Controlling Viscous Fingering Using Time-Dependent Strategies

Stone, Howard; Zheng, Zhong; Kim, Hyoungsoo

doi:10.1103/PhysRevLett.115.174501

Controlling Viscous Fingering Using Time-Dependent Strategies

Journal Article · Tue Oct 20 00:00:00 EDT 2015 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.115.174501· OSTI ID:1390174

Stone, Howard ^[1]; Zheng, Zhong ^[2]; Kim, Hyoungsoo ^[2]

Princeton Univ., NJ (United States). Dept. of Mechanical and Aerospace Engineering; Princeton University
Princeton Univ., NJ (United States). Dept. of Mechanical and Aerospace Engineering

Control and stabilization of viscous fingering of immiscible fluids impacts a wide variety of pressure-driven multiphase flows. Here, we report theoretical and experimental results on time-dependent control strategy by manipulating the gap thickness b(t) in a lifting Hele-Shaw cell in the power-law form b(t) = b₁t^1/7. Experimental results show good quantitative agreement with the predictions of linear stability analysis. Furthermore, by choosing the value of a single time-independent control parameter we can either totally suppress the viscous fingering instability or maintain a series of non-splitting viscous fingers during the fluid displacement process. Besides the gap thickness of a Hele-Shaw cell, in principle, time-dependent control strategies can also be placed on the injection rate, viscosity of the displaced fluid, and interfacial tensions between the two fluids.

View Accepted Manuscript (DOE)

Research Organization:: Princeton Univ., Princeton, NJ (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)

Grant/Contract Number:: SC0008598

OSTI ID:: 1390174

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 17 Vol. 115; ISSN 0031-9007; ISSN PRLTAO

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (33)

Removing the stiffness from interfacial flows with surface tension Hou, Thomas Y.; Lowengrub, John S.; Shelley, Michael J. Journal of Computational Physics, Vol. 114, Issue 2 https://doi.org/10.1006/jcph.1994.1170	journal	October 1994
Boundary Integral Methods for Multicomponent Fluids and Multiphase Materials Hou, T. Y.; Lowengrub, J. S.; Shelley, M. J. Journal of Computational Physics, Vol. 169, Issue 2 https://doi.org/10.1006/jcph.2000.6626	journal	May 2001
A note on the measurement of dynamic contact angles Wilson, S. D. R. Journal of Colloid and Interface Science, Vol. 51, Issue 3 https://doi.org/10.1016/0021-9797(75)90151-4	journal	June 1975
Experimental Demonstration of the Role of Anisotropy in Interfacial Pattern Formation Ben-Jacob, E.; Godbey, R.; Goldenfeld, Nigel D. Dynamics of Curved Fronts https://doi.org/10.1016/b978-0-08-092523-3.50025-3	book	January 1988
Radial fingering in a Hele Shaw cell Paterson, Lincoln Journal of Fluid Mechanics, Vol. 113, Issue -1 https://doi.org/10.1017/S0022112081003613	journal	December 1981
Numerical experiments on Hele Shaw flow with a sharp interface Tryggvason, Gretar; Aref, Hassan Journal of Fluid Mechanics, Vol. 136, Issue -1 https://doi.org/10.1017/S0022112083002037	journal	November 1983
Finger-interaction mechanisms in stratified Hele-Shaw flow Tryggvason, Grétar; Aref, Hassan Journal of Fluid Mechanics, Vol. 154 https://doi.org/10.1017/S0022112085001537	journal	May 1985
The formation of drops through viscous instability Cardoso, Silvana S. S.; Woods, Andrew W. Journal of Fluid Mechanics, Vol. 289 https://doi.org/10.1017/S0022112095001364	journal	April 1995
Modelling the suppression of viscous fingering in elastic-walled Hele-Shaw cells Pihler-Puzović, Draga; Périllat, Raphaël; Russell, Matthew Journal of Fluid Mechanics, Vol. 731 https://doi.org/10.1017/jfm.2013.375	journal	August 2013
Instability of a gravity current within a soap film Goldstein, Raymond E.; Huppert, Herbert E.; Moffatt, H. Keith Journal of Fluid Mechanics, Vol. 753 https://doi.org/10.1017/jfm.2014.395	journal	July 2014
Control of interfacial instabilities using flow geometry Al-Housseiny, Talal T.; Tsai, Peichun A.; Stone, Howard A. Nature Physics, Vol. 8, Issue 10 https://doi.org/10.1038/nphys2396	journal	August 2012
Stretch flow of thin layers of Newtonian liquids: Fingering patterns and lifting forces Lindner, A.; Derks, D.; Shelley, M. J. Physics of Fluids, Vol. 17, Issue 7 https://doi.org/10.1063/1.1939927	journal	July 2005
Controlling viscous fingering in tapered Hele-Shaw cells Al-Housseiny, Talal T.; Stone, Howard A. Physics of Fluids, Vol. 25, Issue 9 https://doi.org/10.1063/1.4819317	journal	September 2013
The Saffman–Taylor instability: From the linear to the circular geometry Thomé, H.; Rabaud, M.; Hakim, V. Physics of Fluids A: Fluid Dynamics, Vol. 1, Issue 2 https://doi.org/10.1063/1.857493	journal	February 1989
Finger breakup in Hele–Shaw cells DeGregoria, A. J.; Schwartz, L. W. Physics of Fluids, Vol. 28, Issue 8 https://doi.org/10.1063/1.865286	journal	January 1985
Nonlinear unstable viscous fingers in Hele–Shaw flows. II. Numerical simulation Meiburg, E.; Homsy, G. M. Physics of Fluids, Vol. 31, Issue 3 https://doi.org/10.1063/1.866824	journal	January 1988
From snowflake formation to growth of bacterial colonies II: Cooperative formation of complex colonial patterns Ben-Jacob, Eshel Contemporary Physics, Vol. 38, Issue 3 https://doi.org/10.1080/001075197182405	journal	May 1997
Hele - Shaw flow and pattern formation in a time-dependent gap Shelley, Michael J.; Tian, Fei-Ran; Wlodarski, Krzysztof Nonlinearity, Vol. 10, Issue 6 https://doi.org/10.1088/0951-7715/10/6/005	journal	November 1997
The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid Saffman, Phillip Geoffrey; Taylor, Geoffrey Ingram Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 245, Issue 1242, p. 312-329 https://doi.org/10.1098/rspa.1958.0085	journal	June 1958
Finger competition in lifting Hele-Shaw flows with a yield stress fluid Fontana, João V.; Miranda, José A. Physical Review E, Vol. 88, Issue 2 https://doi.org/10.1103/PhysRevE.88.023001	journal	August 2013
Control of Viscous Fingering Patterns in a Radial Hele-Shaw Cell Li, Shuwang; Lowengrub, John S.; Fontana, Jake Physical Review Letters, Vol. 102, Issue 17 https://doi.org/10.1103/PhysRevLett.102.174501	journal	April 2009
Suppression of Complex Fingerlike Patterns at the Interface between Air and a Viscous Fluid by Elastic Membranes Pihler-Puzović, D.; Illien, P.; Heil, M. Physical Review Letters, Vol. 108, Issue 7 https://doi.org/10.1103/PhysRevLett.108.074502	journal	February 2012
Minimization of Viscous Fluid Fingering: A Variational Scheme for Optimal Flow Rates Dias, Eduardo O.; Alvarez-Lacalle, Enrique; Carvalho, Márcio S. Physical Review Letters, Vol. 109, Issue 14 https://doi.org/10.1103/PhysRevLett.109.144502	journal	October 2012
Two-Phase Fluid Displacement and Interfacial Instabilities Under Elastic Membranes Al-Housseiny, Talal T.; Christov, Ivan C.; Stone, Howard A. Physical Review Letters, Vol. 111, Issue 3 https://doi.org/10.1103/PhysRevLett.111.034502	journal	July 2013
Diffusion-Limited Aggregation, a Kinetic Critical Phenomenon Witten, T. A.; Sander, L. M. Physical Review Letters, Vol. 47, Issue 19 https://doi.org/10.1103/PhysRevLett.47.1400	journal	November 1981
Experimental Demonstration of the Role of Anisotropy in Interfacial Pattern Formation Ben-Jacob, E.; Godbey, R.; Goldenfeld, Nigel D. Physical Review Letters, Vol. 55, Issue 12 https://doi.org/10.1103/PhysRevLett.55.1315	journal	September 1985
Saffman-Taylor finger width at low interfacial tension DeGregoria, A. J.; Schwartz, L. W. Physical Review Letters, Vol. 58, Issue 17 https://doi.org/10.1103/PhysRevLett.58.1742	journal	April 1987
Selection of Saffman-Taylor fingers in the sector geometry Combescot, R.; Ben Amar, M. Physical Review Letters, Vol. 67, Issue 4 https://doi.org/10.1103/PhysRevLett.67.453	journal	July 1991
Instabilities and pattern formation in crystal growth Langer, J. S. Reviews of Modern Physics, Vol. 52, Issue 1 https://doi.org/10.1103/RevModPhys.52.1	journal	January 1980
Viscous flows in two dimensions Bensimon, David; Kadanoff, Leo P.; Liang, Shoudan Reviews of Modern Physics, Vol. 58, Issue 4 https://doi.org/10.1103/RevModPhys.58.977	journal	October 1986
The Fluid Mechanics of Carbon Dioxide Sequestration Huppert, Herbert E.; Neufeld, Jerome A. Annual Review of Fluid Mechanics, Vol. 46, Issue 1 https://doi.org/10.1146/annurev-fluid-011212-140627	journal	January 2014
Viscous Fingering in Porous Media Homsy, G. M. Annual Review of Fluid Mechanics, Vol. 19, Issue 1 https://doi.org/10.1146/annurev.fl.19.010187.001415	journal	January 1987
Boundary Integral Methods for Multicomponent Fluids and Multiphase Materials J. S., Lowengrub,; M. J., Shelley,; T. Y., Hou, The University of North Carolina at Chapel Hill University Libraries https://doi.org/10.17615/9nwv-nv53	text	January 2001

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Computational Analysis of Interfacial Dynamics in Angled Hele-Shaw Cells: Instability Regimes Lu, Daihui; Municchi, Federico; Christov, Ivan C. Transport in Porous Media, Vol. 131, Issue 3 https://doi.org/10.1007/s11242-019-01371-2	journal	December 2019
Numerical investigation of controlling interfacial instabilities in non-standard Hele-Shaw configurations Morrow, Liam C.; Moroney, Timothy J.; McCue, Scott W. Journal of Fluid Mechanics, Vol. 877 https://doi.org/10.1017/jfm.2019.623	journal	September 2019
Control of radial miscible viscous fingering Sharma, Vandita; Nand, Sada; Pramanik, Satyajit Journal of Fluid Mechanics, Vol. 884 https://doi.org/10.1017/jfm.2019.932	journal	December 2019
Active control of viscous fingering using electric fields Gao, Tao; Mirzadeh, Mohammad; Bai, Peng Nature Communications, Vol. 10, Issue 1 https://doi.org/10.1038/s41467-019-11939-7	journal	September 2019
Fingering instabilities and pattern formation in a two-component dipolar Bose-Einstein condensate Xi, Kui-Tian; Byrnes, Tim; Saito, Hiroki Physical Review A, Vol. 97, Issue 2 https://doi.org/10.1103/physreva.97.023625	journal	February 2018
Control of viscous fingering by nanoparticles Sabet, Nasser; Hassanzadeh, Hassan; Abedi, Jalal Physical Review E, Vol. 96, Issue 6 https://doi.org/10.1103/physreve.96.063114	journal	December 2017
Fingering instabilities and pattern formation in a two-component dipolar Bose-Einstein condensate Xi, Kui-Tian; Byrnes, Tim; Saito, Hiroki arXiv https://doi.org/10.48550/arxiv.1704.04949	text	January 2017
Control of radial miscible viscous fingering Sharma, Vandita; Nand, Sada; Pramanik, Satyajit arXiv https://doi.org/10.48550/arxiv.1906.05621	text	January 2019

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