Lattice-Boltzmann equations for describing segregation in non-ideal mixtures

Philippi, Paulo C.; Mattila, Keijo; Siebert, Diogo Nardelli; Santos, Luís Orlando Emerich dos; Júnior, Luiz Adolfo Hegele; Surmas, Rodrigo

doi:10.1017/jfm.2012.473

Cited by 15 publications

(19 citation statements)

References 32 publications

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“…Also the Fickian diffusion framework provided above is valid only for dilute concentrations of the components in the bulk liquid, while in the drop phase the concentration of both components is quite high. The applicability of the diffusion equation for such a non-ideal system is studied in detail by Philippi et al (2012), but it is not relevant for the scientific question addressed here. For a two-component drop, we should solve (3.2) for each component subject to the same boundary conditions at r = R b and similar initial conditions.…”

Section: Multicomponent Dropmentioning

confidence: 99%

Molecular dynamics study of multicomponent droplet dissolution in a sparingly miscible liquid

et al. 2017

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The dissolution of a multicomponent nanodrop in a sparingly miscible liquid is studied by molecular dynamics (MD) simulations. We studied both binary and ternary systems, in which nanodroplets are formed from one and two components, respectively. Whereas for a single-component droplet the dissolution can easily be calculated, the situation is more complicated for a multicomponent drop, as the interface concentrations of the drop constituents depend on the drop composition, which changes with time. In this study, the variation of the interface concentration with the drop composition is determined from independent 'numerical experiments', which are then used in the theoretical model for the dissolution dynamics of a multicomponent drop. The MD simulations reveal that when the interaction strengths between the drop constituents and the surrounding bulk liquid are significantly different, the concentration of the more soluble component near the drop interface may become larger than in the drop bulk. This effect is the larger the smaller the drop radius. While the present study is limited to binary and ternary systems, the same method can be easily extended to a larger number of components.

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Section: Multicomponent Dropmentioning

confidence: 99%

Molecular dynamics study of multicomponent droplet dissolution in a sparingly miscible liquid

et al. 2017

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“…Equation (24) for the calculation of E (6) αβγ δηξ and Eq. (34) for the calculation of the gradient are no longer valid and the only resulting expressions for calculating the gradient lead to errors of O(h 2 ):…”

Section: Neighboring Requirementsmentioning

confidence: 99%

“…Another negative aspect of the SC model is that the interface tension and the attraction term of the equation of state are dependent on a single parameter, G. Sbragaglia et al [5] proposed a later modification of the Shan-Chen model by using two independent parameters on * diogo.siebert@ufsc.br the pseudopotential to fix this drawback. Other SC model drawbacks are thoroughly discussed in Philippi et al [6].…”

Section: Introductionmentioning

confidence: 99%

“…In other words, the essence is to derive LBEs from the discrete-velocity Boltzmann equation in such a way that the resulting leading-order error terms are higher in order than the physical interface interaction terms. Such high-order LBEs were applied for simulating multicomponent fluids by Philippi et al [6] and were recently investigated by Mattila et al [21].…”

Section: Introductionmentioning

confidence: 99%

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Consistent lattice Boltzmann equations for phase transitions

Mattila

2014

Phys. Rev. E

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Unlike conventional computational fluid dynamics methods, the lattice Boltzmann method (LBM) describes the dynamic behavior of fluids in a mesoscopic scale based on discrete forms of kinetic equations. In this scale, complex macroscopic phenomena like the formation and collapse of interfaces can be naturally described as related to source terms incorporated into the kinetic equations. In this context, a novel athermal lattice Boltzmann scheme for the simulation of phase transition is proposed. The continuous kinetic model obtained from the Liouville equation using the mean-field interaction force approach is shown to be consistent with diffuse interface model using the Helmholtz free energy. Density profiles, interface thickness, and surface tension are analytically derived for a plane liquid-vapor interface. A discrete form of the kinetic equation is then obtained by applying the quadrature method based on prescribed abscissas together with a third-order scheme for the discretization of the streaming or advection term in the Boltzmann equation. Spatial derivatives in the source terms are approximated with high-order schemes. The numerical validation of the method is performed by measuring the speed of sound as well as by retrieving the coexistence curve and the interface density profiles. The appearance of spurious currents near the interface is investigated. The simulations are performed with the equations of state of Van der Waals, Redlich-Kwong, Redlich-Kwong-Soave, Peng-Robinson, and Carnahan-Starling.

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“…(1998). Philippi et al (2012) propuseram um modelo cinético para representar de forma realista a mistura e segregação isotérmica de misturas não ideais utilizando parâmetros de força moleculares. O modelo de color-fluid modificado proposto por Liu et al (2012) é utilizado neste estudo.…”

Section: Métodos De Lattice-boltzmann (Lbm)unclassified

Escoamento De Emulsões Através De Capilares Com Garganta Utilizando O Método De Lattice-Boltzmann

TORQUATO¹

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Torquato, Mariana Luisa de Lima; Carvalho, Márcio da Silveira (Advisor). Emulsion flow through constricted capillary using Lattice-Boltzmann method. Rio de Janeiro, 2015. 133p. Msc. Dissertation -Departamento de Engenharia Mecânica, Pontifícia Universidade Católica do Rio de Janeiro.Emulsion injection in porous medium as an Enhanced Oil Recovery method can turn out to be reality in the operation of onshore and offshore fields, due to increasing rigidity in the disposal of produced water and also due to the potential additional oil production. In order to understand macroscopic behavior of this EOR method, it is necessary to understand the microscopic phenomenon. With this objective, it was performed the numerical modeling of the flow of a droplet immerse in continuous phase through a constricted capillary using the LatticeBoltzmann method. This method was chosen due to its simplicity on being applied to complex rock geometries and multiphasic flow and due to its good commitment in representing microscopic phenomena. Focusing on understanding the influence of each parameter on flow behavior, several simulation studies were performed altering flow velocity, viscosity ratio, ratio between droplet´s and pipe´s diameter and interfacial tension. A reduction in mobility is observed as the droplet passes through the restriction caused by the conjunction of viscous and capillary effects. A negative correlation of mobility reduction factor in relation to the viscosity ratio and to droplet size was noticed, as it had been observed before by Roca-Reyes (2011) in a numerical implementation of level-set method.

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Lattice-Boltzmann equations for describing segregation in non-ideal mixtures

Cited by 15 publications

References 32 publications

Molecular dynamics study of multicomponent droplet dissolution in a sparingly miscible liquid

Molecular dynamics study of multicomponent droplet dissolution in a sparingly miscible liquid

Consistent lattice Boltzmann equations for phase transitions

Escoamento De Emulsões Através De Capilares Com Garganta Utilizando O Método De Lattice-Boltzmann

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