A. J.C.; Verberg, R., Lattice-Boltzmann simulations of particle-fluid suspensions, J. Stat. Phys., 104, 5/6, 1191-1251 (2001) · Zbl 1046.76037
[29] Aidun, C. K.; Lu, Y.; Ding, E. J., Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation, J. Fluid Mech., 373, 287-311 (1998) · Zbl 0933.76092
[30] Mittal, R.; Iaccarino, G., Immersed boundary methods, Annu. Rev. Fluid Mech., 37, 239-261 (2005) · Zbl 1117.76049
[31] Maxey, M. R.; Riley, J. J., Equation of motion for a small rigid sphere in a nonuniform flow, Phys. Fluids, 26, 883-889 (1983) · Zbl 0538.76031
[32] Gao, H.; Li, H.; Wang, L. P., Lattice Boltzmann simulation of turbulent flow laden with finite-size particles, Comput. Math. Appl., 65, 194-210 (2013) · Zbl 1268.76045
[33] Gunstensen, A. K.; Rothman, D. K.; Zaleski, S.; Zanetti, G., Lattice Boltzmann model of immiscible fluids, Phys. Rev. A, 43, 4320 (1991)
[34] Shan, X.; Chen, H., Lattice Boltzmann model for simulating flows with multiple phases and components, Phys. Rev. E, 47, 1815 (1993)
[35] Swift, M. R.; Orlandini, E.; Osborn, W. R.; Yeomans, J. M., Lattice Boltzmann simulations of liquid-gas and binary fluid systems, Phys. Rev. E, 54, 5041 (1996)
[36] Stratford, K.; Adhikari, R.; Pagonabarraga, I.; Desplat, J. C., Lattice Boltzmann for binary fluids with suspended colloids, J. Stat. Phys., 121, 1/2, 163-178 (2005) · Zbl 1107.82055
[37] Stratford, K.; Adhikari, R.; Pagonabarraga, I.; Desplat, J. C.; Cates, M. E., Colloidal jamming at interfaces: a route to fluid-bicontinuous gels, Science, 309, 2198-2201 (2005)
[38] Stratford, K.; Pagonabarraga, I., Parallel simulation of particle suspensions with the lattice Boltzmann method, Comput. Math. Appl., 55, 1585-1593 (2008) · Zbl 1142.76456
[39] Cates, M. E.; Clegg, P. S., Bijels: a new class of soft materials, Soft Matter, 4, 2132-2138 (2008)
[40] Cates, M. E.; Desplat, J. C.; Stansell, P.; Wagner, A. J.; Stratford, K.; Adhikari, R.; Pagonabarrage, I., Physical and computational scaling issues in lattice Boltzmann simulations of binary fluid mixtures, Philos. Trans. R. Soc. A, 363, 1917-1935 (2005)
[41] Shinto, H.; Komiyama, D.; Higashitani, K., Lateral capillary forces between solid bodies on liquid surface: a lattice Boltzmann study, Langmuir, 22, 2058-2064 (2006)
[42] Shinto, H.; Komiyama, D.; Higashitani, K., Lattice Boltzmann study of capillary forces between cylindrical particles, Adv. Powder Technol., 18, 6, 643-662 (2007)
[43] Inamuro, T.; Tomita, R.; Ogino, F., Lattice Boltzmann simulation of drop deformation and breakup in shear flows, Int. J. Mod. Phys. B, 17, 21-26 (2003)
[44] Onishi, J.; Kawasaki, A.; Chen, Y.; Ohashi, H., Lattice Boltzmann simulation of capillary interactions among colloidal particles, Comput. Math. Appl., 55, 1541-1553 (2008) · Zbl 1142.76454
[45] Kim, E.; Stratford, K.; Cates, M. E., Bijels containing magnetic particles: a simulation study, Langmuir, 26, 11, 7928-7936 (2010)
[46] Kim, E. G.; Stratford, K.; Clegg, P. S.; Cates, M. E., Field-induced breakup of emulsion droplets stabilized by colloidal particles, Phys. Rev. E, 85, 020203 (2012)
[47] Joshi, A. S.; Sun, Y., Multiphase lattice Boltzmann method for particle suspensions, Phys. Rev. E, 79, 066703 (2009)
[48] Joshi, A. S.; Sun, Y., Wetting dynamics and particle deposition for an evaporating colloidal drop: a lattice Boltzmann study, Phys. Rev. E, 82, 041401 (2010)
[50] Jansen, F.; Harting, J., From bijels to pickering emulsions: a lattice Boltzmann study, Phys. Rev. E, 83, 046707 (2011)
[51] Günther, F.; Janoschek, F.; Frijters, S.; Harting, J., Lattice Boltzmann simulations of anisotropic particles at liquid interfaces, Comput. Fluids, 80, 184-189 (2013)
[52] Liang, G.; Zeng, Z.; Chen, Y.; Onishi, J.; Ohashi, H.; Chen, S., Simulation of self assemblies of colloidal particles on the substrate using a lattice Boltzmann pseudo-solid model, J. Comput. Phys., 248, 323-338 (2013) · Zbl 1349.82013
[53] Connington, K.; Lee, T., Lattice Boltzmann simulations of forced wetting transitions of drops on superhydrophobic surfaces, J. Comput. Phys., 250, 601-615 (2013)
[54] Connington, K.; Lee, T., A review of spurious currents in the lattice Boltzmann method for multiphase flows, J. Mech. Sci. Technol., 26, 12, 3857-3863 (2012)
[55] Lee, T.; Liu, L., Lattice Boltzmann simulations of micron-scale drop impact on dry surfaces, J. Comput. Phys., 229, 8045 (2010) · Zbl 1426.76603
[56] Dalbe, M. J.; Cosic, D.; Berhanu, M.; Kudrolli, A., Aggregation of frictional particles due to capillary attraction, Phys. Rev. E, 83, 051403 (2011)
[57] Cahn, J. W., Critical-point wetting, J. Chem. Phys., 66, 3667 (1977)
[58] DeGennes, P. G., Wetting: statics and dynamics, Rev. Mod. Phys., 57, 827 (1985)
[59] Lee, T.; Liu, L., Wall boundary conditions in the lattice Boltzmann equation method for non-ideal gases, Phys. Rev. E, 78, 017702 (2008)
[60] Liu, L.; Lee, T., Wall free energy based polynomial boundary conditions for non-ideal gas lattice Boltzmann equation, Int. J. Mod. Phys. C, 20, 11, 1749-1768 (2009) · Zbl 1183.82060
[61] He, X.; Luo, L. S., A priori derivation of the lattice Boltzmann equation, Phys. Rev. E, 55, R6333 (1997)
[62] Lee, T., Effects of incompressibility on the elimination of parasitic currents in the lattice Boltzmann equation method for binary fluids, Comput. Math. Appl., 58, 987 (2009) · Zbl 1189.76414
[63] He, X.; Chen, S.; Doolen, G., A novel thermal model for the lattice Boltzmann method in the incompressible limit, J. Comput. Phys., 146, 282 (1998) · Zbl 0919.76068
[64] Luo, L. S., Unified theory of the lattice Boltzmann model for nonideal gases, Phys. Rev. Lett., 81, 1618 (1998)
[65] Chen, Y.; Chen, S., Dissipative and dispersive behavior of lattice-based models for hydrodynamics, Phys. Rev. E, 61, 2712 (2000)
[66] Lee, T.; Lin, C. L., A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio, J. Comput. Phys., 201, 16 (2005) · Zbl 1087.76089
[67] He, X.; Chen, S.; Zhang, R., A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh-Taylor instability, J. Comput. Phys., 152, 642 (1999) · Zbl 0954.76076
[68] Lee, T.; Lin, C., Pressure evolution lattice Boltzmann equation method for two-phase flow with phase change, Phys. Rev. E, 67, 056703 (2003)
[69] Rowlinson, J. S.; Widom, B., Molecular Theory of Capillarity (1982), Clarendon Press: Clarendon Press Oxford
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