Numerical Study on Viscous Fingering of Reaction Fluid in a Microchannel

Abstract

Abstract: Viscous fingering with simultaneous chemical reaction at interface is investigated in a micro channel based on lattice Boltzmann method. One-variable chemical model admitting two stable states is adopted. We focus on influence of chemical reaction on viscous fingering. It is found that fluid interface become thinner with increase of reaction rate, while changes of steady state concentration (interfacial concentration where rate of chemical reactions is zero) influence position and morphology of viscous fingering. Isolated droplet can be formed from tip of finger.

Key words: lattice Boltzmann method, chemical reaction, viscous fingering

CLC Number:

O363

LEI Timan, MENG Xuhui, GUO Zhaoli. Numerical Study on Viscous Fingering of Reaction Fluid in a Microchannel[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2016, 33(1): 30-38.

References

[1] DICKEY P A, BOSSLER R B. Secondary recovery of oil in the US[M]. American Pretroleum Institute: Dollas, 1950: 444-446.
[2] BHASKAR K R, GARIK P, TURNER B S, et al. Viscous fingering of HCl through gastric mucin[J]. Nature, 1982, 360: 458-461.
[3] BRJYN J R. Fingering instability of gravity currents in thin-layer electrochemical deposition[J]. Physical Review Letters, 1995,74(24): 4843-4846.
[4] RAKOTOMALALA N, SALIN D, WATZKY P. Miscible displacement between two parallel plates: BGK lattice gas simulations[J]. Journal of Fluid Mechanics, 1997, 338: 277-297.
[5] HOMSY G M. Viscous fingering in porous media[J]. Annual Reviews of Fluid Mechanics, 1987,19: 271-311.
[6] NORTON T T, FERNANDEZ E J. Viscous fingering in size exclusion chromatography: Insights from numerical simulation[J]. Industrial & Engineering Chemistry Research, 1996, 35(7): 2460-2468.
[7] POJMAN J A, GUNN G, PATTERSON C, et al. Frontal dispersion polymerization[J]. Journal of Physical Chemistry B, 1998, 102(20): 3927-3929.
[8] WIT A D. Fingering of chemical fronts in porous media[J]. Physical Review Letters, 2001, 87(5): 054502.
[9] SWERNATH S, PUSHPAVANAM S. Instability of a vertical chemical front: Effect of viscosity and density varying with concentration[J]. Physical of Fluids, 2008, 20: 012101.
[10] ADAMSON A W, GAST A P. Physical chemistry of surfaces[M]. United States: Wiley, 1997: 169.
[11] GUO Z L, ZHENG C G, LI Q, WANG C N. Lattice Boltzmann method for hydrodynamics[M]. Hubei: Science Press, 2002: 78,152-154.
[12] 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]. Journal of Fluid Mechanics, 2010,652: 501-528.
[13] WIT A D, HOMSY G M. Viscous fingering in reaction-diffusion systems[J]. Journal of Chemical Physics, 1999,110(17): 8663-8675.
[14] WIT A D, HOMSY G M. Nonlinear interactions of chemical reactions and viscous fingering in porous media[J]. Physical of Fluids, 1999,11(5): 949-951.
[15] SAMFFMAN P G. Viscous fingering in Hele-Shaw cells[J]. Journal of Fluid Mechanics, 1986, 173: 73-94.
[16] HETSRONI G, MOSYAK A, POGREBNYAK E, YARIN L P. Fluid flow in micro-channels[J]. International Journal of Heat and Mass Transfer, 2005, 48(10): 1982-1998.
[17] SULLIVAN S P, AKPA B S, MATTHEWS S M, FISHER A C. Simulation of miscible diffusive mixing in microchannels[J]. Sensors and Actuators B: Chemical, 2007,123(2): 1142-1152.
[18] GUO Z L, ZHENG C G. Theory and applications of lattice Boltzmann method[M]. Beijing: Science Press, 2009: 46-50, 62,66.
[19] FLEKKY E G. Lattice Bhatnagar-Gross-Krook models for miscible fluids[J]. Physical Review E, 1993, 47(6): 4247-4257.
[20] DENG Bing, SHI Baochang, WANG G C. A new lattice Bhatnagar-Gross-Krook model for the convection-dffiusion equation with a source term[J]. Chinese Physics Letters, 2004,22(2): 267-270.
[21] LALLEMAND P, LUO L S. Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability[J]. Physical Review E, 2000, 61(6): 6546-6562.
[22] d' HUMIERES D, GINZBERG I, KRAFCZYK M. Multiple-relaxation-time lattice Boltzmann models in three dimensions[J]. Philosophical Transactions of the Royal Society of London. Series A: Physical Sciences and Engineering, 2002, 360(1792): 437-445.
[23] PAN C X, LUO L S, MILLER C T. An evaluation of lattice Boltzmann schemes for porous medium flow simulation[J]. Computers & Fluids, 2006, 35(8): 898-909.
[24] BAUDET C, HULIN J P, LALLEMAND P. Lattice-gas automata: A model for the simulation of dispersion phenomena[J]. Physical of Fluids, 1989,1(1): 507-512.
[25] CALLEWAERTA M, MALSCHEA W D, OTTEVAEREB H. Assessment and numerical search for minimal Taylor-Aris dispersion in micro-machined channels of nearly rectangular cross-section[J]. Journal of Chromatography A, 2014,1368(14): 70-81.
[26] WIT A D. Miscible density fingering of chemical fronts in porous media: Nonlinear simulations[J]. Physical of Fluids, 2004, 16(1): 163-175.