Comptes Rendus
Coarsening in fluid phase transitions
Comptes Rendus. Physique, Volume 16 (2015) no. 3, pp. 303-315.

We review the understanding of the kinetics of fluid phase separation in various space dimensions. Morphological differences, percolating or disconnected domains, based on overall composition in a binary liquid or on density in a vapor–liquid system, are discussed. Depending upon the morphology, various possible mechanisms for domain growth are pointed out and discussions of corresponding theoretical predictions are provided. On the computational front, useful models and simulation methodologies are presented. Theoretically predicted growth laws have been tested via molecular dynamics simulations of vapor–liquid transitions. In the case of a disconnected structure, the mechanism has been confirmed directly.

Nous passons en revue la compréhension de la cinétique de séparation de phases fluides dans diverses dimensions d'espace. Les différences morphologiques, les domaines de percolation ou déconnectés, basés sur la composition totale binaire ou sur la densité dans un système vapeur–liquide, sont discutés. Selon la morphologie, les différents mécanismes possibles sont présentés et les prédictions théoriques correspondantes discutées. Du côté du calcul par ordinateur, des modèles utiles et des méthodes de simulation sont présentées. Des lois de croissance prédites théoriquement ont été testées au moyen de simulations de dynamique moléculaire des transitions vapeur–liquide. Dans le cas d'une structure déconnectée, le mécanisme a été confirmé directement.

Published online:
DOI: 10.1016/j.crhy.2015.03.006
Keywords: Phase transition, Coarsening, Hydrodynamics, Molecular dynamics

Subir K. Das 1; Sutapa Roy 1, 2, 3; Jiarul Midya 1

1 Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
2 Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, 70569 Stuttgart, Germany
3 Institut für Theoretische Physik IV, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
@article{CRPHYS_2015__16_3_303_0,
     author = {Subir K. Das and Sutapa Roy and Jiarul Midya},
     title = {Coarsening in fluid phase transitions},
     journal = {Comptes Rendus. Physique},
     pages = {303--315},
     publisher = {Elsevier},
     volume = {16},
     number = {3},
     year = {2015},
     doi = {10.1016/j.crhy.2015.03.006},
     language = {en},
}
TY  - JOUR
AU  - Subir K. Das
AU  - Sutapa Roy
AU  - Jiarul Midya
TI  - Coarsening in fluid phase transitions
JO  - Comptes Rendus. Physique
PY  - 2015
SP  - 303
EP  - 315
VL  - 16
IS  - 3
PB  - Elsevier
DO  - 10.1016/j.crhy.2015.03.006
LA  - en
ID  - CRPHYS_2015__16_3_303_0
ER  - 
%0 Journal Article
%A Subir K. Das
%A Sutapa Roy
%A Jiarul Midya
%T Coarsening in fluid phase transitions
%J Comptes Rendus. Physique
%D 2015
%P 303-315
%V 16
%N 3
%I Elsevier
%R 10.1016/j.crhy.2015.03.006
%G en
%F CRPHYS_2015__16_3_303_0
Subir K. Das; Sutapa Roy; Jiarul Midya. Coarsening in fluid phase transitions. Comptes Rendus. Physique, Volume 16 (2015) no. 3, pp. 303-315. doi : 10.1016/j.crhy.2015.03.006. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2015.03.006/

[1] M.E. Fisher Theory of equilibrium critical phenomena, Rep. Prog. Phys., Volume 30 (1967), pp. 615-730

[2] H.E. Stanley Introduction to Phase Transitions and Critical Phenomena, Oxford University Press, 1971

[3] R. Evans The nature of the liquid–vapor interface and other topics in the statistical mechanics of non-uniform, classical fluids, Adv. Phys., Volume 28 (1979), pp. 143-200

[4] K. Binder Theory of first order phase transitions, Rep. Prog. Phys., Volume 50 (1987), pp. 783-859

[5] K. Binder Spinodal decomposition (R.W. Cahn; P. Haasen; E.J. Kramer, eds.), Phase Transformation of Material, Materials Science and Technology, vol. 5, VCH, Weinheim, 1991, pp. 405-471

[6] D. Kashchiev Nucleation: Basic Theory with Applications, Butterworth–Heinemann, Oxford, 2000

[7] R.A.L. Jones Soft Condensed Matter, Oxford University Press, 2002

[8] A. Onuki Phase Transition Dynamics, Cambridge University Press, 2002

[9] A.J. Bray Theory of phase ordering kinetics, Adv. Phys., Volume 51 (2002), pp. 481-587

[10] Kinetics of Phase Transitions (S. Puri; V. Wadhawan, eds.), CRC Press, Boca Raton, 2009

[11] S.K. Das Atomistic simulations of liquid–liquid coexistence in confinement: comparison of thermodynamics and kinetics with bulk, Mol. Simul., Volume 41 (2015), pp. 382-401

[12] I.M. Lifshitz; V.V. Sloyozov The kinetics of precipitation from supersaturation solid solutions, J. Phys. Chem. Solids, Volume 19 (1961), pp. 35-50

[13] D.A. Huse Correlation to late-stage behavior in spinodal decomposition: Lifshitz–Slyozov scaling and Monte Carlo simulations, Phys. Rev. B, Volume 34 (1986), pp. 7845-7850

[14] J.F. Marko; G.T. Barkema Phase ordering in the Ising model with conserved spin, Phys. Rev. E, Volume 52 (1995), pp. 2522-2534

[15] D.W. Heermann; L. Yixue; K. Binder Scaling solution and finite-size effects in the Lifshitz–Slyozov theory, Physica A, Volume 230 (1996), pp. 132-148

[16] J. Vinals; D. Jasnow Finite-size-scaling analysis of domain growth in the kinetic Ising model with conserved and nonconserved order parameters, Phys. Rev. B, Volume 37 (1998), pp. 9582-9589

[17] S. Majumder; S.K. Das Domain coarsening in two dimensions: conserved dynamics and finite-size scaling, Phys. Rev. E, Volume 81 (2010), p. 050102

[18] S. Majumder; S.K. Das Temperature and composition dependence of kinetics of phase separation in solid binary mixtures, Phys. Chem. Chem. Phys., Volume 15 (2013), p. 13209

[19] T. Blanchard; F. Corberi; L.F. Cugliandolo; M. Pico How soon after a zero-temperature quench is the fate of the Ising model sealed?, Europhys. Lett., Volume 106 (2014), p. 66001

[20] K. Binder; D. Stauffer Theory for the slowing down of the relaxation and spinodal decomposition of binary mixtures, Phys. Rev. Lett., Volume 33 (1974), pp. 1006-1009

[21] K. Binder Theory for the dynamics of “clusters.” II. Critical diffusion in binary systems and the kinetics of phase separation, Phys. Rev. B, Volume 15 (1977), pp. 4425-4447

[22] E.D. Siggia Late stages of spinodal decomposition in binary mixtures, Phys. Rev. A, Volume 20 (1979), pp. 595-605

[23] H. Furukawa Effect of inertia on droplet growth in a fluid, Phys. Rev. A, Volume 31 (1985), pp. 1103-1108

[24] H. Furukawa Turbulent growth of percolated droplets in phase separating fluids, Phys. Rev. A, Volume 36 (1987), pp. 2288-2292

[25] M. San Miguel; M. Grant; J.D. Gunton Phase separation in two-dimensional binary fluids, Phys. Rev. A, Volume 31 (1985), pp. 1001-1005

[26] H. Tanaka A new coarsening mechanism of droplet spinodal decomposition, J. Chem. Phys., Volume 103 (1995), p. 2361

[27] H. Tanaka Coarsening mechanisms of droplet spinodal decomposition in binary fluid mixtures, J. Chem. Phys., Volume 105 (1996), pp. 10099-10114

[28] H. Tanaka New mechanisms of droplet coarsening in phase-separating fluid mixtures, J. Chem. Phys., Volume 107 (1997), pp. 3734-3737

[29] F. Perrot; P. Guenoun; T. Baumberger; D. Beysens; Y. Garrabos; B. Le Neindre Nucleation and growth of tightly packed droplets in fluids, Phys. Rev. Lett., Volume 73 (1994), pp. 688-691

[30] J.P. Delville; C. Lalaude; S. Buil; A. Ducasse Late stage kinetics of a phase separation induced by a cw laser wave in binary liquid mixtures, Phys. Rev. E, Volume 59 (2006), pp. 5804-5818

[31] J. Hobley; S. Kajimoto; A. Takamizawa; H. Fukumura Experimentally determined growth exponents during the late stage of spinodal demixing in binary liquid mixtures, Phys. Rev. E, Volume 73 (2006), p. 011502

[32] D. Beysens; Y. Garrabos; D. Chatain; P. Evesque Phase transition under forced vibrations in critical CO2, Europhys. Lett., Volume 86 (2009), p. 16003

[33] S. Tanaka; Y. Kubo; Y. Yokoyama; A. Toda; K. Taguchi; H. Kajioka Kinetics of phase separation and coarsening in dilute surfactant pentaethylene glycol monododecyl ether solutions, J. Chem. Phys., Volume 135 (2011), p. 234503

[34] V.M. Kendon; M.E. Cates; I. Pagonabarraga; J.C. Desplat; P. Blandon Inertial effects in three-dimensional spinodal decomposition of a symmetric binary fluid mixture: a lattice Boltzmann study, J. Fluid Mech., Volume 440 (2001), pp. 147-203

[35] S. Puri; B. Dünweg Temporally linear domain growth in the segregation of binary fluids, Phys. Rev. A, Volume 45 (1992), p. R6977-R6980

[36] C. Datt; S.P. Thampi; R. Govindarajan Morphological evolution of domains in spinodal decomposition, Phys. Rev. E, Volume 91 (2015), p. 010101(R)

[37] M. Laradji; S. Toxvaerd; O.G. Mountain Molecular dynamics simulation of spinodal decomposition in three-dimensional binary fluids, Phys. Rev. Lett., Volume 77 (1996), pp. 2253-2256

[38] A.K. Thakre; W.K. den Ohe; W.J. Briels Domain formation and growth in spinodal decomposition in a binary fluid by molecular dynamics simulations, Phys. Rev. E, Volume 77 (2008), p. 011503

[39] S. Ahmad; S.K. Das; S. Puri Kinetics of phase separation in fluids: a molecular dynamics study, Phys. Rev. E, Volume 82 (2010), p. 040107

[40] S. Ahmad; S.K. Das; S. Puri Crossover in growth laws for phase separating binary fluids: molecular dynamics simulations, Phys. Rev. E, Volume 85 (2012), p. 031140

[41] S. Ahmad; S. Puri; S.K. Das Phase separation of fluids in porous media: a molecular dynamics study, Phys. Rev. E, Volume 90 (2014), p. 040302(R)

[42] S.K. Das; S. Roy; S. Majumder; S. Ahmad Finite-size effects in dynamics: critical versus coarsening phenomena, Phys. Rev. E, Volume 97 (2012), p. 66006

[43] H. Kabrede; R. Hentschke Spinodal decomposition in a 3D Lennard-Jones system, Physica A, Volume 361 (2006), pp. 485-493

[44] S. Majumder; S.K. Das Universality in fluid domain coarsening: the case of vapor–liquid transition, Europhys. Lett., Volume 95 (2012), p. 46002

[45] S. Roy; S.K. Das Nucleation and growth of droplets in vapor–liquid transitions, Phys. Rev. E, Volume 85 (2012), p. 050602

[46] S. Roy; S.K. Das Dynamics and growth of droplets close to the coexistence curve in fluids, Soft Matter, Volume 9 (2013), pp. 4178-4187

[47] S. Roy; S.K. Das Effects of domain morphology on kinetics of fluid phase separation, J. Chem. Phys., Volume 139 (2013), p. 044911

[48] S.W. Koch; R.C. Desai; F.F. Abraham Dynamics of phase separation in two-dimensional fluids: spinodal decomposition, Phys. Rev. A, Volume 27 (1983), pp. 2152-2167

[49] J. Midya, S.K. Das, in preparation.

[50] D.S. Fisher; D.A. Huse Nonequilibrium dynamics of spin glass, Phys. Rev. B, Volume 38 (1988), pp. 373-385

[51] S.N. Majumdar; A.J. Bray; S.J. Cornell; C. Sire Global persistence exponent for nonequilibrium critical dynamics, Phys. Rev. Lett., Volume 77 (1996), pp. 3704-3707

[52] J.-P. Hansen; I.R. McDonald Theory of Simple Liquids, Academic Press, London, 2008

[53] D.P. Landau; K. Binder A Guide to Monte Carlo Simulations in Statistical Physics, Cambridge University Press, 2009

[54] I. Schmidt; K. Binder Dynamics of wetting transitions: a time-dependent Ginzburg–Landau treatment, Z. Phys. B, Condens. Matter, Volume 67 (1987), p. 369

[55] S.K. Das; J. Horbach; K. Binder Kinetics of phase separation in thin films: lattice versus continuum models for solid binary mixtures, Phys. Rev. E, Volume 79 (2009), p. 021602

[56] P.C. Hohenberg; B.I. Halperin Theory of dynamic critical phenomena, Rev. Mod. Phys., Volume 49 (1977), pp. 436-479

[57] K. Kaski; K. Binder; J.D. Gunton A study of cell distribution functions of the three dimensional Ising model, Phys. Rev. B, Volume 29 (1984), pp. 3996-4009

[58] S. Ramaswamy The mechanics and statistics of active matter, Annu. Rev. Condens. Matter Phys., Volume 1 (2010), pp. 323-345

[59] M.P. Allen; D.J. Tildesley Computer Simulations of Liquid, Clarendon, Oxford, 1987

[60] D. Frenkel; B. Smit Understanding Molecular Simulation: From Algorithms to Applications, Academic Press, San Diego, 2002

[61] D.C. Rapaport The Art of Molecular Dynamics Simulations, Cambridge University Press, 2004

[62] P. Nikuman; M. Karttunen; I. Vattulainen How would you integrate the equations of motion in dissipative particle dynamics simulations?, Comput. Phys. Commun., Volume 153 (2003), pp. 407-423

[63] S.D. Stoyanov; R.D. Groot From molecular dynamics to hydrodynamics: a novel Galilean invariant thermostat, J. Chem. Phys., Volume 122 (2005), p. 114112

[64] C. Pastorino; T. Kreer; M. Müller; K. Binder Comparison of dissipative particle dynamics and Langevin thermostats for out-of-equilibrium simulations of polymeric systems, Phys. Rev. E, Volume 76 (2007), p. 026706

[65] A. Winkler; P. Virnau; K. Binder; R.G. Winkler; G. Gompper Hydrodynamic mechanisms of spinodal decomposition in confined colloid–polymer mixtures: a multiparticle collision dynamics study, J. Chem. Phys., Volume 138 (2013), p. 0544901

[66] E.A. Koopman; C.P. Lowe Advantages of a Lowe–Andersen thermostat in molecular dynamics simulations, J. Chem. Phys., Volume 124 (2006), p. 204103

[67] S. Roy; S.K. Das Finite-size scaling study of shear viscosity anomaly at liquid–liquid criticality, J. Chem. Phys., Volume 141 (2014), p. 234502

[68] J.V. Sengers; R.A. Perkins Fluids near critical points (M.J. Assael; A.R.H. Goodwin; V. Vesovic; W.A. Wakehan, eds.), Transport Properties of Fluids: Advances in Transport Properties, IUPAC, RSC publishing, Cambridge, 2014, pp. 337-361

[69] A. Chen; E.H. Chimowitz; S. De; Y. Shapir Universal dynamic exponent at the gas liquid transition from molecular dynamics, Phys. Rev. Lett., Volume 95 (2005), p. 255701

[70] S. Roy; S.K. Das Transport phenomena in fluids: finite-size scaling for critical behavior, Europhys. Lett., Volume 94 (2011), p. 36001

[71] R.F. Berg; M.R. Moldover; G.A. Zimmerli Viscoelasticity of Xenon near the critical point, Phys. Rev. Lett., Volume 82 (1999), pp. 920-923

[72] H.C. Burstyn; J.V. Sengers Decay rate of critical concentration fluctuation in a binary liquid, Phys. Rev. A, Volume 25 (1982), pp. 448-465

[73] J.K. Bhattacharjee; I. Iwanowski; U. Kaatze Bulk viscosity universality and scaling function near the binary liquid consolute point, J. Chem. Phys., Volume 131 (2009), p. 174502

[74] J.K. Bhattacharjee; U. Kaatze; S.Z. Mirzaev Sound attenuation near the demixing point of binary liquids: interplay of critical dynamics and noncritical kinetics, Rep. Prog. Phys., Volume 73 (2010), p. 066601

[75] A.Z. Panagiotopoulos Direct determination of phase coexistence properties of fluids by Monte Carlo simulation in a new ensemble, Mol. Phys., Volume 61 (1987), pp. 813-826

[76] M.E. Fisher; M.N. Barber Scaling theory for finite-size effects in the critical region, Phys. Rev. Lett., Volume 28 (1972), pp. 1516-1519

[77] S. Ahmad; F. Corberi; S.K. Das; E. Lippiello; S. Puri; M. Zannetti Aging and crossover in phase separating fluid mixtures, Phys. Rev. E, Volume 86 (2012), p. 061129

[78] S. Majumder; S.K. Das Effects of density conservation and hydrodynamics on aging in nonequilibrium processes, Phys. Rev. Lett., Volume 111 (2013), p. 055503

[79] R.A.L. Jones; Laura J. Norton; Edward J. Kramer; Frank S. Bates; Pierre Wiltzius Surface-directed spinodal decomposition, Phys. Rev. Lett., Volume 66 (1991), pp. 1326-1329

[80] S. Puri; K. Binder Surface-directed spinodal decomposition: phenomenology and numerical results, Phys. Rev. A, Volume 46 (1992), p. R4487-R4489

[81] H. Tanaka Interplay between wetting and phase separation in binary fluid mixtures: roles of hydrodynamics, J. Phys. Condens. Matter, Volume 13 (2001), pp. 4637-4674

[82] S. Bastea; S. Puri; J.L. Lebowitz Surface-directed spinodal decomposition in binary fluid mixtures, Phys. Rev. E, Volume 63 (2001), p. 041513

[83] S.K. Das; S. Puri; J. Horbach; K. Binder Spinodal decomposition in thin films: molecular-dynamics simulations of a binary Lennard-Jones fluid mixture, Phys. Rev. E, Volume 73 (2001), p. 031604

[84] S.K. Das; S. Puri; J. Horbach; K. Binder Molecular dynamics study of phase separation kinetics in thin films, Phys. Rev. Lett., Volume 96 (2006), p. 016107

[85] M.J.A. Hore; M. Laradji Dissipative particle dynamics simulation of the interplay between spinodal decomposition and wetting in thin film binary fluids, J. Chem. Phys., Volume 132 (2010), p. 024908

[86] K. Binder; S. Puri; S.K. Das; J. Horbach Phase separation in confined geometries, J. Stat. Phys., Volume 138 (2010), pp. 51-84

[87] P.K. Jaiswal; K. Binder; S. Puri Phase separation of binary mixtures in thin films: effects of an initial concentration gradient across the film, Phys. Rev. E, Volume 85 (2012), p. 041602

[88] P.K. Jaiswal; S. Puri; S.K. Das Hydrodynamic crossovers in surface-directed spinodal decomposition and surface enrichment, Europhys. Lett., Volume 97 (2012), p. 16005

[89] E.A.G. Jamie; R.P.A. Dullens; D.G.A.L. Aarts Spinodal decomposition of a confined colloid–polymer system, J. Chem. Phys., Volume 137 (2012), p. 204902

[90] S.J. Mitchell; D.P. Landau Phase separation in a compressible 2D Ising model, Phys. Rev. Lett., Volume 97 (2006), p. 025701

Cited by Sources:

Comments - Policy