Hostname: page-component-745bb68f8f-lrblm Total loading time: 0 Render date: 2025-01-09T22:19:25.471Z Has data issue: false hasContentIssue false
  • English
  • Français

Experimental study on miscible viscous fingering involving viscosity changes induced by variations in chemical species concentrations due to chemical reactions

Published online by Cambridge University Press:  04 January 2007

YUICHIRO NAGATSU ,
KENJI MATSUDA ,
YOSHIHITO KATO  and
YUTAKA TADA
YUICHIRO NAGATSU
Affiliation:
Department of Material Engineering, Graduate School of Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, Aichi, 466-8555, Japan
KENJI MATSUDA
Affiliation:
Department of Material Engineering, Graduate School of Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, Aichi, 466-8555, Japan
YOSHIHITO KATO
Affiliation:
Department of Material Engineering, Graduate School of Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, Aichi, 466-8555, Japan
YUTAKA TADA
Affiliation:
Department of Material Engineering, Graduate School of Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, Aichi, 466-8555, Japan
Get access Rights & Permissions [Opens in a new window]

Abstract

When a reactive and miscible less-viscous liquid displaces a more-viscous liquid in a Hele-Shaw cell, reactive miscible viscous fingering takes place. We succeed in showing experimentally how a reactive miscible viscous fingering pattern in a radial Hele-Shaw cell changes when the viscosity of the more-viscous liquid is varied owing to variation in chemical species concentration induced by an instantaneous chemical reaction. This is done by making use of a polymer solution's dependence of viscosity on pH. When the viscosity is increased by the chemical reaction, the shielding effect is suppressed and the fingers are widened. As a result, the ratio of the area occupied by the fingering pattern in a circle whose radius is the length of the longest finger is larger in the reactive case than in the non-reactive case. When the viscosity is decreased by the chemical reaction, in contrast, the shielding effect is enhanced and the fingers are narrowed. These lead to the area ratio being smaller in the reactive case than in the non-reactive case. A physical model to explain this change in the fingering pattern caused by the chemical reaction is proposed.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 571 , 25 January 2007 , pp. 475 - 493
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Ben-Jacob, E., Godbey, R., Goldenfeld, N. D., Koplik, J., Levine, H., Mueller, T. & Sander, L. M. 1985 Experimental demonstration of the role of anisotropy in interfacial pattern formation. Phys. Rev. Lett. 55, 1315–1318.CrossRefGoogle 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, 458–461.CrossRefGoogle ScholarPubMed
Broyles, B. S., Shalliker, R. A., Cherrak, D. E. & Guiochon, G. 1998 Visualization of viscous fingering in chromatographic columns. J. Chromatog. A 822, 173–187.CrossRefGoogle Scholar
van Damme, H., Obrecht, F., Levitz, P., Gatineau, L. & Laroche, C. 1986 Fractal viscous fingering in clay slurries. Nature 320, 731–733.CrossRefGoogle Scholar
Couder, Y., Gérard, N. & Rabaud, M. 1986 Narrow fingers in the SaS0022112006003636_inlinean-Taylor instability. Phys. Rev. A 34, 51755178.CrossRefGoogle ScholarPubMed
DeWit, A. 2004 Miscible density fingering of chemical fronts in porous media: nonlinear simulations. Phys. Fluids 16, 163–175.CrossRefGoogle Scholar
DeWit, A. & Homsy, G. M. 1999a Viscous fingering in reaction–diffusion systems. J. Chem. Phys. 110, 8663–8675.CrossRefGoogle Scholar
DeWit, A. & Homsy, G. M. 1999b Nonlinear interaction of chemical reactions and viscous fingering in porous media. Phys. Fluids 11, 949–951.CrossRefGoogle Scholar
DeWit, A., DeKepper, P., Benyaich, K., Dewel, G. & Borckmans, P. 2003 Hydrodynamical instability of spatially extended bistable chemical systems. Chem. Engng Sci. 58, 4823–4831.CrossRefGoogle 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.CrossRefGoogle Scholar
Hill, S. 1952 Channeling in packed columns. Chem. Engng Sci. 1, 247–253.CrossRefGoogle Scholar
Homsy, G. M. 1987 Viscous fingering in porous media. Annu. Rev. Fluid Mech. 19, 271–311.CrossRefGoogle Scholar
Hornof, V. & Baig, F. U. 1995 Influence of interfacial reaction and mobility ratio on the displacement in a Hele-Shaw cell. Exps. Fluids 18, 448–453.CrossRefGoogle Scholar
Ignés-Mullol, J., Zhao, H. & Maher, J. V. 1995 Velocity fluctuations of fracturelike disruptions of associating polymer solutions. Phys. Rev. E 51, 1338–1343.CrossRefGoogle ScholarPubMed
Jahoda, M. & Hornof, V. 2000 Concentration profiles of reactant in a viscous finger formed during the interfacially reactive immiscible displacement in porous media. Powder Technol. 110, 253–257.CrossRefGoogle Scholar
Lemaire, E., Levitz, P., Daccord, G. & van Damme, H. 1991 From viscous fingering to viscoelastic fracturing in colloidal fluids. Phys. Rev. Lett. 67, 2009–2012.CrossRefGoogle ScholarPubMed
Lindner, A., Bonn, D. & Meunier, J. 2000 Viscous fingering in a shear thinning fluid. Phys. Fluids 12, 256–261.CrossRefGoogle Scholar
Lindner, A., Bonn, D., Corvera Poiré, E., Ben Amar, M. & Meunier, J. 2002 Viscous fingering in non-Newtonian fluids. J. Fluid Mech. 469, 237–256.CrossRefGoogle Scholar
McCloud, K. V. & Maher, J. V. 1995 Experimental perturbations to SaS0022112006003636_inlinean–Taylor flow. Phys. Rep. 260, 139–185.CrossRefGoogle Scholar
Nagatsu, Y. & Ueda, T. 2001 Effects of reactant concentrations on reactive miscible viscous fingering. AIChE J. 47, 1711–1720.CrossRefGoogle Scholar
Nagatsu, Y. & Ueda, T. 2003 Effects of finger-growth velocity on reactive miscible viscous fingering. AIChE J. 49, 789–792.CrossRefGoogle Scholar
Nagatsu, Y. & Ueda, T. 2004 Analytical study of effects of finger-growth velocity on reaction characteristics of reactive miscible viscous fingering by using a convection–diffusion-reaction model. Chem. Engng Sci. 59, 3817–3826.CrossRefGoogle Scholar
Nakamura, T. 1981 Water soluble polymers (Enlarged version). Kagaku Kougyousya (in Japanese).Google Scholar
Nittmann, J., Daccord, G. & Stanley, H. E. 1985 Fractal growth of viscous fingers: quantitative characterization of a fluid instability phenomenon. Nature 314, 141–144.CrossRefGoogle 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, 1705–1716.CrossRefGoogle Scholar
Pojman, J. A., Gunn, G., Patterson, C., Owens, J. & Simmons, C. 1998 Frontal dispersion polymerization. J. Phys. Chem. B 102, 3927–3929.CrossRefGoogle Scholar
SaS0022112006003636_inlinean, 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, 312–329.Google Scholar
Tanveer, S. 2000 Surprises in viscous fingering. J. Fluid Mech. 409, 273–308.CrossRefGoogle Scholar
Vlad, D. H. & Maher, J. V. 2000 Tip-splitting instabilities in the SaS0022112006003636_inlinean–Taylor flow of constant viscosity elastic fluids. Phy. Rev. E 61, 5439–5444.CrossRefGoogle ScholarPubMed
Vlad, D. H., Ignés-Mullol, J. & Maher, J. V. 1999 Velocity-jump instabilities in Hele-Shaw flow of associating polymer solutions. Phys. Rev. E 60, 4423–4430.CrossRefGoogle ScholarPubMed
Zhao, H. & Maher, J. V. 1993 Associating-polymer effects in a Hele-Shaw experiment. Phys. Rev. E 47, 4278–4283.CrossRefGoogle Scholar
Zocchi, G., Shaw, B., Libchaber, A. & Kadanoff, L. 1987 Finger narrowing under local perturbations in the SaS0022112006003636_inlinean–Taylor problem. Phys. Rev. A 36, 1894–1900.CrossRefGoogle ScholarPubMed