Lattice Boltzmann simulation of mixtures with multicomponent van der Waals equation of state

Ridl, Kent Stephen; Wagner, A. James

doi:10.1103/physreve.98.043305

Cited by 23 publications

(7 citation statements)

References 38 publications

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“…The details of the numerical implementation are discussed in the Supplementary Information [2]. It is possible to solve the Cahn-Hilliard equation using a lattice Boltzmann scheme, and on flat manifolds, it has been suggested that extension to more fluid components is more straightforward in this approach [35,49]. However, for our purpose here, it is more expensive and require us to use a higher order quadrature.…”

Section: The Vielbein Lattice Boltzmann Approachmentioning

confidence: 99%

“…In this work, we have chosen to employ the free energy model, though our framework can be adapted to account for the pseudo-potential and color models. Our approach can also be extended to account for more fluid components [1,36,49,53,62], as well as coupled to other dynamical equations, including those for liquid crystals [16,56] and viscoelastic fluids [23,39].…”

Section: Introductionmentioning

confidence: 99%

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Multicomponent flow on curved surfaces: A vielbein lattice Boltzmann approach

et al. 2019

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We develop and implement a novel lattice Boltzmann scheme to study multicomponent flows on curved surfaces, coupling the continuity and Navier-Stokes equations with the Cahn-Hilliard equation to track the evolution of the binary fluid interfaces. Standard lattice Boltzmann method relies on regular Cartesian grids, which makes it generally unsuitable to study flow problems on curved surfaces. To alleviate this limitation, we use a vielbein formalism to write down the Boltzmann equation on an arbitrary geometry, and solve the evolution of the fluid distribution functions using a finite difference method. Focussing on the torus geometry as an example of a curved surface, we demonstrate drift motions of fluid droplets and stripes embedded on the surface of a torus. Interestingly, they migrate in opposite directions: fluid droplets to the outer side while fluid stripes to the inner side of the torus. For the latter we demonstrate that the global minimum configuration is unique for small stripe widths, but it becomes bistable for large stripe widths. Our simulations are also in agreement with analytical predictions for the Laplace pressure of the fluid stripes, and their damped oscillatory motion as they approach equilibrium configurations, capturing the corresponding decay timescale and oscillation frequency. Finally, we simulate the coarsening dynamics of phase separating binary fluids in the hydrodynamics and diffusive regimes for tori of various shapes, and compare the results against those for a flat two-dimensional surface. Our lattice Boltzmann scheme can be extended to other surfaces and coupled to other dynamical equations, opening up a vast range of applications involving complex flows on curved geometries.

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Section: The Vielbein Lattice Boltzmann Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multicomponent flow on curved surfaces: A vielbein lattice Boltzmann approach

et al. 2019

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“…Several LB models have been proposed to study ternary fluid systems. Travasso et al proposed a free energy model to study phase separation of ternary mixtures under shear [35]; Spencer et al proposed a color model to study N > 2 component systems [36]; Ridl et al proposed a model combining N Van der Waals equation of states to study the stability of multicomponent mixtures [37]; Semprebon et al proposed a ternary free energy approach [38] to model liquids with equal density, showing that the method can simulate drop morphologies on SLIPS [39] and their dynamic properties [40] for a wide range of surface tensions and contact angles.…”

Section: Introductionmentioning

confidence: 99%

Wetting boundaries for a ternary high-density-ratio lattice Boltzmann method

et al. 2019

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We extend a recently proposed ternary free energy lattice Boltzmann model with high density contrast [1], by incorporating wetting boundaries at solid walls. The approaches are based on forcing and geometric schemes, with implementations optimised for ternary (and more generally higher order multicomponent) models. Advantages and disadvantages of each method are addressed by performing both static and dynamic tests, including the capillary filling dynamics of a liquid displacing the gas phase, and the self-propelled motion of a train of drops. Furthermore, we measure dynamic angles and show that the slip length critically depends on the equilibrium value of the contact angles, and whether it belongs to liquid-liquid or liquid-gas interfaces. These results validate the model capabilities of simulating complex ternary fluid dynamic problems near solid boundaries, for example drop impact solid substrates covered by a lubricant layer.

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“…An asymmetric effect of components in a mixture has also been considered by Ridl and Wagner [17] in a comprehensive investigation on mixtures of multiple Van der Waals fluids. Their work is based on a free-energy LB method in which the forcing stems from a gradient in the chemical potential rather than from pseudo-potential functions.…”

Section: An Asymmetric Eosmentioning

confidence: 99%