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Viscous fingering of miscible annular ring

Published online by Cambridge University Press:  06 April 2021

Vandita Sharma Open the ORCID record for Vandita Sharma [Opens in a new window] ,
Hamirul Bin Othman ,
Yuichiro Nagatsu Open the ORCID record for Yuichiro Nagatsu [Opens in a new window]  and
Manoranjan Mishra Open the ORCID record for Manoranjan Mishra [Opens in a new window]
Vandita Sharma
Affiliation:
Department of Mathematics, Indian Institute of Technology Ropar, 140001Rupnagar, India
Hamirul Bin Othman
Affiliation:
Department of Chemical Engineering, Tokyo University of Agriculture and Technology, 184-8588Tokyo, Japan
Yuichiro Nagatsu*
Affiliation:
Department of Chemical Engineering, Tokyo University of Agriculture and Technology, 184-8588Tokyo, Japan
Manoranjan Mishra*
Affiliation:
Department of Mathematics, Indian Institute of Technology Ropar, 140001Rupnagar, India
*
†Email addresses for correspondence: manoranjan@iitrpr.ac.in, nagatsu@cc.tuat.ac.jp
†Email addresses for correspondence: manoranjan@iitrpr.ac.in, nagatsu@cc.tuat.ac.jp
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Abstract

Miscible viscous fingering (VF) of the annulus of a more viscous fluid radially displaced by a less viscous fluid is investigated through both numerical computations and experimental study. We aim to understand how VF with finiteness in a radial displacement different from the classical radial VF and the instability of a slice displaced rectilinearly with a uniform velocity. It is observed that the VF of a miscible annular ring is a persistent phenomenon in contrast to the transient nature of VF of a miscible slice. Although new fingers cease to appear after some time but due to the radial spreading of the area available for VF, a finite number of fingers always remain at a later time when diffusion is the ultimate dominating force. A statistical analysis is performed for the numerical data and it is found that the second moment of the averaged profile, variance, is a non-monotonic function of time, contrary to variance in classical radial VF and rectilinear VF with one fluid sandwiched between layers of another. The minimum in the variance indicates the interaction of two fronts which is visible in terms of pressure fingers, but not the concentration fingers indicating a faster growth of pressure than the concentration growth. In addition, for existence of critical parameters for instability in terms of viscosity contrast and amount of sample, the variation of the finger length with flow rate is found to be dependent on the amount of the more viscous fluid confined in the annulus.

JFM classification

Interfacial Flows (free surface): Fingering instability Low-Reynolds-number flows: Hele-Shaw flows Low-Reynolds-number flows: Porous media
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 916 , 10 June 2021 , A14
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Beeson-Jones, T.H. & Woods, A.W. 2015 On the selection of viscosity to suppress the Saffman–Taylor instability in a radially spreading annulus. J. Fluid Mech. 782, 127–143.CrossRefGoogle Scholar
Cardoso, S.S.S. & Woods, A.W. 1995 The formation of drops through viscous instability. J. Fluid Mech. 289, 351–378.CrossRefGoogle Scholar
Chaudhuri, A. & Vishnudas, R. 2018 A systematic numerical modeling study of various polymer injection conditions on immiscible and miscible viscous fingering and oil recovery in a five-spot setup. Fuel 232, 431–443.CrossRefGoogle Scholar
Chen, C.-Y., Huang, C.-W., Gadêlha, H. & Miranda, J.A. 2008 Radial viscous fingering in miscible Hele-Shaw flows: a numerical study. Phys. Rev. E 78, 016306.CrossRefGoogle ScholarPubMed
Chen, C.-Y., Huang, Y.-C., Huang, Y.-S. & Miranda, J.A. 2015 Enhanced mixing via alternating injection in radial Hele-Shaw flows. Phys. Rev. E 92, 043008.CrossRefGoogle ScholarPubMed
Chui, J.Y.Y., de Anna, P. & Juanes, R. 2015 Interface evolution during radial miscible viscous fingering. Phys. Rev. E 92, 041003.CrossRefGoogle ScholarPubMed
COMSOL Multiphysics® v. 5. 4., COMSOL AB, Stockholm, Sweden.Google Scholar
Daripa, P. & Gin, C. 2016 Studies on dispersive stabilization of porous media flows. Phys. Fluids 28 (8), 082105.CrossRefGoogle Scholar
De Wit, A., Bertho, Y. & Martin, M. 2005 Viscous fingering of miscible slices. Phys. Fluids (1994-present) 17 (5), 054114.CrossRefGoogle Scholar
Edstrom, L., Samuelsson, J. & Fornstedt, T. 2011 Deformations of overloaded bands under ph-stable conditions in reversed phase chromatography. J. Chromatogr. 1218, 1966–1973.CrossRefGoogle ScholarPubMed
George, P.L. & Borouchaki, H. 1998 Delaunay Triangulation and Meshing: Application to Finite Elements. Hermès.Google Scholar
Glycerine, Producers’ Association 1963 Physical Properties of Glycerine and its Solutions. Glycerine Producers’ Association.Google Scholar
Guiochon, G., Felinger, A., Shirazi, D.G. & Katti, A.M. 2008 Fundamentals of Preparative and Nonlinear Chromatography, 2nd edn. Academic Press, Elsevier.Google Scholar
Homsy, G.M. 1987 Viscous fingering in porous media. Annu. Rev. Fluid Mech. 19 (1), 271–311.CrossRefGoogle Scholar
Hota, T.K., Pramanik, S. & Mishra, M. 2015 Onset of fingering instability in a finite slice of adsorbed solute. Phys. Rev. E 92, 023013.CrossRefGoogle Scholar
Jha, B., Cueto-Felgueroso, L. & Juanes, R. 2011 Quantifying mixing in viscously unstable porous media flows. Phys. Rev. E 84, 066312.CrossRefGoogle ScholarPubMed
Kretz, V., Berest, P., Hulin, J.P. & Salin, D. 2003 An experimental study of the effects of density and viscosity contrasts on macrodispersion in porous media. Water Resour. Res. 39 (2), 1032.CrossRefGoogle Scholar
MATLAB 2018 9.7.0.1190202 (R2019b). The MathWorks Inc.Google Scholar
Mayfield, K.J., Shalliker, R.A., Catchpoole, H.J., Sweeney, A.P., Wong, V. & Guiochon, G. 2005 Viscous fingering induced flow instability in multidimensional liquid chromatography. J. Chromatogr. 1080 (2), 124–131.CrossRefGoogle ScholarPubMed
Mishra, M., Martin, M. & De Wit, A. 2008 Differences in miscible viscous fingering of finite width slices with positive or negative log-mobility ratio. Phys. Rev. E 78, 066306.CrossRefGoogle ScholarPubMed
Pramanik, S. & Mishra, M. 2013 Linear stability analysis of korteweg stresses effect on miscible viscous fingering in porous media. Phys. Fluids (1994-present) 25 (7), 074104.CrossRefGoogle Scholar
Pramanik, S. & Mishra, M. 2015 Effect of Péclet number on miscible rectilinear displacement in a Hele-Shaw cell. Phys. Rev. E 91, 033006.CrossRefGoogle Scholar
Pramanik, S., De Wit, A. & Mishra, M. 2015 Viscous fingering and deformation of a miscible circular blob in a rectilinear displacement in porous media. J. Fluid Mech. 782, R2.CrossRefGoogle Scholar
Preparata, F.P. & Shamos, M.I. 1988 Computational Geometry: An Introduction. Springer.Google Scholar
Rana, C., Pramanik, S., Martin, M., De Wit, A. & Mishra, M.. 2019 Influence of Langmuir adsorption and viscous fingering on transport of finite size samples in porous media. Phys. Rev. Fluids 4, 104001.CrossRefGoogle Scholar
Shalliker, R.A., Catchpoole, H.J., Dennis, G.R. & Guiochon, G. 2007 Visualising viscous fingering in chromatography columns: high viscosity solute plug. J. Chromatogr. 1142 (1), 48–55.CrossRefGoogle ScholarPubMed
Sharma, V., Nand, S., Pramanik, S., Chen, C.-Y. & Mishra, M 2020 Control of radial miscible viscous fingering. J. Fluid Mech. 884, A16.CrossRefGoogle 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.CrossRefGoogle Scholar
Sharma, V., Pramanik, S. & Mishra, M. 2017 Dynamics of a highly viscous circular blob in homogeneous porous media. Fluids 2 (2), 32.CrossRefGoogle Scholar
Tan, C.T. & Homsy, G.M. 1987 Stability of miscible displacements in porous media: radial source flow. Phys. Fluids 30 (5), 1239–1245.CrossRefGoogle Scholar
Tan, C.T. & Homsy, G.M. 1988 Simulation of nonlinear viscous fingering in miscible displacement. Phys. Fluids (1958–1988) 31 (6), 1330–1338.CrossRefGoogle Scholar
Vishnudas, R. & Chaudhuri, A. 2017 A comprehensive numerical study of immiscible and miscible viscous fingers during chemical enhanced oil recovery. Fuel 194, 480–490.CrossRefGoogle Scholar
Zhou, X., Dong, M. & Maini, B. 2013 The dominant mechanism of enhanced heavy oil recovery by chemical flooding in a two-dimensional physical model. Fuel 108, 261–268.CrossRefGoogle Scholar