Morphological characterization of spinodal decomposition kinetics

Sofonea, Victor; Mecke, Klaus

doi:10.1007/s100510050672

Cited by 77 publications

(93 citation statements)

References 7 publications

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“…When hydrodynamics comes into play, the liquid-vapor system behaves similarly to binary fluids so that a growth exponent α = 2/3 is expected [36]. Previous numerical studies used molecular dynamics simulations [39,40] and a LB model based on a free energy functional [41,42,43]. In molecular dynamics simulations it was found evidence for the growth exponent 1/2 [39,40].…”

Section: Introductionmentioning

confidence: 99%

“…By using the free-energy LB model, Osborn et al [41] found the growth exponents 2/3 and 1/2 at low and high viscosity, respectively, independently on the system composition. Mecke and Sofonea [42,43], using the same algorithm for an off-symmetric system, found a crossover from 2/3 to 1/2 at low viscosity, and 1/3 at high viscosity. We will compare results of our model with the aforementioned ones.…”

Section: Introductionmentioning

confidence: 99%

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Finite-difference lattice Boltzmann model with flux limiters for liquid-vapor systems

Sofonea

Lamura²,

Gonnella

et al. 2004

Phys. Rev. E

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In this paper we apply a finite difference lattice Boltzmann model to study the phase separation in a two-dimensional liquid-vapor system. Spurious numerical effects in macroscopic equations are discussed and an appropriate numerical scheme involving flux limiter techniques is proposed to minimize them and guarantee a better numerical stability at very low viscosity. The phase separation kinetics is investigated and we find evidence of two different growth regimes depending on the value of the fluid viscosity as well as on the liquid-vapor ratio.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Finite-difference lattice Boltzmann model with flux limiters for liquid-vapor systems

Sofonea

Lamura²,

Gonnella

et al. 2004

Phys. Rev. E

Self Cite

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“…[2,3,4,5] developed an algorithm based on implementing a pressure tensor and Shan et al [6,7,8] developed an algorithm based on mimicking microscopic interactions. These algorithms have been succesfully applied to simulations of phase-separation [9], drop-collisions [1,10], wetting dynamics and spreading [11], and the study of dynamic contact angles [12,13,14]. Only recently has it been shown that both algorithms perform very similarly when higher order corrections are taken into account [15].…”

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confidence: 99%

Interface width and bulk stability: Requirements for the simulation of deeply quenched liquid-gas systems

Wagner

Pooley

2007

Phys. Rev. E

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Simulations of liquid-gas systems with extended interfaces are observed to fail to give accurate results for two reasons: the interface can get "stuck" on the lattice or a density overshoot develops around the interface. In the first case the bulk densities can take a range of values, dependent on the initial conditions. In the second case inaccurate bulk densities are found. In this communication we derive the minimum interface width required for the accurate simulation of liquid gas systems with a diffuse interface. We demonstrate this criterion for lattice Boltzmann simulations of a van der Waals gas. When combining this criterion with predictions for the bulk stability we can predict the parameter range that leads to stable and accurate simulation results. This allows us to identify parameter ranges leading to high density ratios of over 1000. This is despite the fact that lattice Boltzmann simulations of liquid-gas systems were believed to be restricted to modest density ratios of less than 20 [1].Application of lattice Boltzmann methods to the simulation of liquid-gas systems has been one of the early successful applications of lattice Boltzmann. Two very different algorithms were developed to do this: Swift et. al. [2,3,4,5] developed an algorithm based on implementing a pressure tensor and Shan et al. [6,7,8] developed an algorithm based on mimicking microscopic interactions. These algorithms have been succesfully applied to simulations of phase-separation [9], drop-collisions [1, 10], wetting dynamics and spreading [11], and the study of dynamic contact angles [12,13,14]. Only recently has it been shown that both algorithms perform very similarly when higher order corrections are taken into account [15].Previously there have been only heuristic analysis of what range of paramteres lead to accurate simulation results. In some parameter ranges not too far from the critical point too thin interefaces can lead to interfaces that stick to the lattice. This can lead to non-unique bulk densities for the liquid and gas phases that depend on the inital contitions. Further from the critical point density overshooting is observed at the interfaces. This also leads to incorrect bulk densities. In this communication we present a criterion that allows us to predict the range of acceptable values for the interface width. We will show that the accuracy of the algorithm rapidly deteriorates when this limit is exceeded. The second important contribution of this communication is a more general definition of the equation of state. Usual lattice Boltzmann methods recover the ideal gas equation of state with a pressure of p = ρ/3 when the gas is dilute. While relaxing this requirement has no effect on the interfacial properties it allows us to adjust the bulk-stability of the lattice Boltzmann method. Taken together this allows us to determine sets of paramters for which very deep quenches can be simulated. This is an important result since lattice Boltzmann methods were previously believed to be limited to density ranges of...

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“…As a mesoscopic approach and a bridge between the molecular dynamics method at the microscopic level and the conventional numerical method at the macroscopic level, the lattice Boltzmann (LB) method [1] has been successfully applied to various fields during the past two decades, ranging from the multiphase system [2][3][4], magnetohydrodynamics [5][6][7], reaction-diffusion system [8][9][10], compressible fluid dynamics [11][12][13][14][15][16][17][18], simulations of linear and nonlinear partial differential equations [19], etc. Its popularity is mainly owed to its kinetic nature [20], which makes the physics at mesoscopic scale can be incorporated easily.…”

Section: Introductionmentioning

confidence: 99%

Lattice Boltzmann study on Kelvin-Helmholtz instability: Roles of velocity and density gradients

Gan

Zhang

et al. 2011

Phys. Rev. E

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Morphological characterization of spinodal decomposition kinetics

Cited by 77 publications

References 7 publications

Finite-difference lattice Boltzmann model with flux limiters for liquid-vapor systems

Finite-difference lattice Boltzmann model with flux limiters for liquid-vapor systems

Interface width and bulk stability: Requirements for the simulation of deeply quenched liquid-gas systems

Lattice Boltzmann study on Kelvin-Helmholtz instability: Roles of velocity and density gradients

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