Benchmarking of three-dimensional multicomponent lattice Boltzmann equation

Xu, Xu; Burgin, Kallum; Ellis, M.M.; Halliday, Ian

doi:10.1103/physreve.96.053308

Cited by 9 publications

(23 citation statements)

References 26 publications

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“…Ba et al derived an equivalent scheme based upon a multiple-relaxation-time LB variant, after Lallemand and Luo [24]. One could also derive schemes based upon inverse multiple-relaxation-time LB variants [25,26]. However, all would contain equivalent evolution equation source terms, i.e., those independent of F β in Eq.…”

Section: A Lattice Boltzmann Bhatnagar-gross-krook Scheme For Large mentioning

confidence: 99%

Kinematics of chromodynamic multicomponent lattice Boltzmann simulation with a large density contrast

Burgin

Spendlove

et al. 2019

Phys. Rev. E

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The utility of an enhanced chromodynamic, color gradient or phase-field multicomponent lattice Boltzmann (MCLB) equation for immiscible fluids with a density difference was demonstrated by Wen et al. [Phys. Rev. E 100, 023301 (2019)] and Ba et al. [Phys. Rev. E 94, 023310 (2016)], who advanced earlier work by Liu et al. [Phys. Rev. E 85, 046309 (2012)] by removing certain error terms in the momentum equations. But while these models' collision scheme has been carefully enhanced by degrees, there is, currently, no quantitative consideration in the macroscopic dynamics of the segregation scheme which is common to all. Here, by analysis of the kinetic-scale segregation rule (previously neglected when considering the continuum behavior) we derive, bound, and test the emergent kinematics of the continuum fluids' interface for this class of MCLB, concurrently demonstrating the circular relationship with-and competition between-the models' dynamics and kinematics. The analytical and numerical results we present in Sec. V confirm that, at the kinetic scale, for a range of density contrast, color is a material invariant. That is, within numerical error, the emergent interface structure is isotropic (i.e., without orientation dependence) and Galilean-invariant (i.e., without dependence on direction of motion). Numerical data further suggest that reported restrictions on the achievable density contrast in rapid flow, using chromodynamic MCLB, originate in the effect on the model's kinematics of the terms deriving from our term F 1i in the evolution equation, which correct its dynamics for large density differences. Taken with Ba's applications and validations, this result significantly enhances the theoretical foundation of this MCLB variant, bringing it somewhat belatedly further into line with the schemes of Inamuro et al. [J. Comput. Phys. 198, 628 (2004)] and the free-energy scheme [see, e.g., Phys. Rev. E. 76, 045702(R) (2007), and references therein] which, in contradistinction to the present scheme and perhaps wisely, postulate appropriate kinematics a priori.

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Section: A Lattice Boltzmann Bhatnagar-gross-krook Scheme For Large mentioning

confidence: 99%

Kinematics of chromodynamic multicomponent lattice Boltzmann simulation with a large density contrast

Burgin

Spendlove

et al. 2019

Phys. Rev. E

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“…This model also inherits the assumption from Einstein's work that there is a very low concentration of particles/droplets. Taylor's model, like Einstein's, is exact when the assumptions are met and is shown to be accurate in its target regime (low Reynolds and Capillary numbers) [3], however this is of limited applicability in real emulsion systems; droplets are likely to get deformed and/or concentrated emulsions may be required.…”

Section: Emulsion Modelsmentioning

confidence: 99%

“…where τ s and τ a are the symmetric and anti-symmetric parts of the relaxation parameter. τ s is now linked to viscosity as ν = c 2 s 2 (2τ s − 1) and τ a is calculated from τ s as τ a = 0.5 + Λ τs−0.5 where Λ = 3 16 . This two-relaxation-times (TRT) method has other advantages over LBGK too, such as improving the accuracy and stability of the method at small or large viscosities.…”

Section: Lattice-boltzmannmentioning

confidence: 99%

“…A three-dimensional equivalent to this model has been compared [3] with the Taylor-Einstein equation shown in (2.6). The agreement with the exact theoretical equation is excellent over a moderate range of viscosity ratio.…”

Section: Multi-componentmentioning

confidence: 99%

“…s − 1 , whilst the overall τ s and τ a are some function of the fluid relaxation parameters τ (k) s and τ (k) a (see Section 3.3). The anti-symmetric relaxation parameter can be calculated from the symmetric part as τ a = 0.5 + Λ τs−0.5 where Λ = 3 16 . The magic parameter, Λ , is chosen to provide an exact position for solid walls [97], though other choices are possible [98].…”

Section: Eilbm For Multiple Immiscible Fluids With a Trt Collision Stepmentioning

confidence: 99%

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Development of explicit and constitutive lattice-Boltzmann models for food product rheology

Burgin¹

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Emulsions are found throughout various industries including oil extraction, biological materials, and food products such as milk, condiments, and spreads. The study of their rheology is therefore important due to its impact on manufacturing efficiency and end product desirability. A key rheological measure is the emulsion viscosity, the fluid's resistance to flow, which affects the power required in production as well as the taste and texture. An emulsion's viscosity displays complex behaviour due to the droplet interfaces and interactions. Similarly, the sheared self-diffusion coefficient measures the amount of movement the droplets exhibit, due to the interactions between droplets. The presented mesoscopic lattice-Boltzmann models allow for these macroscopic properties to emerge from the simulations due to the explicit modelling of the droplets. A continuous surface force is applied to the lattice fluids to model droplet interfaces. The model is implemented in such a way as to allow the simulation of hundreds of droplets with limited computing power. The model is initially applied to a pipe flow, with the development of a pressure boundary condition. Boundary effects from the solid walls require their removal, using Lees-Edwards boundary conditions to represent bulk flow in a sheared system. The boundary conditions are extended to the multi-component flow, which allowed simulations to provide results for various emulsion systems with varying droplet concentrations, surface tensions, viscosity ratios, and shear rates. Trends and results from experimental and theoretical literature are recovered and constitutive models of emulsion viscosity have been evaluated. The agreement of these two dimensional lattice-Boltzmann models with three dimensional experimental results shows the usefulness of the method. The structure of the droplets and clustering behaviour they exhibit are examined and compared to solid particle suspension literature. Finally, the model is used in exploratory simulations to examine the effect of droplet bidispersity on the macroscopic properties; the witnessed effect agrees well with solid suspension literature. This mesoscopic model will allow for phenomenon on this scale to be more easily studied and may provide more accurate information for multi-scale analysis.

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Three-dimensional single framework multicomponent lattice Boltzmann equation method for vesicle hydrodynamics

Spendlove

Schenkel

et al. 2021

Physics of Fluids

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Benchmarking of three-dimensional multicomponent lattice Boltzmann equation

Cited by 9 publications

References 26 publications

Kinematics of chromodynamic multicomponent lattice Boltzmann simulation with a large density contrast

Kinematics of chromodynamic multicomponent lattice Boltzmann simulation with a large density contrast

Development of explicit and constitutive lattice-Boltzmann models for food product rheology

Three-dimensional single framework multicomponent lattice Boltzmann equation method for vesicle hydrodynamics

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