Lattice Boltzmann Study of Hydrodynamic Spinodal Decomposition

Osborn, W. R.; Orlandini, Enzo; Swift, Michael; Yeomans, J. M.; Banavar, Jayanth R.

doi:10.1103/physrevlett.75.4031

Cited by 123 publications

(103 citation statements)

References 19 publications

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“…After initial growth all the quantities suggest the existence of the growth exponent 1/2. This is in accordance with previous studies on liquid-vapor systems at high viscosity [41] at symmetric composition when growth is expected to be described by the AllenCahn theory of interfaces dynamics which gives an exponent 1/2 [38] and hydrodynamics is not operating. Due to limits imposed by system size we cannot access very long times to probe whether the hydrodynamic regime is the late regime as previously argued [41].…”

Section: Simulation Resultssupporting

confidence: 92%

“…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%

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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: Simulation Resultssupporting

confidence: 92%

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

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show abstract

“…Similar values have been reported by other authors 6,8,17 , but our results allow us to exclude a smooth transition between n = 1 3 and n = 2 3 as proposed by one of these papers 6 . The measured growth exponent contradicts, however, the results of Osborn et al 13 , who reported n = 0.56 ± 0.03. We believe that the reason for this discrepancy is precisely the same as in the case of critical quenches, namely the absence of fluctuations in their model, which seem to play a vital role for early time and off-critical quenches.…”

Section: Phase Separation In Binary Immiscible Fluidscontrasting

confidence: 92%

Lattice-gas simulations of minority-phase domain growth in binary immiscible and ternary amphiphilic fluids

1997

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We investigate the growth kinetics of binary immiscible fluids and emulsions in two dimensions using a hydrodynamic lattice-gas model. We perform off-critical quenches in the binary fluid case and find that the domain size within the minority phase grows algebraically with time in accordance with theoretical predictions. In the late time regime we find a growth exponent n = 0.45 over a wide range of concentrations, in good agreement with other simulations. In the early time regime we find no universal growth exponent but a strong dependence on the concentration of the minority phase. In the ternary amphiphilic fluid case the kinetics of self assembly of the droplet phase are studied for the first time. At low surfactant concentrations, we find that, after an early algebraic growth, a nucleation regime dominates the late-time kinetics, which is enhanced by an increasing concentration of surfactant. With a further increase in the concentration of surfactant, we see a crossover to logarithmically slow growth, and finally saturation of the oil droplets, which we fit phenomenologically to a stretched exponential function. Finally, the transition between the droplet and the sponge phase is studied.

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“…This value of z can also be directly inferred from the damping rate in the overdamped case, eq. (35). Analogously, for the transverse current we have from eqs.…”

Section: A Linear Hydrodynamicsmentioning

confidence: 90%

“…Recently, there has been growing interest in understanding the critical properties of these and related lipid bilayer systems [19][20][21][22][23][24][25][26][27][28], especially, since they constitute the building blocks that form the membranes of biological cells [29]. Isothermal non-ideal fluid models have also been used to study phase-separation [30][31][32][33][34][35][36], capillary waves [37][38][39] and supercooled liquids close to the glass transition [40][41][42][43][44]. All these works, however, did not address the critical dynamics of an isothermal fluid.…”

Section: Introductionmentioning

confidence: 99%

Critical dynamics of an isothermal compressible nonideal fluid

Groß

Varnik

2012

Phys. Rev. E

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A pure fluid at its critical point shows a dramatic slow-down in its dynamics, due to a divergence of the order-parameter susceptibility and the coefficient of heat transport. Under isothermal conditions, however, sound waves provide the only possible relaxation mechanism for order-parameter fluctuations. Here we study the critical dynamics of an isothermal, compressible non-ideal fluid via scaling arguments and computer simulations of the corresponding fluctuating hydrodynamics equations. We show that, below a critical dimension of 4, the order-parameter dynamics of an isothermal fluid effectively reduces to "model A," characterized by overdamped sound waves and a divergent bulk viscosity. In contrast, the shear viscosity remains finite above two dimensions. Possible applications of the model are discussed.

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Lattice Boltzmann Study of Hydrodynamic Spinodal Decomposition

Cited by 123 publications

References 19 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

Lattice-gas simulations of minority-phase domain growth in binary immiscible and ternary amphiphilic fluids

Critical dynamics of an isothermal compressible nonideal fluid

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