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Double-diffusive viscous fingering induced by an active dye

Published online by Cambridge University Press:  29 July 2025

Y. Nagatsu Open the ORCID record for Y. Nagatsu [Opens in a new window]  and
A. De Wit Open the ORCID record for A. De Wit [Opens in a new window]
Y. Nagatsu
Affiliation:
Department of Chemical Engineering, Tokyo University of Agriculture and Technology, 2-24-16 Naka-cho, Koganei, Tokyo 184-8588, Japan
A. De Wit*
Affiliation:
Nonlinear Physical Chemistry Unit, CP231, Université libre de Bruxelles (ULB), 1050 Brussels, Belgium
*
Corresponding author: A. De Wit, anne.de.wit@ulb.be
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Abstract

Viscous fingering is a hydrodynamic instability typically occurring when a less viscous fluid displaces a more viscous one and which deforms the interface between the two fluids into finger-shaped intrusions. For miscible fluids, the fingering pattern is usually followed visually by adding a passive dye into one of the two fluids. The reverse displacement of a less viscous fluid by a more viscous one is classically stable, featuring a planar interface. Here, we show experimentally that in some cases, the dye can actively modify the viscosity of a polymer solution and trigger fingering in the reverse displacement. This dye-induced destabilisation is shown to be due to double-diffusive effects triggering a non-monotonic viscosity profile with a maximum because the dye diffuses faster than the polymer.

JFM classification

Low-Reynolds-number flows: Hele-Shaw flows Mass Transport: Coupled diffusion and flow Convection: Convection in porous media

Information

Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 1016 , 10 August 2025 , R3
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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References

Al-Housseiny, T.T., Tsai, P.A. & Stone, H.A. 2012 Control of interfacial instabilities using flow geometry. Nat. Phys. 8 (10), 747–750.10.1038/nphys2396CrossRefGoogle Scholar
Azaiez, J. & Sajjadi, M. 2012 Stability of double-diffusive double-convective miscible displacements in porous media. Phys. Rev. E 85 (2), 026306.10.1103/PhysRevE.85.026306CrossRefGoogle ScholarPubMed
Bhaskar, K.R., Garik, P., Turner, B.S., Bradley, J.D., Bansil, R., Stanley, H.E. &LaMont, J.T. 1992 Viscous fingering of HCl through gastric mucin. Nature 360 (6403), 458–461.10.1038/360458a0CrossRefGoogle ScholarPubMed
Broyles, B.S., Shalliker, R.A., Cherrak, D.E. & Guiochon, G. 1998 Visualization of viscous fingering in chromatographic columns. J. Chromatogr. A 822 (2), 173–187.10.1016/S0021-9673(98)00568-8CrossRefGoogle Scholar
Bunton, P., Dice, B., Pojman, J.A., De Wit, A. & Brau, F. 2016 a Reconstruction by fluorescence imaging of the spatio-temporal evolution of the viscosity field in Hele-Shaw flows. Phys. Fluids 26 (11), 114106.10.1063/1.4901957CrossRefGoogle Scholar
Bunton, P., Marin, D., Stewart, S., Meiburg, E. & De Wit, A. 2016 b Schlieren imaging of viscous fingering in a horizontal Hele-Shaw cell. Exp. Fluids 57, 28.10.1007/s00348-016-2121-0CrossRefGoogle Scholar
Bunton, P., Tullier, M.P., Meiburg, E. & Pojman, J.A. 2017 The effect of a crosslinking chemical reaction on pattern formation in viscous fingering of miscible fluids in a Hele-Shaw cell. Chaos 27 (10), 104614.10.1063/1.5001285CrossRefGoogle Scholar
Chan, C.K. & Liang, N.Y. 1997 Observations of surfactant driven instability in a Hele-Shaw cell. Phys. Rev. Lett 79 (22), 4381–4384.10.1103/PhysRevLett.79.4381CrossRefGoogle Scholar
Dastvareh, B., Azaiez, J. & Tsai, P.A. 2019 Nanocatalytic chemo-hydrodynamic instability: deposition effects. Phys. Rev. E 100 (5), 053102.10.1103/PhysRevE.100.053102CrossRefGoogle Scholar
De Wit, A. 2020 Chemo-hydrodynamic patterns and instabilities. Annu. Rev. Fluid Mech. 52 (1), 531–555.10.1146/annurev-fluid-010719-060349CrossRefGoogle Scholar
De Wit, A. & Homsy, G.M. 1999 Nonlinear interaction of chemical reactions and viscous fingering in porous media. Phys. Fluids 11 (5), 949–951.10.1063/1.869988CrossRefGoogle Scholar
Dias, E.O., Alvarez-Lacalle, E., Carvalho, M.S. & Miranda, J.A. 2012 Minimization of viscous fluid fingering: a variational scheme for optimal flow rates. Phys. Rev. Lett 109 (14), 144502.10.1103/PhysRevLett.109.144502CrossRefGoogle ScholarPubMed
Escala, D.M., De Wit, A., Carballido-Landeira, J. & Muñuzuri, A.P. 2019 Viscous fingering induced by a pH-sensitive clock reaction. Langmuir 35, 4182–4188.10.1021/acs.langmuir.8b03834CrossRefGoogle ScholarPubMed
Escala, D.M. & Muñuzuri, A.P. 2021 A bottom-up approach to construct or deconstruct a fluid instability. Sci. Rep., 11, 24368.10.1038/s41598-021-03676-zCrossRefGoogle ScholarPubMed
Escala, D.M., Muñuzuri, A.P., De Wit, A. & Carballido-Landeira, J. 2017 Temporal viscosity modulations driven by a pH sensitive polymer coupled to a pH-shifting chemical reaction. Phys. Chem. Chem. Phys. 19, 11914–1191.10.1039/C7CP00426ECrossRefGoogle Scholar
Fernandez, J. & Homsy, G.M 2003 Viscous fingering with chemical reaction: effect of in-situ production of surfactants. J. Fluid Mech., 480, 267–281.10.1017/S0022112002003683CrossRefGoogle Scholar
Haudin, F., Callewaert, M., De Malsche, W. & De Wit, A. 2016 Influence of nonideal mixing properties on viscous fingering in micropillar array columns. Phys. Rev. Fluids 1 (7), 074001.10.1103/PhysRevFluids.1.074001CrossRefGoogle Scholar
Hejazi, S.H. & Azaiez, J. 2010 b Non-linear interactions of dynamic reactive interfaces in porous media. Chem. Engng Sci. 65 (2), 938–949.10.1016/j.ces.2009.09.045CrossRefGoogle Scholar
Hejazi, S.H. & Azaiez, J. 2010 c Hydrodynamic instability in the transport of miscible reactive slices through porous media. Phys. Rev. E 81 (5), 056321.10.1103/PhysRevE.81.056321CrossRefGoogle ScholarPubMed
Hejazi, S.H., Trevelyan, P.M.J., Azaiez, J. & De Wit, A. 2010 a Viscous fingering of a miscible reactive A + B $\to$ C interface: a linear stability analysis. J. Fluid Mech. 652, 501–528.10.1017/S0022112010000327CrossRefGoogle Scholar
Homsy, G.M. 1987 Viscous fingering in porous media. Annu. Rev. Fluid Mech. 19 (1), 271–311.10.1146/annurev.fl.19.010187.001415CrossRefGoogle Scholar
Krechetnikov, R. & Homsy, G.M. 2004 On a new surfactant-driven fingering phenomenon in a Hele-Shaw cell. J. Fluid Mech. 509, 103–124.10.1017/S0022112004009061CrossRefGoogle Scholar
Kuster, S., Riolfo, L.A., Zalts, A., El Hasi, C., Almarcha, C., Trevelyan, P.M.J., De Wit, A. & D’Onofrio, A. 2011 Differential diffusion effects on buoyancy-driven instabilities of acid-base fronts: the case of a color indicator. Phys. Chem. Chem. Phys 13 (38), 17295.10.1039/c1cp21185dCrossRefGoogle ScholarPubMed
Mishra, M., Trevelyan, P.M.J., Almarcha, C. & De Wit, A. 2010 Influence of double diffusive effects on miscible viscous fingering. Phys. Rev. Lett 105 (20), 204501.10.1103/PhysRevLett.105.204501CrossRefGoogle ScholarPubMed
Nagatsu, Y. & De Wit, A. 2011 Viscous fingering of a miscible reactive A + B $\to$ C interface for an infinitely fast chemical reaction: nonlinear simulations. Phys. Fluids 23, 043103.10.1063/1.3567176CrossRefGoogle Scholar
Nagatsu, Y., Ishii, Y., Tada, Y. & De Wit, A. 2014 Hydrodynamic fingering instability induced by a precipitation reaction. Phys. Rev. Lett. 113 (2), 024502.10.1103/PhysRevLett.113.024502CrossRefGoogle ScholarPubMed
Nagatsu, Y., Kondo, Y., Kato, Y. & Tada, Y. 2009 Effects of moderate Damköhler number on miscible viscous fingering involving viscosity decrease due to a chemical reaction. J. Fluid Mech. 625, 97–124.10.1017/S0022112008005429CrossRefGoogle Scholar
Nagatsu, Y., Matsuda, K., Kato, Y. & Tada, Y. 2007 Experimental study on miscible viscous fingering involving viscosity changes induced by variations in chemical species concentrations due to chemical reactions. J. Fluid Mech. 571, 475–493.10.1017/S0022112006003636CrossRefGoogle Scholar
Petitjeans, P., Chen, C.Y., Meiburg, E. & Maxworthy, T. 1999 Miscible quarter five-spot displacements in a Hele-Shaw cell and the role of flow-induced dispersion. Phys. Fluids 11 (7), 1705–1716.10.1063/1.870037CrossRefGoogle Scholar
Pihler-Puzovic, D., Illien, P., Heil, M. & Juel, A. 2012 Suppression of complex fingerlike patterns at the interface between air and a viscous fluid by elastic membranes. Phys. Rev. Lett. 108 (7), 074502.10.1103/PhysRevLett.108.074502CrossRefGoogle Scholar
Podgorski, T., Sostarecz, M.C., Zorman, S. & Belmonte, A. 2007 Fingering instabilities of a reactive micellar interface. Phys. Rev. E 76 (1), 016202.10.1103/PhysRevE.76.016202CrossRefGoogle ScholarPubMed
Pritchard, D. 2009 The linear stability of double-diffusive miscible rectilinear displacements in a Hele-Shaw cell. Eur. J. Mech. B/Fluids 28 (4), 564–577.10.1016/j.euromechflu.2009.01.004CrossRefGoogle Scholar
Riolfo, L.A., Nagatsu, Y., Iwata, S., Maes, R., Trevelyan, P.M.J. & De Wit, A. 2012 Experimental evidence of reaction-driven miscible viscous fingering. Phys. Rev. E 85 (1), 015304(R).10.1103/PhysRevE.85.015304CrossRefGoogle ScholarPubMed
Saffman, P.G. & Taylor, G.I. 1958 The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid. Proc. R. Soc. Lond. A 245 (1242), 312–329.Google Scholar
Sharma, V., Pramanik, S., Chen, C.-Y. & Mishra, M. 2019 A numerical study on reaction-induced radial fingering instability. J. Fluid Mech. 862, 624–638.10.1017/jfm.2018.963CrossRefGoogle Scholar
Suzuki, R.X., Nagatsu, Y., Mishra, M. & Ban, T. 2019 Fingering pattern induced by spinodal decomposition in hydrodynamically stable displacement in a partially miscible system. Phys. Rev. Fluids 4 (10), 104005.10.1103/PhysRevFluids.4.104005CrossRefGoogle Scholar
Tafur, N., Escala, D.M., Soto, A. & Muñuzuri, A.P. 2021 Highly viscous fluid displaced by a chemically controlled reactive interface. Chaos 31 (2), 023135.10.1063/5.0031058CrossRefGoogle ScholarPubMed
Tam, K.C. & Tiu, C. 1990 Role of ionic species and valency on the steady shear behavior of partially hydrolyzed polyacrylamide solutions. Colloid Polym. Sci. 268 (10), 911–920.10.1007/BF01469369CrossRefGoogle Scholar
Tang, H., Grivas, W., Homentcovschi, D., Geer, J. & Singler, T. 2000 Stability considerations associated with the meniscoid particle band at advancing interfaces in Hele‐Shaw suspension flows. Phys. Rev. Lett 85 (10), 2112–2115.10.1103/PhysRevLett.85.2112CrossRefGoogle ScholarPubMed
Tchelepi, H.A. & Orr, F.M. 1994 Interaction of viscous fingering, permeability heterogeneity, and gravity segregation in three dimensions. SPE Reservoir Engng 9 (4), 266–271.10.2118/25235-PACrossRefGoogle Scholar
Vlad, D.H. & Maher, J.V. 2000 Tip-splitting instabilities in the channel Saffman–Taylor flow of constant viscosity elastic fluids. Phys. Rev. E 61 (5), 5439–5444.10.1103/PhysRevE.61.5439CrossRefGoogle ScholarPubMed