A Lattice Boltzmann Model of Binary-Fluid Mixtures

Orlandini, Enzo; Swift, Michael; Yeomans, J. M.

doi:10.1209/0295-5075/32/6/001

Cited by 168 publications

(162 citation statements)

References 20 publications

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“…This utilizes the immiscible binary fluid BGK model proposed by [9,10] with the inclusion of a body force [7] . Rather than considering separately the two density components of the binary fluid, ρ1 and ρ 2 , we work with the total fluid density, ρ = ρ 1 +ρ 2 , and the concentration difference or order parameter, d = ρ 1 -ρ 2 .…”

Section: Methodsmentioning

confidence: 99%

“…From the evolution of the distribution functions the macroscopic quantities can be obtained. The total fluid density, ρ = ρ 1 ρ 2, the total fluid velocity, u, and the density difference, d = ρ 1 ρ 2, can be found from the distribution functions as: are then selinteractionsimulate two ideal gases with repulsive interactin energy [9,10] and are given by: …”

Section: Methodsmentioning

confidence: 99%

“…The parameters which have not yet been defined can in general be selected to determine the properties of the simulation, [7,9,10] . Here we define them and give the value used here and, for the parameters of particular importance to our simulation, we briefly discuss their significance.…”

Section: Methodsmentioning

confidence: 99%

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Variation in the Thickness of A Fluid Interface Due to Internal Wave Propagation: A Lattice Boltzmann Simulation

Buick¹,

Hann²,

Cosgrove³

2004

American J. of Applied Sciences

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Abstract:The change in the thickness of an interface between two immiscible fluids due to the propagation of an internal capillary-gravity wave along the interface is considered using a Bhatnagar, Gross and Krook (BGK) lattice Boltzmann model of a binary of fluid. The vertical thickness of the interface is recorded from the simulations since this is the most easily measured quantities in any simulation or experiment. The vertical thickness is then related to the actual thickness (perpendicular to the interface) which is seen to vary with the phase of the wave. The positions of the maxima and minimum thicknesses are seen to be approximately constant relative to the phase of the propagating wave and the range of variation of the thickness decreases at approximately the same rate as the wave amplitude is damped. A simplified model for the interface is considered which predicts a similar variation due to the interface being stretched as the internal wave propagates.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Variation in the Thickness of A Fluid Interface Due to Internal Wave Propagation: A Lattice Boltzmann Simulation

Buick¹,

Hann²,

Cosgrove³

2004

American J. of Applied Sciences

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“…In order to simulate the effects of microemulsions, lattice Boltzmann models with amphiphile surfactants are largely based on the free energy model of Orlandini et al [7], see for example references [8][9][10][11]. The model used here is simpler, since the purpose is primarily to investigate the deformative effects of surface tension rather than the effects on the interface structure.…”

Section: Introductionmentioning

confidence: 99%

Simulation of multiphase flows with variable surface tension using the Lattice Boltzmann method

Stensholt

2010

WIT Transactions on Engineering Sciences

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Methods for implementing variable surface tension on two popular LatticeBoltzmann models, the original gradient-based chromodynamic model, and the Shan-Chen model, are explored and examined. The experiment, inspired by the work of Greenspan, consists of reducing the surface tension at two poles of a circular droplet due to a diffusive solute (surfactant). Both Lattice Boltzmann models are able to simulate the expected initial deformation where the droplet is stretched along the pole axis, and contracts at the equator. We observed no furrowing to the droplet, which verifies the work of He and Dembo who concluded that variation in surface tension cannot alone account for such furrowing. We were able to simulate the process as the surfactant diffuses over the entire interface and the spatial variation in surface tension vanishes. The droplet reverts back to its original circular shape with the overall surface tension reduced. Variable surface tension is easier to implement with the chromodynamic model. The physically direct Shan-Chen model, which has superior isotropic qualities, can also be used for variable surface tension. However, coordinating the decline of the surface tension with the reduction in the separation forces is a more delicate matter, and the diffusivity of the interface increases if the surface tension is weakened.

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“…al. [9,10] where the correct equilibrium of the fluid is imposed by choosing an appropriate free energy and including it in such a way that the fluid spontaneously reaches the equilibrium described by its minimum.Previous lattice Boltzmann models of amphiphilic systems have been based on a single order …”

mentioning

confidence: 99%

A lattice Boltzmann model of ternary fluid mixtures

1999

Self Cite

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Abstract. -A lattice Boltzmann model is introduced which simulates oil-water-surfactant mixtures. The model is based on a Ginzburg-Landau free energy with two scalar order parameters. Diffusive and hydrodynamic transport is included. Results are presented showing how the surfactant diffuses to the oil-water interfaces thus lowering the surface tension and leading to spontaneous emulsification. The rate of emulsification depends on the viscosity of the ternary fluid.Introduction. -The addition of surfactant to a binary mixture of oil and water can produce many different complex structures on a mesoscopic length scale. The surfactant molecules move to the interface and lower the oil-water interfacial tension. This can result in, for example, lamellar, micellar, microemulsion or hexagonal arrangements of the oil and water domains [1,2].The equilibrium behaviour of such amphiphilic systems is well understood. However the dynamics of the self-assembly of the mesoscale phases and their rheology are less well investigated. This is a difficult problem because of the interplay between several relevant transport mechanisms, the diffusion of the constituent components and their hydrodynamic flow. To date models of amphiphilic rheology which treat hydrodynamic effects include time-dependent Ginzburg-Landau approaches [3,4], molecular dynamics[5] and a lattice gas cellular automaton scheme based on microscopic interactions [6,7].The aim of this Letter is to introduce an alternative numerical scheme that can model the dynamics of amphiphilic systems in such a way that diffusive and hydrodynamic mechanisms are included. The numerical approach that we use is lattice Boltzmann simulations which have emerged as a useful tool to study the dynamics of complex fluids [8]. We base our approach on that described by Orlandini et. al. [9,10] where the correct equilibrium of the fluid is imposed by choosing an appropriate free energy and including it in such a way that the fluid spontaneously reaches the equilibrium described by its minimum.Previous lattice Boltzmann models of amphiphilic systems have been based on a single order

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A Lattice Boltzmann Model of Binary-Fluid Mixtures

Cited by 168 publications

References 20 publications

Variation in the Thickness of A Fluid Interface Due to Internal Wave Propagation: A Lattice Boltzmann Simulation

Variation in the Thickness of A Fluid Interface Due to Internal Wave Propagation: A Lattice Boltzmann Simulation

Simulation of multiphase flows with variable surface tension using the Lattice Boltzmann method

A lattice Boltzmann model of ternary fluid mixtures

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