Lattice Boltzmann study of spinodal decomposition in two dimensions.

A lattice Boltzmann model using the Shan-Chen prescription for a binary immiscible fluid is described, and the macroscopic equations obeyed by the model are derived. The model is used to quantitatively examine spinodal decomposition of a two-dimensional binary fluid. This model allows examination of the early-time period corresponding to interface formation, and shows agreement with analytical solutions of the linearized Cahn-Hilliard equation, despite the fact that the model contains no explicit free-energy functional. This regime has not, to the knowledge of the authors, been previously observed using any lattice Boltzmann method. In agreement with other models, a scaling law with the exponent 2/3 is observed for late-time domain growth. Breakdown of scaling is also observed for certain sets of simulation parameters.

[1]  Hiroshi Furukawa,et al.  A dynamic scaling assumption for phase separation , 1985 .

[2]  P. Coveney,et al.  Erratum: Lattice-gas simulations of domain growth, saturation, and self-assembly in immiscible fluids and microemulsions [Phys. Rev. E55, 708 (1997)] , 1997 .

[3]  Grant,et al.  Monte Carlo renormalization-group study of spinodal decomposition: Scaling and growth. , 1989, Physical review. B, Condensed matter.

[4]  Banavar,et al.  Lattice Boltzmann study of hydrodynamic spinodal decomposition. , 1995, Physical review letters.

[5]  Peter V. Coveney,et al.  A ternary lattice Boltzmann model for amphiphilic fluids , 2000, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[6]  M. S. Rao,et al.  Novel Monte Carlo Approach to the Dynamics of Fluids: Single-Particle Diffusion, Correlation Functions, and Phase Ordering of Binary Fluids. , 1996, Physical review letters.

[7]  Shiyi Chen,et al.  A lattice Boltzmann model for multiphase fluid flows , 1993, comp-gas/9303001.

[8]  Alexander J. Wagner,et al.  Breakdown of Scale Invariance in the Coarsening of Phase-Separating Binary Fluids , 1998 .

[9]  I. Pagonabarraga,et al.  Inertial effects in three-dimensional spinodal decomposition of a symmetric binary fluid mixture: a lattice Boltzmann study , 2001, Journal of Fluid Mechanics.

[10]  M. Grant,et al.  Spinodal Decomposition in Fluids , 1999 .

[11]  Xiaowen Shan,et al.  Multicomponent lattice-Boltzmann model with interparticle interaction , 1995, comp-gas/9503001.

[12]  T. Lookman,et al.  Growth kinetics in multicomponent fluids , 1994, comp-gas/9405003.

[13]  A. Bray.  Theory of phase-ordering kinetics , 1994, cond-mat/9501089.

[14]  M. Cieplak,et al.  Boltzmann cellular automata studies of the spinodal decomposition , 1995 .

[15]  Shan,et al.  Simulation of nonideal gases and liquid-gas phase transitions by the lattice Boltzmann equation. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[16]  M. E. Cates,et al.  3D spinodal decomposition in the inertial regime , 1999, cond-mat/9902346.

[17]  Y. Pomeau,et al.  Lattice-gas automata for the Navier-Stokes equation. , 1986, Physical review letters.

[18]  Shan,et al.  Lattice Boltzmann model for simulating flows with multiple phases and components. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[19]  N. Martys,et al.  Critical properties and phase separation in lattice Boltzmann fluid mixtures. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  J. E. Hilliard,et al.  Free Energy of a Nonuniform System. I. Interfacial Free Energy , 1958 .

[21]  Coveney,et al.  Computer simulations of domain growth and phase separation in two-dimensional binary immiscible fluids using dissipative particle dynamics. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[22]  Chen,et al.  Hydrodynamic spinodal decomposition: Growth kinetics and scaling functions. , 1993, Physical review. B, Condensed matter.

[23]  Y. Qian,et al.  Lattice BGK Models for Navier-Stokes Equation , 1992 .

[24]  Daniel H. Rothman,et al.  Immiscible cellular-automaton fluids , 1988 .

[25]  Eric D. Siggia,et al.  Late stages of spinodal decomposition in binary mixtures , 1979 .

[26]  Toxvaerd,et al.  Computer simulation of phase separation in a two-dimensional binary fluid mixture. , 1993, Physical review letters.

[27]  Lapedes,et al.  Domain growth, wetting, and scaling in porous media. , 1993, Physical review letters.

[28]  Grant,et al.  Phase separation in two-dimensional binary fluids. , 1985, Physical review. A, General physics.

[29]  S. Wolfram.  Cellular automaton fluids 1: Basic theory , 1986 .

[30]  S. Orszag,et al.  Lattice BGK Models for the Navier-Stokes Equation: Nonlinear Deviation in Compressible Regimes , 1993 .

[31]  Towards the simplest hydrodynamic lattice-gas model , 2002, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[32]  Spinodal decomposition of off-critical quenches with a viscous phase using dissipative particle dynamics in two and three spatial dimensions , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[33]  Chen,et al.  Effects of hydrodynamics on phase transition kinetics in two-dimensional binary fluids. , 1995, Physical review letters.

[34]  Farrell,et al.  Spinodal decomposition in a two-dimensional fluid model. , 1989, Physical review. B, Condensed matter.

[35]  Tanaka.  Double phase separation in a confined, symmetric binary mixture: Interface quench effect unique to bicontinuous phase separation. , 1994, Physical review letters.

[36]  M. E. Cates,et al.  Inertia, coarsening and fluid motion in binary mixtures , 1999 .

[37]  Y. Qian,et al.  Complete Galilean-invariant lattice BGK models for the Navier-Stokes equation , 1998 .