Pore-scale study on reactive mixing of miscible solutions with viscous fingering in porous media. (English) Zbl 1410.76363
Summary: In this paper, the reactive mixing process with viscous fingering of two miscible solutions is studied at pore scale using the lattice Boltzmann method. This single-phase flow obeys the Navier-Stokes equations with a concentration-dependent viscosity. The concentration transport is governed by the advection-diffusion-reaction equation, in which the interfacial reaction rate is described by a function of the concentration of a single reacting solute and admits two stable states separated by an unstable one. The reaction effects on mixing process with viscous fingering are explored in a single pore with different reaction rates, Péclet numbers and viscosity ratios. It is found that generally the reaction can suppress the mixing process significantly by sharping the solution interfaces. Such restriction is more obvious with increasing reaction rate, and even shares the similar fashion for different Péclet numbers and viscosity ratios. The reactive mixing process with viscous fingering is further investigated in artificial homogeneous and heterogeneous porous media with different parameters, and similar results are observed.
MSC:
| 76M28 | Particle methods and lattice-gas methods |
| 65M75 | Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs |
| 76S05 | Flows in porous media; filtration; seepage |
| 80A32 | Chemically reacting flows |
Keywords:
lattice Boltzmann method; miscible mixing; chemical reaction; viscous fingering; pore scaleReferences:
| [1] | Losey, M. W.; Schmidt, M. A.; Jensen, K. F., Microfabricated multiphase packed-bed reactors: characterization of mass transfer and reactions, Ind Eng Chem Res, 40, 2555-2562, (2001) |
| [2] | Katija, K.; Dabiri, J. O., A viscosity-enhanced mechanism for biogenic Ocean mixing, Nature London, 460, 624-626, (2009) |
| [3] | Baldyga, J.; Czarnocki, R.; Shekunov, B. Y.; Smith, K. B., Particle formation in supercritical fluidsscale-up problem, Chem Eng Res Des, 88, 331-341, (2010) |
| [4] | Dunn, D. A.; Feygin, I., Challenges and solutions to ultra-high-throughput screening assay miniaturization: submicroliter fluid handling, Drug Discov Today, 5, 84-91, (2000) |
| [5] | Cirpka, O. A.; Kitanidis, P. K., Characterization of mixing and dilution in heterogeneous aquifers by means of local temporal moments, Water Resour Res, 36, 1221-1236, (2000) |
| [6] | Tartakovsky, A. M.; Meakin, P., Stochastic Langevin model for flow and transport in porous media, Phys Rev Lett, 101, 044502, (2008) |
| [7] | Le Borgne, T.; Dentz, M.; Bolster, D.; Carrera, J.; de Dreuzy, J.; Davy, P., Non-Fickian mixing: temporal evolution of the scalar dissipation rate in heterogeneous porous media, Adv Water Resour, 33, 1468-1475, (2010) |
| [8] | Jha, B.; Cueto-Felgueroso, L.; Juanes, R., Fluid mixing from viscous fingering, Phys Rev Lett, 106, 194502, (2011) |
| [9] | Jha, B.; Cueto-Felgueroso, L.; Juanes, R., Quantifying mixing in viscously unstable porous media flows, Phys Rev E, 84, 066312, (2011) |
| [10] | Liu, G. J.; Guo, Z. L., Pore-scale study of the non-linear mixing of fluids with viscous fingering in anisotropic porous media, Commun Comput Phys, 17, 1019-1036, (2015) · Zbl 1373.76314 |
| [11] | Liu, G. J., Pore-scale study on the interaction between interfacial instability and mixing of miscible fluids in porous media, (2014), [D] Hubei: Huazhong Univ. Sci. Technol. |
| [12] | Wit, A. D.; Homsy, G. M., Viscous fingering in reaction-diffusion systems, J Chem Phys, 110, 8663-8675, (1999) |
| [13] | Wit, A. D.; Homsy, G. M., Nonlinear interactions of chemical reactions and viscous fingering in porous media, Phys Fluids, 11, 949-951, (1999) · Zbl 1147.76545 |
| [14] | Nasgstsu, Y.; Wit, A. D., Viscous fingering of a miscible reactive a+b=c interface for an infinitely fast chemical reaction: nonlinear simulation, Phys Fluids, 23, 043103, (2011) |
| [15] | Hejazi, S. H.; Trevelyan, P. M.J.; Azaiez, J.; Wit, A. D., Viscous fingering of a miscible reactive a+b-c interface: a linear stability analysis, J Fluid Mech, 652, 501-528, (2010) · Zbl 1193.76058 |
| [16] | Guo, Z. L.; Shu, C., Lattice Boltzmann method and its applications in engineering, 25-28, 329-338, (2013), World Scientific Publisher · Zbl 1278.76001 |
| [17] | Rakotomalala, N.; Salin, D.; Watzky, P., Miscible displacement between two parallel plates: BGK lattice gas simulations, J Fluid Mech, 338, 277-297, (1997) · Zbl 0889.76067 |
| [18] | Kang, Q. J.; Chen, L.; Valocchi, A. J.; Viswanathan, H. S., Pore-scale study of dissolution-induced changed in permeability and porosity of porous media, J Hydrol, 517, 1049-1055, (2014) |
| [19] | Wit, A. D., Fingering of chemical fronts, (2003), [D] Bruxelles: Universit Libre de Bruxelles · Zbl 1186.76131 |
| [20] | Wit, A. D., Fingering of chemical fronts in porous media, Phys Rev Lett, 87, 054502, (2001) |
| [21] | Wit, A. D., Miscible density fingering of chemical fronts in porous media: nonlinear simulations, Phys Fluids, 16, 163-175, (2004) · Zbl 1186.76131 |
| [22] | Guo, Z. L.; Zheng, C. G., Analysis of lattice Boltzmann equation for microscale gas flows: relaxation times, boundary conditions and the Knudsen layer, Int J Comput Fluid D, 22, 465-473, (2008) · Zbl 1184.76793 |
| [23] | He, X. Y.; Luo, L. S., Lattice Boltzmann model for the incompressible Navier Stokes equation, J Stst Phys, 88, 927-944, (1997) · Zbl 0939.82042 |
| [24] | Inamuro, T., A lattice kinetic scheme for incompressible viscous flows with heat transfer, Philos Trans R Soc London Sec A, 360, 477-484, (2002) · Zbl 1018.76034 |
| [25] | Liu, G. J.; Guo, Z. L.; Shi, B. C., A coupled lattice Boltzmann model for fluid flow and diffusion in a porous medium, Acta Phys Sin, 65, 014702, (2016) |
| [26] | D’Humires, D.; Ginzburg, I., Viscosity independent numerical errors for lattice Boltzmann models: from recurrence equations to magic collision numbers, Comput Math Appl, 58, 823-840, (2009) · Zbl 1189.76405 |
| [27] | Pan, C. X.; Luo, L. S.; Miller, C. T., An evaluation of lattice Boltzmann schemes for porous medium flow simulation, Comput Fluids, 35, 898-909, (2006) · Zbl 1177.76323 |
| [28] | Lallemand, P.; Luo, L. S., Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance, and stability, Phys Rev E, 61, 6546-6562, (2000) |
| [29] | Deng, B.; Shi, B. C.; Wang, G. C., A new lattice Bhatnagar-Gross-Krook model for the convection-dffiusion equation with a source term, Chinese Phys Lett, 22, 267-270, (2004) |
| [30] | Inamuro, T.; Yoshino, M.; Inoue, H.; Mizuno, R.; Ogino, F., A lattice Boltzmann method for a binary miscible fluid mixture and its application to a heat transfer problem, J Comput Phys, 179, 201C215, (2002) · Zbl 1065.76164 |
| [31] | Ladd, A. J.C., Numerical simulations of particulate suspensions via a discretized Boltzmann equation. part 1. theoretical foundation, J Fluid Mech, 271, 285-309, (1994) · Zbl 0815.76085 |
| [32] | 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 |
| [33] | Baudet, C.; Hulin, J. P.; Lallemand, P.; D’Humires, D., Lattice-gas automata: a model for the simulation of dispersion phenomena, Phys Fluids, 1, 507-512, (1989) · Zbl 1222.76071 |
| [34] | Guo, Z. L.; Zheng, C. G.; Shi, B. C., Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method, Chin Phys, 11, 366-374, (2002) |
| [35] | Shi, B. C.; Deng, B.; Du, R.; Chen, X. W., A new scheme for source trem in LBGK model for convection-diffusion equation, Comput Math Appl, 55, 1568-1575, (2008) · Zbl 1142.76477 |
| [36] | Wang, M.; Wang, J.; Pan, N.; Chen, S., Mesoscopic predictions of the effective thermal conductivity for microscale random porous media, Phys Rev E, 75, 036702, (2007) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
