Study of phase-field lattice Boltzmann models based on the conservative Allen-Cahn equation

Begmohammadi, Amirhosein; Haghani-Hassan-Abadi, Reza; Fakhari, Abbas; Bolster, Diogo

doi:10.1103/physreve.102.023305

Cited by 17 publications

(2 citation statements)

References 45 publications

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“…The Allen–Cahn equation can be discretized using techniques from traditional computational fluid dynamics (CFD) such as finite-volume and finite-element methods. However, for the present work the mesoscale approach based on the lattice-Boltzmann method (LBM) is more appropriate [ 58 – 60 ]. In the last two decades the lattice Boltzmann method has emerged as a computationally efficient alternative to traditional CFD techniques, mainly due to the capability of handling multi-physics problems involving soft-matter and fluid flow and the relative ease of parallel implementation [ 58 , 59 , 61 ].…”

Section: Problem Setup and Numerical Methodologymentioning

confidence: 99%

Instability of a liquid sheet with viscosity contrast in inertial microfluidics

Patel

Stark

2021

Eur. Phys. J. E

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Flows at moderate Reynolds numbers in inertial microfluidics enable high throughput and inertial focusing of particles and cells with relevance in biomedical applications. In the present work, we consider a viscosity-stratified three-layer flow in the inertial regime. We investigate the interfacial instability of a liquid sheet surrounded by a density-matched but more viscous fluid in a channel flow. We use linear stability analysis based on the Orr–Sommerfeld equation and direct numerical simulations with the lattice Boltzmann method (LBM) to perform an extensive parameter study. Our aim is to contribute to a controlled droplet production in inertial microfluidics. In the first part, on the linear stability analysis we show that the growth rate of the fastest growing mode $$\xi ^{*}$$ ξ ∗ increases with the Reynolds number $$\text {Re}$$ Re and that its wavelength $$\lambda ^{*}$$ λ ∗ is always smaller than the channel width w for sufficiently small interfacial tension $$\Gamma $$ Γ . For thin sheets we find the scaling relation $$\xi ^{*} \propto mt^{2.5}_{s}$$ ξ ∗ ∝ m t s 2.5 , where m is viscosity ratio and $$t_{s}$$ t s the sheet thickness. In contrast, for thicker sheets $$\xi ^{*}$$ ξ ∗ decreases with increasing $$t_s$$ t s or m due to the nearby channel walls. Examining the eigenvalue spectra, we identify Yih modes at the interface. In the second part on the LBM simulations, the thin liquid sheet develops two distinct dynamic states: waves traveling along the interface and breakup into droplets with bullet shape. For smaller flow rates and larger sheet thicknesses, we also observe ligament formation and the sheet eventually evolves irregularly. Our work gives some indication how droplet formation can be controlled with a suitable parameter set $$\{\lambda ,t_{s},m,\Gamma ,\text {Re}\}$$ { λ , t s , m , Γ , Re } . Graphical Abstract

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Section: Problem Setup and Numerical Methodologymentioning

confidence: 99%

Instability of a liquid sheet with viscosity contrast in inertial microfluidics

Patel

Stark

2021

Eur. Phys. J. E

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“…Similarly, Wang et al [25] used the time-derivative term to remove the additional terms and offered an alternative algorithm to calculate the gradient of the order parameter using the nonequilibrium part of the distribution function. Recently, Begmohammadi et al [26] conducted a comparative investigation on the differences among the above LBE models and showed the additional terms can be negligible in the limit of low Mach numbers. More recently, Zu et al [27] proposed a modified LBE version in which the difference of equilibrium distribution function is added to correctly recover the local conservative ACE.…”

Section: Introductionmentioning

confidence: 99%

Discrete unified gas kinetic scheme for the conservative Allen-Cahn equation

Zhang¹,

Liu²,

Guo³

et al. 2022

Preprint

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In this paper, the discrete unified gas kinetic scheme (DUGKS) with an improved microflux across the cell interface for the conservative Allen-Cahn equation (CACE) is proposed. In the context of DUGKS, the recovered kinetic equation from the flux evaluation with linear reconstruction in the previous DUGKS is analyzed. It is found that the calculated microflux across the cell interface is only the solution to the target kinetic equation with first order accuracy, which can result in an inaccurate CACE since the force term is involved or the first moment of the collision model has no conservation property. To correctly recover the kinetic equation up to the second order accuracy, the value of the distribution function that will propagate along the characteristic line with ending point at the cell interface is appropriated by the parabolic reconstruction instead of the linear reconstruction. To validate the accuracy of the present DUGKS for the CACE, several benchmark problems, including the diagonal translation of a circular interface, the rotation of a Zaleska disk and the deformation of a circular interface, have been simulated. Numerical results show that the present DUGKS scheme is able to capture the interface with improved accuracy when compared with the previous DUGKS.

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Efficient and structure-preserving time-dependent auxiliary variable method for a conservative Allen–Cahn type surfactant system

Yang

Kim

2022

Engineering with Computers

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Study of phase-field lattice Boltzmann models based on the conservative Allen-Cahn equation

Cited by 17 publications

References 45 publications

Instability of a liquid sheet with viscosity contrast in inertial microfluidics

Instability of a liquid sheet with viscosity contrast in inertial microfluidics

Discrete unified gas kinetic scheme for the conservative Allen-Cahn equation

Efficient and structure-preserving time-dependent auxiliary variable method for a conservative Allen–Cahn type surfactant system

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