Thermodynamic coarsening arrested by viscous fingering in partially miscible binary mixtures

Fu, Xiaojing; Cueto-Felgueroso, Luis; Juanes, Ruben

doi:10.1103/physreve.94.033111

Thermodynamic coarsening arrested by viscous fingering in partially miscible binary mixtures

Journal Article · Tue Sep 20 00:00:00 EDT 2016 · Physical Review E

DOI:https://doi.org/10.1103/physreve.94.033111· OSTI ID:1505596

Fu, Xiaojing ^[1]; Cueto-Felgueroso, Luis ^[2]; Juanes, Ruben ^[3]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); none
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Technical Univ. of Madrid, Madrid (Spain)
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

We view the evolution of binary mixtures far from equilibrium, and demonstrate that the interplay between phase separation and hydrodynamic instability can arrest the Ostwald ripening process characteristic of nonflowing mixtures. We describe a model binary system in a Hele-Shaw cell using a phase-field approach with explicit dependence of both phase fraction and mass concentration. When the viscosity contrast between phases is large (as is the case for gas and liquid phases), an imposed background flow leads to viscous fingering, phase branching, and pinch off. This dynamic flow disorder limits phase growth and arrests thermodynamic coarsening. Because of this, the system reaches a regime of statistical steady state in which the binary mixture is permanently driven away from equilibrium.

View Accepted Manuscript (DOE)

Research Organization:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Univ. of Texas, Austin, TX (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

Grant/Contract Number:: FE0013999

OSTI ID:: 1505596

Alternate ID(s):: OSTI ID: 1325613

Journal Information:: Physical Review E, Journal Name: Physical Review E Journal Issue: 3 Vol. 94; ISSN PLEEE8; ISSN 2470-0045

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (54)

The Structure of Internal Layers for Unstable Nonlinear Diffusion Equations Witelski, Thomas P. Studies in Applied Mathematics, Vol. 97, Issue 3 https://doi.org/10.1002/sapm1996973277	journal	October 1996
A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening Allen, Samuel M.; Cahn, John W. Acta Metallurgica, Vol. 27, Issue 6 https://doi.org/10.1016/0001-6160(79)90196-2	journal	June 1979
The kinetics of precipitation from supersaturated solid solutions Lifshitz, I. M.; Slyozov, V. V. Journal of Physics and Chemistry of Solids, Vol. 19, Issue 1-2 https://doi.org/10.1016/0022-3697(61)90054-3	journal	April 1961
Phase-field simulation of 2-D Ostwald ripening in the high volume fraction regime Fan, Danan; Chen, S. P.; Chen, Long-Qing Acta Materialia, Vol. 50, Issue 8 https://doi.org/10.1016/S1359-6454(01)00393-7	journal	May 2002
A two-phase diffuse-interface model for Hele–Shaw flows with large property contrasts Sun, Y.; Beckermann, C. Physica D: Nonlinear Phenomena, Vol. 237, Issue 23 https://doi.org/10.1016/j.physd.2008.06.010	journal	December 2008
On the tip-splitting instability of viscous fingers Lajeunesse, E.; Couder, Y. Journal of Fluid Mechanics, Vol. 419 https://doi.org/10.1017/S0022112000001324	journal	September 2000
Three-dimensional miscible displacement simulations in homogeneous porous media with gravity override Riaz, A.; Meiburg, E. Journal of Fluid Mechanics, Vol. 494 https://doi.org/10.1017/S0022112003005974	journal	November 2003
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
Miscible displacements in capillary tubes. Part 2. Numerical simulations Chen, Ching-Yao; Meiburg, Eckart Journal of Fluid Mechanics, Vol. 326 https://doi.org/10.1017/S0022112096008245	journal	November 1996
A phase-field model of two-phase Hele-Shaw flow Cueto-Felgueroso, Luis; Juanes, Ruben Journal of Fluid Mechanics, Vol. 758 https://doi.org/10.1017/jfm.2014.512	journal	October 2014
Vapor-Liquid Equilibrium. XI. A New Expression for the Excess Free Energy of Mixing Wilson, Grant M. Journal of the American Chemical Society, Vol. 86, Issue 2 https://doi.org/10.1021/ja01056a002	journal	January 1964
Miscible droplets in a porous medium and the effects of Korteweg stresses Chen, Ching-Yao; Wang, Lilin; Meiburg, Eckart Physics of Fluids, Vol. 13, Issue 9 https://doi.org/10.1063/1.1387468	journal	September 2001
Modeling pinchoff and reconnection in a Hele-Shaw cell. I. The models and their calibration Lee, Hyeong-Gi; Lowengrub, J. S.; Goodman, J. Physics of Fluids, Vol. 14, Issue 2 https://doi.org/10.1063/1.1425843	journal	February 2002
Modeling pinchoff and reconnection in a Hele-Shaw cell. II. Analysis and simulation in the nonlinear regime Lee, Hyeong-Gi; Lowengrub, J. S.; Goodman, J. Physics of Fluids, Vol. 14, Issue 2 https://doi.org/10.1063/1.1425844	journal	February 2002
Free Energy of a Nonuniform System. I. Interfacial Free Energy Cahn, John W.; Hilliard, John E. The Journal of Chemical Physics, Vol. 28, Issue 2 https://doi.org/10.1063/1.1744102	journal	February 1958
Simulation of nonlinear viscous fingering in miscible displacement Tan, C. T.; Homsy, G. M. Physics of Fluids, Vol. 31, Issue 6 https://doi.org/10.1063/1.866726	journal	January 1988
Spiral precipitation patterns in confined chemical gardens Haudin, Florence; Cartwright, Julyan H. E.; Brau, Fabian Proceedings of the National Academy of Sciences, Vol. 111, Issue 49 https://doi.org/10.1073/pnas.1409552111	journal	November 2014
A dynamic scaling assumption for phase separation Furukawa, Hiroshi Advances in Physics, Vol. 34, Issue 6 https://doi.org/10.1080/00018738500101841	journal	January 1985
Theory of phase-ordering kinetics Bray, A. J. Advances in Physics, Vol. 43, Issue 3 https://doi.org/10.1080/00018739400101505	journal	June 1994
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
Late stages of spinodal decomposition in binary mixtures Siggia, Eric D. Physical Review A, Vol. 20, Issue 2 https://doi.org/10.1103/PhysRevA.20.595	journal	August 1979
Turbulence in binary fluid mixtures Ruiz, Ricardo; Nelson, David R. Physical Review A, Vol. 23, Issue 6 https://doi.org/10.1103/PhysRevA.23.3224	journal	June 1981
Turbulent suppression of spinodal decomposition Pine, D. J.; Easwar, N.; Maher, J. V. Physical Review A, Vol. 29, Issue 1 https://doi.org/10.1103/PhysRevA.29.308	journal	January 1984
Theory and simulation of Ostwald ripening Yao, Jian Hua; Elder, K. R.; Guo, Hong Physical Review B, Vol. 47, Issue 21 https://doi.org/10.1103/PhysRevB.47.14110	journal	June 1993
Phase-field model of solute trapping during solidification Wheeler, A. A.; Boettinger, W. J.; McFadden, G. B. Physical Review E, Vol. 47, Issue 3 https://doi.org/10.1103/PhysRevE.47.1893	journal	March 1993
Phase-field model for Hele-Shaw flows with arbitrary viscosity contrast. I. Theoretical approach Folch, R.; Casademunt, J.; Hernández-Machado, A. Physical Review E, Vol. 60, Issue 2 https://doi.org/10.1103/PhysRevE.60.1724	journal	August 1999
Phase-field model for Hele-Shaw flows with arbitrary viscosity contrast. II. Numerical study Folch, R.; Casademunt, J.; Hernández-Machado, A. Physical Review E, Vol. 60, Issue 2 https://doi.org/10.1103/PhysRevE.60.1734	journal	August 1999
Ordering of viscous liquid mixtures under a steady shear flow Shou, Zhenyu; Chakrabarti, Amitabha Physical Review E, Vol. 61, Issue 3 https://doi.org/10.1103/PhysRevE.61.R2200	journal	March 2000
Phase-field model of Hele-Shaw flows in the high-viscosity contrast regime Hernández-Machado, A.; Lacasta, A. M.; Mayoral, E. Physical Review E, Vol. 68, Issue 4 https://doi.org/10.1103/PhysRevE.68.046310	journal	October 2003
Quantitative phase-field modeling of two-phase growth Folch, R.; Plapp, M. Physical Review E, Vol. 72, Issue 1 https://doi.org/10.1103/PhysRevE.72.011602	journal	July 2005
Enhanced mixing via alternating injection in radial Hele-Shaw flows Chen, Ching-Yao; Huang, Yi-Cheng; Huang, Yu-Sheng Physical Review E, Vol. 92, Issue 4 https://doi.org/10.1103/PhysRevE.92.043008	journal	October 2015
Nonlocal Interface Dynamics and Pattern Formation in Gravity-Driven Unsaturated Flow through Porous Media Cueto-Felgueroso, Luis; Juanes, Ruben Physical Review Letters, Vol. 101, Issue 24 https://doi.org/10.1103/PhysRevLett.101.244504	journal	December 2008
Fluid Mixing from Viscous Fingering Jha, Birendra; Cueto-Felgueroso, Luis; Juanes, Ruben Physical Review Letters, Vol. 106, Issue 19 https://doi.org/10.1103/PhysRevLett.106.194502	journal	May 2011
Macroscopic Phase-Field Model of Partial Wetting: Bubbles in a Capillary Tube Cueto-Felgueroso, Luis; Juanes, Ruben Physical Review Letters, Vol. 108, Issue 14 https://doi.org/10.1103/PhysRevLett.108.144502	journal	April 2012
Synergetic Fluid Mixing from Viscous Fingering and Alternating Injection Jha, Birendra; Cueto-Felgueroso, Luis; Juanes, Ruben Physical Review Letters, Vol. 111, Issue 14 https://doi.org/10.1103/PhysRevLett.111.144501	journal	October 2013
Spinodal Decomposition in Homogeneous and Isotropic Turbulence Perlekar, Prasad; Benzi, Roberto; Clercx, Herman J. H. Physical Review Letters, Vol. 112, Issue 1 https://doi.org/10.1103/PhysRevLett.112.014502	journal	January 2014
Hydrodynamic Fingering Instability Induced by a Precipitation Reaction Nagatsu, Y.; Ishii, Y.; Tada, Y. Physical Review Letters, Vol. 113, Issue 2 https://doi.org/10.1103/PhysRevLett.113.024502	journal	July 2014
Development of Viscous Fingering Patterns Maher, J. V. Physical Review Letters, Vol. 54, Issue 14 https://doi.org/10.1103/PhysRevLett.54.1498	journal	April 1985
Temporal fluctuations in a turbulently stirred binary liquid mixture Tong, P.; Goldburg, W. I.; Stavans, J. Physical Review Letters, Vol. 62, Issue 23 https://doi.org/10.1103/PhysRevLett.62.2668	journal	June 1989
Uncovering the analytical Saffman-Taylor finger in unstable viscous fingering and diffusion-limited aggregation Arnéodo, A.; Couder, Y.; Grasseau, G. Physical Review Letters, Vol. 63, Issue 9 https://doi.org/10.1103/PhysRevLett.63.984	journal	August 1989
Nucleation of a binary liquid mixture under steady-state shear Min, K. Y.; Goldburg, W. I. Physical Review Letters, Vol. 70, Issue 4 https://doi.org/10.1103/PhysRevLett.70.469	journal	January 1993
String Phase in Phase-Separating Fluids under Shear Flow Hashimoto, Takeji; Matsuzaka, Katsuo; Moses, Elisha Physical Review Letters, Vol. 74, Issue 1 https://doi.org/10.1103/PhysRevLett.74.126	journal	January 1995
Breakdown of Scale Invariance in the Coarsening of Phase-Separating Binary Fluids Wagner, Alexander J.; Yeomans, J. M. Physical Review Letters, Vol. 80, Issue 7 https://doi.org/10.1103/PhysRevLett.80.1429	journal	February 1998
Phase Separation in a Chaotic Flow Berthier, Ludovic; Barrat, Jean-Louis; Kurchan, Jorge Physical Review Letters, Vol. 86, Issue 10 https://doi.org/10.1103/PhysRevLett.86.2014	journal	March 2001
Fingering of Chemical Fronts in Porous Media De Wit, A. Physical Review Letters, Vol. 87, Issue 5 https://doi.org/10.1103/PhysRevLett.87.054502	journal	July 2001
Phase-Field Formulation for Quantitative Modeling of Alloy Solidification Karma, Alain Physical Review Letters, Vol. 87, Issue 11 https://doi.org/10.1103/PhysRevLett.87.115701	journal	August 2001
Turbulence and Coarsening in Active and Passive Binary Mixtures Berti, S.; Boffetta, G.; Cencini, M. Physical Review Letters, Vol. 95, Issue 22 https://doi.org/10.1103/PhysRevLett.95.224501	journal	November 2005
Theory of dynamic critical phenomena Hohenberg, P. C.; Halperin, B. I. Reviews of Modern Physics, Vol. 49, Issue 3 https://doi.org/10.1103/RevModPhys.49.435	journal	July 1977
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
Diffuse-Interface Methods in Fluid Mechanics Anderson, D. M.; McFadden, G. B.; Wheeler, A. A. Annual Review of Fluid Mechanics, Vol. 30, Issue 1 https://doi.org/10.1146/annurev.fluid.30.1.139	journal	January 1998
Phase-Field Simulation of Solidification Boettinger, W. J.; Warren, J. A.; Beckermann, C. Annual Review of Materials Research, Vol. 32, Issue 1 https://doi.org/10.1146/annurev.matsci.32.101901.155803	journal	August 2002
Ostwald Ripening of Two-Phase Mixtures Voorhees, P. W. Annual Review of Materials Science, Vol. 22, Issue 1 https://doi.org/10.1146/annurev.ms.22.080192.001213	journal	August 1992
Studien über die Bildung und Umwandlung fester Körper Ostwald, W. Zeitschrift für Physikalische Chemie, Vol. 22U, Issue 1 https://doi.org/10.1515/zpch-1897-2233	journal	January 1897
A biharmonic-modified forward time stepping method for fourth order nonlinear diffusion equations Lu, Hsiang-Wei; Ju, Ning; Bertozzi, Andrea L. Discrete and Continuous Dynamical Systems, Vol. 29, Issue 4 https://doi.org/10.3934/dcds.2011.29.1367	journal	December 2010

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