1
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Ju L, Guo Z, Yan B, Sun S. Implementation of contact line motion based on the phase-field lattice Boltzmann method. Phys Rev E 2024; 109:045307. [PMID: 38755877 DOI: 10.1103/physreve.109.045307] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2023] [Accepted: 03/27/2024] [Indexed: 05/18/2024]
Abstract
This paper proposes a strategy to implement the free-energy-based wetting boundary condition within the phase-field lattice Boltzmann method. The greatest advantage of the proposed method is that the implementation of contact line motion can be significantly simplified while still maintaining good accuracy. For this purpose, the liquid-solid free energy is treated as a part of the chemical potential instead of the boundary condition, thus avoiding complicated interpolations with irregular geometries. Several numerical testing cases, including droplet spreading processes on the idea flat, inclined, and curved boundaries, are conducted, and the results demonstrate that the proposed method has good ability and satisfactory accuracy to simulate contact line motions.
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Affiliation(s)
- Long Ju
- Computational Transport Phenomena Laboratory (CTPL), King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Kingdom of Saudi Arabia
| | - Zhaoli Guo
- Institute of Interdisciplinary Research for Mathematics and Applied Science, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Bicheng Yan
- Energy Resource and Petroleum Engineering Program, Physical Science and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Kingdom of Saudi Arabia
| | - Shuyu Sun
- Computational Transport Phenomena Laboratory (CTPL), King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Kingdom of Saudi Arabia
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2
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Silva DPF, Coelho RCV, Pagonabarraga I, Succi S, Telo da Gama MM, Araújo NAM. Lattice Boltzmann simulation of deformable fluid-filled bodies: progress and perspectives. SOFT MATTER 2024; 20:2419-2441. [PMID: 38420837 PMCID: PMC10933750 DOI: 10.1039/d3sm01648j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2023] [Accepted: 02/20/2024] [Indexed: 03/02/2024]
Abstract
With the rapid development of studies involving droplet microfluidics, drug delivery, cell detection, and microparticle synthesis, among others, many scientists have invested significant efforts to model the flow of these fluid-filled bodies. Motivated by the intricate coupling between hydrodynamics and the interactions of fluid-filled bodies, several methods have been developed. The objective of this review is to present a compact foundation of the methods used in the literature in the context of lattice Boltzmann methods. For hydrodynamics, we focus on the lattice Boltzmann method due to its specific ability to treat time- and spatial-dependent boundary conditions and to incorporate new physical models in a computationally efficient way. We split the existing methods into two groups with regard to the interfacial boundary: fluid-structure and fluid-fluid methods. The fluid-structure methods are characterised by the coupling between fluid dynamics and mechanics of the flowing body, often used in applications involving membranes and similar flexible solid boundaries. We further divide fluid-structure-based methods into two subcategories, those which treat the fluid-structure boundary as a continuum medium and those that treat it as a discrete collection of individual springs and particles. Next, we discuss the fluid-fluid methods, particularly useful for the simulations of fluid-fluid interfaces. We focus on models for immiscible droplets and their interaction in a suspending fluid and describe benchmark tests to validate the models for fluid-filled bodies.
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Affiliation(s)
- Danilo P F Silva
- Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal.
- Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal
| | - Rodrigo C V Coelho
- Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal.
- Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal
| | - Ignacio Pagonabarraga
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Carrer de Martí Franqués 1, 08028 Barcelona, Spain
- Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, 08028 Barcelona, Spain
| | - Sauro Succi
- Center for Life Nano Science at La Sapienza, Istituto Italiano di Tecnologia, 295 Viale Regina Elena, I/00161 Roma, Italy
- Harvard Institute for Applied Computational Science, Cambridge, MA 02138, USA
| | - Margarida M Telo da Gama
- Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal.
- Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal
| | - Nuno A M Araújo
- Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal.
- Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal
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3
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Haghani R, Erfani H, McClure JE, Flekkøy EG, Berg CF. Color-gradient-based phase-field equation for multiphase flow. Phys Rev E 2024; 109:035301. [PMID: 38632731 DOI: 10.1103/physreve.109.035301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2023] [Accepted: 01/22/2024] [Indexed: 04/19/2024]
Abstract
In this paper, the underlying problem with the color-gradient (CG) method in handling density-contrast fluids is explored. It is shown that the CG method is not fluid invariant. Based on nondimensionalizing the CG method, a phase-field interface-capturing model is proposed which tackles the difficulty of handling density-contrast fluids. The proposed formulation is developed for incompressible, immiscible two-fluid flows without phase-change phenomena, and a solver based on the lattice Boltzmann method is proposed. Coupled with an available robust hydrodynamic solver, a binary fluid flow package that handles fluid flows with high density and viscosity contrasts is presented. The macroscopic and lattice Boltzmann equivalents of the formulation, which make the physical interpretation of it easier, are presented. In contrast to existing color-gradient models where the interface-capturing equations are coupled with the hydrodynamic ones and include the surface tension forces, the proposed formulation is in the same spirit as the other phase-field models such as the Cahn-Hilliard and the Allen-Cahn equations and is solely employed to capture the interface advected due to a flow velocity. As such, similarly to other phase-field models, a so-called mobility parameter comes into play. In contrast, the mobility is not related to the density field but a constant coefficient. This leads to a formulation that avoids individual speed of sound for the different fluids. On the lattice Boltzmann solver side, two separate distribution functions are adopted to solve the formulation, and another one is employed to solve the Navier-Stokes equations, yielding a total of three equations. Two series of numerical tests are conducted to validate the accuracy and stability of the model, where we compare simulated results with available analytical and numerical solutions, and good agreement is observed. In the first set the interfacial evolution equations are assessed, while in the second set the hydrodynamic effects are taken into account.
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Affiliation(s)
- Reza Haghani
- PoreLab, Department of Geoscience and Petroleum, Norwegian University of Science and Technology (NTNU), 7031 Trondheim, Norway
| | - Hamidreza Erfani
- PoreLab, Department of Geoscience and Petroleum, Norwegian University of Science and Technology (NTNU), 7031 Trondheim, Norway
| | - James E McClure
- National Security Institute, Virginia Tech, RB1311 Research Center Drive, Blacksburg, Virginia 24061, USA
| | - Eirik Grude Flekkøy
- PoreLab, the Njord Center, Department of Physics, University of Oslo, 0371 Oslo, Norway
| | - Carl Fredrik Berg
- PoreLab, Department of Geoscience and Petroleum, Norwegian University of Science and Technology (NTNU), 7031 Trondheim, Norway
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4
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Saito S, Takada N, Baba S, Someya S, Ito H. Generalized equilibria for color-gradient lattice Boltzmann model based on higher-order Hermite polynomials: A simplified implementation with central moments. Phys Rev E 2023; 108:065305. [PMID: 38243429 DOI: 10.1103/physreve.108.065305] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2023] [Accepted: 11/19/2023] [Indexed: 01/21/2024]
Abstract
We propose generalized equilibria of a three-dimensional color-gradient lattice Boltzmann model for two-component two-phase flows using higher-order Hermite polynomials. Although the resulting equilibrium distribution function, which includes a sixth-order term on the velocity, is computationally cumbersome, its equilibrium central moments (CMs) are velocity-independent and have a simplified form. Numerical experiments show that our approach, as in Wen et al. [Phys. Rev. E 100, 023301 (2019)2470-004510.1103/PhysRevE.100.023301] who consider terms up to third order, improves the Galilean invariance compared to that of the conventional approach. Dynamic problems can be solved with high accuracy at a density ratio of 10; however, the accuracy is still limited to a density ratio of 1000. For lower density ratios, the generalized equilibria benefit from the CM-based multiple-relaxation-time model, especially at very high Reynolds numbers, significantly improving the numerical stability.
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Affiliation(s)
- Shimpei Saito
- Research Institute for Energy Conservation (iECO), National Institute of Advanced Industrial Science and Technology (AIST), 1-2-1 Namiki, Tsukuba 3058564, Japan
| | - Naoki Takada
- Research Institute for Energy Conservation (iECO), National Institute of Advanced Industrial Science and Technology (AIST), 1-2-1 Namiki, Tsukuba 3058564, Japan
| | - Soumei Baba
- Research Institute for Energy Conservation (iECO), National Institute of Advanced Industrial Science and Technology (AIST), 1-2-1 Namiki, Tsukuba 3058564, Japan
| | - Satoshi Someya
- Research Institute for Energy Conservation (iECO), National Institute of Advanced Industrial Science and Technology (AIST), 1-2-1 Namiki, Tsukuba 3058564, Japan
| | - Hiroshi Ito
- Research Institute for Energy Conservation (iECO), National Institute of Advanced Industrial Science and Technology (AIST), 1-2-1 Namiki, Tsukuba 3058564, Japan
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5
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Wang D, Liu F, Sun J, Li Y, Wang Q, Jiao Y, Song K, Wang S, Ma R. Lattice-Boltzmann simulation of Two-phase Flow in Carbonate Porous Media retrieved from Computed Microtomography. Chem Eng Sci 2023. [DOI: 10.1016/j.ces.2023.118514] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
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6
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Lu J, Adams NA, Yu P. Analysis and reconstruction of the multiphase lattice Boltzmann flux solver for multiphase flows with large density ratios. Phys Rev E 2022; 106:045305. [PMID: 36397589 DOI: 10.1103/physreve.106.045305] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2022] [Accepted: 09/27/2022] [Indexed: 06/16/2023]
Abstract
The multiphase lattice Boltzmann flux solver (MLBFS) has been proposed to tackle complex geometries with nonuniform meshes. It also has been proven to have good numerical stability for multiphase flows with large density ratios. However, the reason for the good numerical stability of MLBFS at large density ratios has not been well established. The present paper reveals the relation between MLBFS and the macroscopic weakly compressible multiphase model by recovering the macroscopic equations of MLBFS (MEs-MLBFS) with actual numerical dissipation terms. By directly solving MEs-MLBFS, the reconstructed MLBFS (RMLBFS) that involves only macroscopic variables in the computational processes is proposed. The analysis of RMLBFS indicates that by combining the predictor step, the corrector step of MLBFS introduces some numerical dissipation terms which contribute to the good numerical stability of MLBFS. By retaining these numerical dissipation terms, RMLBFS can maintain the numerical stability of MLBFS even at large density ratios.
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Affiliation(s)
- Jinhua Lu
- Department of Mechanical Engineering, Chair of Aerodynamics and Fluid Mechanics, Technical University of Munich, Boltzmannstraße 15, Garching 85748, Germany and Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Nikolaus A Adams
- Department of Mechanical Engineering, Chair of Aerodynamics and Fluid Mechanics, Technical University of Munich, Boltzmannstraße 15, Garching 85748, Germany and Munich Institute of Integrated Materials, Energy and Process Engineering, Technical University of Munich, Lichtenbergstr. 4a, Garching 85748, Germany
| | - Peng Yu
- Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, China
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7
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Subhedar A. Color-gradient lattice Boltzmann model for immiscible fluids with density contrast. Phys Rev E 2022; 106:045308. [PMID: 36397459 DOI: 10.1103/physreve.106.045308] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2021] [Accepted: 08/30/2022] [Indexed: 06/16/2023]
Abstract
We present a color-gradient-based lattice Boltzmann model for immiscible fluids with a large density contrast. The model employs the velocity-based equilibrium distribution function, initially proposed for the phase-field-based model by Zu and He [Phys. Rev. E 87, 043301 (2013)1539-375510.1103/PhysRevE.87.043301], with a modification necessary to satisfy the kinematic condition at the interface. Different from the existing color-gradient models, the present model allows to specify interface mobility that is independent of the fluid density ratio. Further, we provide a unified framework, which uses the recursive representation of the lattice Boltzmann equation, to derive the governing equations of the system. The emergent color dynamics thus obtained, through an analysis of the segregation operator, is shown to obey the locally conservative Allen-Cahn equation. We use a series of benchmarks, which include a stationary drop, a layered Poiseuille flow, translation of a drop under a forced velocity field, the Rayleigh-Taylor instability, and the capillary intrusion test to demonstrate the model's ability in dealing with complex flow problems.
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Affiliation(s)
- A Subhedar
- Department of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
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8
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Kang DH, Yun TS. Local hybrid Allen-Cahn model in phase-field lattice Boltzmann method for incompressible two-phase flow. Phys Rev E 2022; 105:045307. [PMID: 35590596 DOI: 10.1103/physreve.105.045307] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2021] [Accepted: 03/19/2022] [Indexed: 06/15/2023]
Abstract
For simulating incompressible two-phase fluid flows, several phase-field lattice Boltzmann (LB) methods based on the local Allen-Cahn (AC) equation have been intensively proposed in recent years. We present a local hybrid AC model for the phase-field LB method. In the proposed model, the local and nonlocal AC equations are linearly combined using a local weight assigned in the interface or bulk phase regions individually. Five numerical problems, namely diagonal translation, Zalesak's disk rotation, static bubble, two bubbles of different radii, and Rayleigh-Taylor instability, are simulated for validation. The numerical results agree well with the analytical solutions or available previous results. Additionally, the numerical dispersion and the coarsening phenomenon are considerably suppressed in the proposed model. Finally, the performance of the proposed model is validated by conducting a drainage simulation in porous media and compared with the global hybrid AC model.
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Affiliation(s)
- Dong Hun Kang
- School of Civil and Environmental Engineering, Yonsei University, Seoul 03722, Korea
| | - Tae Sup Yun
- School of Civil and Environmental Engineering, Yonsei University, Seoul 03722, Korea
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9
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Zhang X, Zhang J, Liu H, Jia P. Rayleigh-Plateau Instability of a Particle-Laden Liquid Column: A Lattice Boltzmann Study. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2022; 38:3453-3468. [PMID: 35274953 DOI: 10.1021/acs.langmuir.1c03262] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Colloidal particles known to be capable of stabilizing fluid-fluid interfaces have been widely applied in emulsion preparation, but their precise role and underlying influencing mechanism remain poorly understood. In this study, a perturbed liquid column with particles evenly distributed on its surface is investigated using a three-dimensional lattice Boltzmann method, which is built upon the color-gradient two-phase flow model but with a new capillary force model and a momentum exchange method for particle dynamics. The developed method is first validated by simulating the wetting behavior of a particle on a fluid interface and the classic Rayleigh-Plateau instability and is then used to explore the effects of particle concentration and contact angle on the capillary instability of the particle-laden liquid column. It is found that increasing the particle concentration can enhance the stability of the liquid column and thus delay the breakup, and the liquid column is most stable under slightly hydrophobic conditions, which corresponds to the lowest initial liquid-gas interfacial free energy. Due to different pressure gradients inside and outside the liquid column and the capillary force being directed away from the neck, hydrophobic particles tend to assemble in a less compact manner near the neck of the deformed liquid column, while hydrophilic particles prefer to gather far away from the neck. For hydrophobic particles, in addition to the influence of the initial liquid-gas interfacial free energy, the self-assembly of particles in a direction opposite to the liquid flow also contributes to opposing the rupture of the liquid column.
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Affiliation(s)
- Xitong Zhang
- School of Energy and Power Engineering, Xi'an Jiaotong University, 28 West Xianning Road, Xi'an 710049, China
| | - Jiangang Zhang
- School of Energy and Power Engineering, Xi'an Jiaotong University, 28 West Xianning Road, Xi'an 710049, China
| | - Haihu Liu
- School of Energy and Power Engineering, Xi'an Jiaotong University, 28 West Xianning Road, Xi'an 710049, China
| | - Pan Jia
- School of Science, Harbin Institute of Technology, Shenzhen University Town, Xili, Nanshan District, Shenzhen 518055, China
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10
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Zhang S, Tang J, Wu H. Phase-field lattice Boltzmann model for two-phase flows with large density ratio. Phys Rev E 2022; 105:015304. [PMID: 35193185 DOI: 10.1103/physreve.105.015304] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2021] [Accepted: 12/07/2021] [Indexed: 06/14/2023]
Abstract
In this work, a lattice Boltzmann (LB) model based on the phase-field method is proposed for simulating large density ratio two-phase flows. An improved multiple-relaxation-time (MRT) LB equation is first developed to solve the conserved Allen-Cahn (AC) equation. By utilizing a nondiagonal relaxation matrix and modifying the equilibrium distribution function and discrete source term, the conserved AC equation can be correctly recovered by the proposed MRT LB equation with no deviation term. Therefore, the calculations of the temporal derivative term in the previous LB models are successfully avoided. Numerical tests demonstrate that satisfactory accuracy can be achieved by the present model to solve the conserved AC equation. What is more, the discrete force term of the MRT LB equation for the incompressible Navier-Stokes equations is also simplified and modified in the present work. An alternative scheme to calculate the gradient terms of the order parameter involved in the discrete force term through the nonequilibrium part of the distribution function is also developed. To validate the ability of the present LB model for simulating large density ratio two-phase flows, series of benchmarks, including two-phase Poiseuille flow, droplet impacting on thin liquid film, and planar Taylor bubble are simulated. It is found that the results predicted by the present LB model agree well with the analytical, numerical, and experimental results.
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Affiliation(s)
- Shengyuan Zhang
- School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Jun Tang
- School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Huiying Wu
- School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
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11
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An X, Dong B, Wang Y, Zhang Y, Zhou X, Li W. Coupled lattice Boltzmann-large eddy simulation model for three-dimensional multiphase flows at large density ratio and high Reynolds number. Phys Rev E 2021; 104:045305. [PMID: 34781498 DOI: 10.1103/physreve.104.045305] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2021] [Accepted: 09/19/2021] [Indexed: 11/07/2022]
Abstract
A coupled lattice Boltzmann-large eddy simulation model is developed for modeling three-dimensional multiphase flows at large density ratios and high Reynolds numbers. In the framework of the lattice Boltzmann method, the model is proposed based on the standard Smagorinsky subgrid-scale approach, and a reconstructed multiple-relaxation-time collision operator is adopted. The conservative Allen-Cahn equation and Navier-Stokes equations are solved through the lattice Boltzmann discretization scheme for the interface tracking and velocity field evolution, respectively. Relevant benchmark cases are carried out to validate the performance of this model in simulating multiphase flows at a large density ratio and a high Reynolds number, including a stationary droplet, the process of spinodal decomposition, the Rayleigh-Taylor instability, the phenomenon of a droplet splashing on a thin liquid film, and the liquid jet breakup process. The maximum values of density ratio and Re number are 1000 and 10 240, respectively. The capability and reliability of the proposed model have been demonstrated by the good agreement between simulation results and the analytical solutions or the previously available results.
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Affiliation(s)
- Xiang An
- Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, School of Energy and Power Engineering, Dalian University of Technology, Dalian 116024, People's Republic of China
| | - Bo Dong
- Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, School of Energy and Power Engineering, Dalian University of Technology, Dalian 116024, People's Republic of China
| | - Yong Wang
- Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, School of Energy and Power Engineering, Dalian University of Technology, Dalian 116024, People's Republic of China
| | - Yajin Zhang
- Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, School of Energy and Power Engineering, Dalian University of Technology, Dalian 116024, People's Republic of China
| | - Xun Zhou
- Institute of Refrigeration and Air Conditioning Technology, Henan University of Science and Technology, Luoyang 471003, People's Republic of China
| | - Weizhong Li
- Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, School of Energy and Power Engineering, Dalian University of Technology, Dalian 116024, People's Republic of China
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12
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Xu X, Hu Y, Dai B, Yang L, Han J, He Y, Zhu J. Modified phase-field-based lattice Boltzmann model for incompressible multiphase flows. Phys Rev E 2021; 104:035305. [PMID: 34654078 DOI: 10.1103/physreve.104.035305] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2020] [Accepted: 09/02/2021] [Indexed: 11/07/2022]
Abstract
Based on the phase-field theory, a multiple-relaxation-time (MRT) lattice Boltzmann model is proposed for the immiscible multiphase fluids. In this model, the local Allen-Chan equation is chosen as the target equation to capture the phase interface. Unlike previous MRT schemes, an off-diagonal relaxation matrix is adopted in the present model so that the target phase-field equation can be recovered exactly without any artificial terms. To check the necessity of removing those artificial terms, comparative studies were carried out among different MRT schemes with or without correction. Results show that the artificial terms can be neglected at low March number but will cause unphysical diffusion or interface undulation instability for the relatively large March number cases. The present modified model shows superiority in reducing numerical errors by adjusting the free parameters. As the interface transport coupled to the fluid flow, a pressure-evolution lattice Boltzmann equation is adopted for hydrodynamic properties. Several benchmark cases for multiphase flow were conducted to test the validity of the present model, including the static drop test, Rayleigh-Taylor instability, and single rising bubble test. For the rising bubble simulation at high density ratios, bubble dynamics obtained by the present modified MRT lattice Boltzmann model agree well with those obtained by the FEM-based level set and FEM-based phase-field models.
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Affiliation(s)
- Xingchun Xu
- National Key Laboratory of Science and Technology on Advanced Composites in Special Environments, Harbin Institute of Technology, Harbin 150080, China
| | - Yanwei Hu
- School of Energy Science & Engineering, Harbin Institute of Technology, Harbin 150001, China
| | - Bing Dai
- National Key Laboratory of Science and Technology on Advanced Composites in Special Environments, Harbin Institute of Technology, Harbin 150080, China
| | - Lei Yang
- National Key Laboratory of Science and Technology on Advanced Composites in Special Environments, Harbin Institute of Technology, Harbin 150080, China
| | - Jiecai Han
- National Key Laboratory of Science and Technology on Advanced Composites in Special Environments, Harbin Institute of Technology, Harbin 150080, China
| | - Yurong He
- School of Energy Science & Engineering, Harbin Institute of Technology, Harbin 150001, China
| | - Jiaqi Zhu
- National Key Laboratory of Science and Technology on Advanced Composites in Special Environments, Harbin Institute of Technology, Harbin 150080, China.,Key Laboratory of Micro-systems and Micro-structures Manufacturing, Ministry of Education, Harbin 150080, China
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13
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Li S, Lu Y, Jiang F, Liu H. Lattice Boltzmann simulation of three-phase flows with moving contact lines on curved surfaces. Phys Rev E 2021; 104:015310. [PMID: 34412346 DOI: 10.1103/physreve.104.015310] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2020] [Accepted: 06/13/2021] [Indexed: 11/07/2022]
Abstract
A numerical method for simulating three-phase flows with moving contact lines on arbitrarily complex surfaces is developed in the framework of the lattice Boltzmann method. In this method, the immiscible three-phase flow is modeled through a multiple-relaxation-time color-gradient model, which not only allows for a full range of interfacial tensions but also produces stable outcomes for a wide range of viscosity ratios. A characteristic line model is introduced to implement the wetting boundary condition, which is not only easy to implement but is also able to handle arbitrarily complex boundaries with prescribed contact angles. The developed method is first validated by the simulation of a Janus droplet resting on a flat surface, a perfect Janus droplet deposited on a cylinder, and the capillary intrusion of ternary fluids for various viscosity ratios. It is then used to study a compound droplet subject to a uniform incoming flow passing through a multipillar structure, where three different values of surface wettability are considered. The simulated results show that the surface wettability has significant impact on the droplet dynamic behavior and final fluid distribution.
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Affiliation(s)
- Sheng Li
- School of Energy and Power Engineering, Xi'an Jiaotong University, 28 West Xianning Road, Xi'an 710049, China
| | - Yang Lu
- School of Energy and Power Engineering, Xi'an Jiaotong University, 28 West Xianning Road, Xi'an 710049, China
| | - Fei Jiang
- Department of Mechanical Engineering and Blue Energy Center for SGE Technology (BEST), Yamaguchi University, Ube 7558611, Japan and International Institute for Carbon-Neutral Energy Research (WPI-I2CNER), Kyushu University, Fukuoka 8190395, Japan
| | - Haihu Liu
- School of Energy and Power Engineering, Xi'an Jiaotong University, 28 West Xianning Road, Xi'an 710049, China
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14
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Huang J, Xiao F, Labra C, Sun J, Yin X. DEM-LBM simulation of stress-dependent absolute and relative permeabilities in porous media. Chem Eng Sci 2021. [DOI: 10.1016/j.ces.2021.116633] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
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15
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Li W, Liu D, Desbrun M, Huang J, Liu X. Kinetic-Based Multiphase Flow Simulation. IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 2021; 27:3318-3334. [PMID: 32054580 DOI: 10.1109/tvcg.2020.2972357] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Multiphase flows exhibit a large realm of complex behaviors such as bubbling, glugging, wetting, and splashing which emerge from air-water and water-solid interactions. Current fluid solvers in graphics have demonstrated remarkable success in reproducing each of these visual effects, but none have offered a model general enough to capture all of them concurrently. In contrast, computational fluid dynamics have developed very general approaches to multiphase flows, typically based on kinetic models. Yet, in both communities, there is dearth of methods that can simulate density ratios and Reynolds numbers required for the type of challenging real-life simulations that movie productions strive to digitally create, such as air-water flows. In this article, we propose a kinetic model of the coupling of the Navier-Stokes equations with a conservative phase-field equation, and provide a series of numerical improvements over existing kinetic-based approaches to offer a general multiphase flow solver. The resulting algorithm is embarrassingly parallel, conservative, far more stable than current solvers even for real-life conditions, and general enough to capture the typical multiphase flow behaviors. Various simulation results are presented, including comparisons to both previous work and real footage, to highlight the advantages of our new method.
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Liu T, Wang M. Critical REV Size of Multiphase Flow in Porous Media for Upscaling by Pore-Scale Modeling. Transp Porous Media 2021. [DOI: 10.1007/s11242-021-01621-2] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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17
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Li Q, Yu Y, Huang RZ. Achieving thermodynamic consistency in a class of free-energy multiphase lattice Boltzmann models. Phys Rev E 2021; 103:013304. [PMID: 33601620 DOI: 10.1103/physreve.103.013304] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2020] [Accepted: 12/18/2020] [Indexed: 06/12/2023]
Abstract
The free-energy lattice Boltzmann (LB) model is one of the major multiphase models in the LB community. The present study is focused on a class of free-energy LB models in which the divergence of thermodynamic pressure tensor or its equivalent form expressed by the chemical potential is incorporated into the LB equation via a forcing term. Although this class of free-energy LB models may be thermodynamically consistent at the continuum level, it suffers from thermodynamic inconsistency at the discrete lattice level owing to numerical errors [Guo et al., Phys. Rev. E 83, 036707 (2010)10.1103/PhysRevE.83.036707]. The numerical error term mainly includes two parts: one comes from the discrete gradient operator and the other can be identified in a high-order Chapman-Enskog analysis. In this paper, we propose an improved scheme to eliminate the thermodynamic inconsistency of the aforementioned class of free-energy LB models. The improved scheme is constructed by modifying the equation of state of the standard LB equation, through which the discretization of ∇(ρc_{s}^{2}) is no longer involved in the force calculation and then the numerical errors can be significantly reduced. Numerical simulations are subsequently performed to validate the proposed scheme. The numerical results show that the improved scheme is capable of eliminating the thermodynamic inconsistency and can significantly reduce the spurious currents in comparison with the standard forcing-based free-energy LB model.
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Affiliation(s)
- Q Li
- School of Energy Science and Engineering, Central South University, Changsha 410083, China
| | - Y Yu
- School of Energy Science and Engineering, Central South University, Changsha 410083, China
| | - R Z Huang
- School of Energy Science and Engineering, Central South University, Changsha 410083, China
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18
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Spendlove J, Xu X, Halliday OJ, Schenkel T, Halliday I. Chromodynamic multirelaxation-time lattice Boltzmann scheme for fluids with density difference. Phys Rev E 2020; 102:013309. [PMID: 32794994 DOI: 10.1103/physreve.102.013309] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2019] [Accepted: 05/29/2020] [Indexed: 11/07/2022]
Abstract
We develop, after Dellar [Phys. Rev. E. 65, 036309 (2002)10.1103/PhysRevE.65.036309; J. Comput. Phys. 190, 351 (2003)10.1016/S0021-9991(03)00279-1], a multiple-relaxation-time (MRT), chromodynamic, multicomponent lattice Boltzmann equation (MCLBE) scheme for simulation of isothermal, immiscible fluid flow with a density contrast. It is based on Lishchuk's method [Brackbill, Kothe, and Zemach, J. Comp. Phys. 100, 335 (1992)10.1016/0021-9991(92)90240-Y; Lishchuk, Care, and Halliday, Phys. Rev. E. 67, 036701, (2003)10.1103/PhysRevE.76.036701] and the segregation of d'Ortona et al. [Phys. Rev. E. 51, 3718, (1995)10.1103/PhysRevE.51.3718]. We focus on fundamental model verifiability but do relate some of our data to that from previous approaches, due to Ba et al. [Phys. Rev. E 94, 023310 (2016)10.1103/PhysRevE.94.023310] and earlier Liu et al. [Phys. Rev. E 85, 046309 (2012)10.1103/PhysRevE.85.046309], who pioneered large density difference chromodynamic MCLBE and showed the practical benefits of an MRT collision model. Specifically, we test the extent to which chromodynamic MCLBE MRT schemes comply with the kinematic condition of mutual impenetrability and the continuous traction condition by developing analytical benchmarking flows. We conclude that our data, taken with those of Ba et al., verify the utility of MRT chromodynamic MCLBE.
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Affiliation(s)
- J Spendlove
- Materials & Engineering Research Institute, Sheffield Hallam University, Howard Street, Sheffield S1 1WB, United Kingdom
| | - X Xu
- Materials & Engineering Research Institute, Sheffield Hallam University, Howard Street, Sheffield S1 1WB, United Kingdom.,Department of Engineering and Mathematics, Sheffield Hallam University, Howard Street, Sheffield S1 1WB, United Kingdom
| | - O J Halliday
- National Centre for Atmospheric Science, Department of Meteorology, University of Reading, Reading RG6 6AH, United Kingdom
| | - T Schenkel
- Materials & Engineering Research Institute, Sheffield Hallam University, Howard Street, Sheffield S1 1WB, United Kingdom.,Department of Engineering and Mathematics, Sheffield Hallam University, Howard Street, Sheffield S1 1WB, United Kingdom
| | - I Halliday
- Materials & Engineering Research Institute, Sheffield Hallam University, Howard Street, Sheffield S1 1WB, United Kingdom
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19
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Wen B, Zhao L, Qiu W, Ye Y, Shan X. Chemical-potential multiphase lattice Boltzmann method with superlarge density ratios. Phys Rev E 2020; 102:013303. [PMID: 32794892 DOI: 10.1103/physreve.102.013303] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2019] [Accepted: 06/17/2020] [Indexed: 11/07/2022]
Abstract
The liquid-gas density ratio is a key property of multiphase flow methods to model real fluid systems. Here, a chemical-potential multiphase lattice Boltzmann method is constructed to realize extremely large density ratios. The simulations show that the method reaches very low temperatures, at which the liquid-gas density ratio is more than 10^{14}, while the thermodynamic consistency is still preserved. Decoupling the mesh space from the momentum space through a proportional coefficient, a smaller mesh step provides denser lattice nodes to exactly describe the transition region and the resulting dimensional transformation has no loss of accuracy. A compact finite-difference method is applied to calculate the discrete derivatives in the mesh space with high-order accuracy. These enhance the computational accuracy of the nonideal force and suppress the spurious currents to a very low level, even if the density ratio is up to tens of thousands. The simulation of drop splashing verifies that the present model is Galilean invariant for the dynamic flow field. An upper limit of the chemical potential is used to reduce the influence of nonphysical factors and improve the stability.
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Affiliation(s)
- Binghai Wen
- Guangxi Key Lab of Multi-Source Information Mining & Security, Guangxi Normal University, Guilin 541004, China
| | - Liang Zhao
- College of Physical Science and Technology, Yangzhou University, Jiangsu 225009, China
| | - Wen Qiu
- Guangxi Key Lab of Multi-Source Information Mining & Security, Guangxi Normal University, Guilin 541004, China
| | - Yong Ye
- Guangxi Key Lab of Multi-Source Information Mining & Security, Guangxi Normal University, Guilin 541004, China
| | - Xiaowen Shan
- Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, China
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20
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Suo S, Liu M, Gan Y. An LBM-PNM framework for immiscible flow: With applications to droplet spreading on porous surfaces. Chem Eng Sci 2020. [DOI: 10.1016/j.ces.2020.115577] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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21
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Subhedar A, Reiter A, Selzer M, Varnik F, Nestler B. Interface tracking characteristics of color-gradient lattice Boltzmann model for immiscible fluids. Phys Rev E 2020; 101:013313. [PMID: 32069649 DOI: 10.1103/physreve.101.013313] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2019] [Indexed: 06/10/2023]
Abstract
We study the interface tracking characteristics of a color-gradient-based lattice Boltzmann model for immiscible flows. Investigation of the local density change in one of the fluid phases, via a Taylor series expansion of the recursive lattice Boltzmann equation, leads to the evolution equation of the order parameter that differentiates the fluids. It turns out that this interface evolution follows a conservative Allen-Cahn equation with a mobility which is independent of the fluid viscosities and surface tension. The mobility of the interface, which solely depends upon lattice speed of sound, can have a crucial effect on the physical dynamics of the interface. Further, we find that, when the equivalent lattice weights inside the segregation operator are modified, the resulting differential operators have a discretization error that is anisotropic to the leading order. As a consequence, the discretization errors in the segregation operator, which ensures a finite interface width, can act as a source of the spurious currents. These findings are supported with the help of numerical simulations.
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Affiliation(s)
- A Subhedar
- Institute for Digital Materials Science, Karlsruhe University of Applied Sciences, Moltkestraße 30, 76133 Karlsruhe, Germany
| | - A Reiter
- Institute for Digital Materials Science, Karlsruhe University of Applied Sciences, Moltkestraße 30, 76133 Karlsruhe, Germany
| | - M Selzer
- Institute for Digital Materials Science, Karlsruhe University of Applied Sciences, Moltkestraße 30, 76133 Karlsruhe, Germany
- Institute of Applied Materials-Computational Materials Science, Karlsruhe Institute of Technology, Straße am Forum 7, 76131 Karlsruhe, Germany
| | - F Varnik
- Interdisciplinary Centre for Advanced Materials Simulation, Ruhr-Universität Bochum, Universitätsstrasse 150, 44780 Bochum, Germany
| | - B Nestler
- Institute for Digital Materials Science, Karlsruhe University of Applied Sciences, Moltkestraße 30, 76133 Karlsruhe, Germany
- Institute of Applied Materials-Computational Materials Science, Karlsruhe Institute of Technology, Straße am Forum 7, 76131 Karlsruhe, Germany
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22
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Leclaire S, Vidal D, Fradette L, Bertrand F. Validation of the pressure drop–flow rate relationship predicted by lattice Boltzmann simulations for immiscible liquid–liquid flows through SMX static mixers. Chem Eng Res Des 2020. [DOI: 10.1016/j.cherd.2019.10.035] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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23
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Pore-scale study of the effects of surface roughness on relative permeability of rock fractures using lattice Boltzmann method. Chem Eng Sci 2019. [DOI: 10.1016/j.ces.2019.115178] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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24
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Burgin K, Spendlove J, Xu X, Halliday I. Kinematics of chromodynamic multicomponent lattice Boltzmann simulation with a large density contrast. Phys Rev E 2019; 100:043310. [PMID: 31770993 DOI: 10.1103/physreve.100.043310] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2019] [Indexed: 06/10/2023]
Abstract
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)2470-004510.1103/PhysRevE.100.023301] and Ba et al. [Phys. Rev. E 94, 023310 (2016)2470-004510.1103/PhysRevE.94.023310], who advanced earlier work by Liu et al. [Phys. Rev. E 85, 046309 (2012)PLEEE81539-375510.1103/PhysRevE.85.046309] 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)JCTPAH0021-999110.1016/j.jcp.2004.01.019] and the free-energy scheme [see, e.g., Phys. Rev. E. 76, 045702(R) (2007)10.1103/PhysRevE.76.045702, and references therein] which, in contradistinction to the present scheme and perhaps wisely, postulate appropriate kinematics a priori.
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Affiliation(s)
- K Burgin
- Materials & Engineering Research Institute, Sheffield Hallam University, Howard Street, S1 1WB, United Kingdom
| | - J Spendlove
- Materials & Engineering Research Institute, Sheffield Hallam University, Howard Street, S1 1WB, United Kingdom
| | - X Xu
- Materials & Engineering Research Institute, Sheffield Hallam University, Howard Street, S1 1WB, United Kingdom
- Department of Engineering and Mathematics, Sheffield Hallam University, Howard Street, S1 1WB, United Kingdom
| | - I Halliday
- Materials & Engineering Research Institute, Sheffield Hallam University, Howard Street, S1 1WB, United Kingdom
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25
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Wen ZX, Li Q, Yu Y, Luo KH. Improved three-dimensional color-gradient lattice Boltzmann model for immiscible two-phase flows. Phys Rev E 2019; 100:023301. [PMID: 31574674 DOI: 10.1103/physreve.100.023301] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2019] [Indexed: 06/10/2023]
Abstract
In this paper, an improved three-dimensional color-gradient lattice Boltzmann (LB) model is proposed for simulating immiscible two-phase flows. Compared with the previous three-dimensional color-gradient LB models, which suffer from the lack of Galilean invariance and considerable numerical errors in many cases owing to the error terms in the recovered macroscopic equations, the present model eliminates the error terms and therefore improves the numerical accuracy and enhances the Galilean invariance. To validate the proposed model, numerical simulations are performed. First, the test of a moving droplet in a uniform flow field is employed to verify the Galilean invariance of the improved model. Subsequently, numerical simulations are carried out for the layered two-phase flow and three-dimensional Rayleigh-Taylor instability. It is shown that, using the improved model, the numerical accuracy can be significantly improved in comparison with the color-gradient LB model without the improvements. Finally, the capability of the improved color-gradient LB model for simulating dynamic two-phase flows at a relatively large density ratio is demonstrated via the simulation of droplet impact on a solid surface.
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Affiliation(s)
- Z X Wen
- School of Energy Science and Engineering, Central South University, Changsha 410083, China
| | - Q Li
- School of Energy Science and Engineering, Central South University, Changsha 410083, China
| | - Y Yu
- School of Energy Science and Engineering, Central South University, Changsha 410083, China
| | - Kai H Luo
- Department of Mechanical Engineering, University College London, Torrington Place, London WC1E 7JE, United Kingdom
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26
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Yang Z, Zhong C, Zhuo C. Phase-field method based on discrete unified gas-kinetic scheme for large-density-ratio two-phase flows. Phys Rev E 2019; 99:043302. [PMID: 31108650 DOI: 10.1103/physreve.99.043302] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2018] [Indexed: 11/07/2022]
Abstract
In this paper, a phase-field method under the framework of discrete unified gas-kinetic scheme (DUGKS) for incompressible multiphase fluid flows is proposed. Two kinetic models are constructed to solve the conservative Allen-Cahn equation that accounts for the interface behavior and the incompressible hydrodynamic equations that govern the flow field, respectively. With a truncated equilibrium distribution function as well as a temporal derivative added to the source term, the macroscopic governing equations can be exactly recovered from the kinetic models through the Chapman-Enskog analysis. Calculation of source terms involving high-order derivatives existed in the quasi-incompressible model is simplified. A series of benchmark cases including four interface-capturing tests and four binary flow tests are carried out. Results compared to that of the lattice Boltzmann method (LBM) have been obtained. A convergence rate of second order can be guaranteed in the test of interface diagonal translation. The capability of the present method to track the interface that undergoes a severe deformation has been verified. Stationary bubble and spinodal decomposition problems, both with a density ratio as high as 1000, are conducted and reliable solutions have been provided. The layered Poiseuille flow with a large viscosity ratio is simulated and numerical results agree well with the analytical solutions. Variation of positions of the bubble front and spike tip during the evolution of Rayleigh-Taylor instability has been predicted precisely. However, the detailed depiction of complicated interface patterns appearing during the evolution process is failed, which is mainly caused by the relatively large numerical dissipation of DUGKS compared to that of LBM. A high-order DUGKS is needed to overcome this problem.
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Affiliation(s)
- Zeren Yang
- National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China
| | - Chengwen Zhong
- National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China
| | - Congshan Zhuo
- National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China
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27
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Xu M, Liu H. Prediction of immiscible two-phase flow properties in a two-dimensional Berea sandstone using the pore-scale lattice Boltzmann simulation. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2018; 41:124. [PMID: 30324324 DOI: 10.1140/epje/i2018-11735-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2018] [Accepted: 09/17/2018] [Indexed: 06/08/2023]
Abstract
Immiscible two-phase flow in porous media is commonly encountered in industrial processes and environmental issues, such as enhanced oil recovery and the migration of fluids in an unsaturated zone. To deepen the current understanding of its underlying mechanism, this work focuses on the factors that influence the relative permeability and specific interfacial length of a two-phase flow in porous media, i.e., fluid saturation, viscosity ratio and contact angle. The lattice Boltzmann color-gradient model is adopted for pore-scale investigations, and the main findings are obtained as follows. Firstly, the relative permeability of each fluid increases as its saturation increases. The specific interfacial length first increases and then decreases as the saturation of the wetting fluid increases, and reaches a maximum when the permeabilities of both fluids are equal. Secondly, as the viscosity ratio of wetting to non-wetting fluids increases, the relative permeability of the wetting fluid will increase while that of the non-wetting fluid will decrease. The specific interfacial length will increase with increasing the viscosity difference between fluids. Finally, as the contact angle (measured from the wetting fluid) increases, the relative permeability of the wetting fluid overall increases while that of the non-wetting fluid decreases. Increasing contact angle always leads to a decrease in the specific interfacial length.
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Affiliation(s)
- Meng Xu
- School of Energy and Power Engineering, Xi'an Jiaotong University, 28 West Xianning Road, 710049, Xi'an, China
| | - Haihu Liu
- School of Energy and Power Engineering, Xi'an Jiaotong University, 28 West Xianning Road, 710049, Xi'an, China.
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28
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Nazari M, Sani HM, Kayhani MH, Daghighi Y. DIFFERENT STAGES OF LIQUID FILM GROWTH IN A MICROCHANNEL: TWO-PHASE LATTICE BOLTZMANN STUDY. BRAZILIAN JOURNAL OF CHEMICAL ENGINEERING 2018. [DOI: 10.1590/0104-6632.20180353s20160700] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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29
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Saito S, De Rosis A, Festuccia A, Kaneko A, Abe Y, Koyama K. Color-gradient lattice Boltzmann model with nonorthogonal central moments: Hydrodynamic melt-jet breakup simulations. Phys Rev E 2018; 98:013305. [PMID: 30110870 DOI: 10.1103/physreve.98.013305] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2018] [Indexed: 06/08/2023]
Abstract
We develop a lattice Boltzmann (LB) model for immiscible two-phase flow simulations with central moments (CMs). This successfully combines a three-dimensional nonorthogonal CM-based LB scheme [De Rosis, Phys. Rev. E 95, 013310 (2017)2470-004510.1103/PhysRevE.95.013310] with our previous color-gradient LB model [Saito, Abe, and Koyama, Phys. Rev. E 96, 013317 (2017)2470-004510.1103/PhysRevE.96.013317]. Hydrodynamic melt-jet breakup simulations show that the proposed model is significantly more stable, even for flow with extremely high Reynolds numbers, up to O(10^{6}). This enables us to investigate the phenomena expected under actual reactor conditions.
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Affiliation(s)
| | | | | | | | - Yutaka Abe
- University of Tsukuba, Tsukuba 305-8573, Japan
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30
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Liang H, Xu J, Chen J, Wang H, Chai Z, Shi B. Phase-field-based lattice Boltzmann modeling of large-density-ratio two-phase flows. Phys Rev E 2018; 97:033309. [PMID: 29776082 DOI: 10.1103/physreve.97.033309] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2017] [Indexed: 06/08/2023]
Abstract
In this paper, we present a simple and accurate lattice Boltzmann (LB) model for immiscible two-phase flows, which is able to deal with large density contrasts. This model utilizes two LB equations, one of which is used to solve the conservative Allen-Cahn equation, and the other is adopted to solve the incompressible Navier-Stokes equations. A forcing distribution function is elaborately designed in the LB equation for the Navier-Stokes equations, which make it much simpler than the existing LB models. In addition, the proposed model can achieve superior numerical accuracy compared with previous Allen-Cahn type of LB models. Several benchmark two-phase problems, including static droplet, layered Poiseuille flow, and spinodal decomposition are simulated to validate the present LB model. It is found that the present model can achieve relatively small spurious velocity in the LB community, and the obtained numerical results also show good agreement with the analytical solutions or some available results. Lastly, we use the present model to investigate the droplet impact on a thin liquid film with a large density ratio of 1000 and the Reynolds number ranging from 20 to 500. The fascinating phenomena of droplet splashing is successfully reproduced by the present model and the numerically predicted spreading radius exhibits to obey the power law reported in the literature.
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Affiliation(s)
- Hong Liang
- Department of Physics, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Jiangrong Xu
- Department of Physics, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Jiangxing Chen
- Department of Physics, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Huili Wang
- School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Zhenhua Chai
- School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
- Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Baochang Shi
- School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
- Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China
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31
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Cheng Z, Ba Y, Sun J, Wang C, Cai S, Fu X. A numerical study of droplet dynamic behaviors on a micro-structured surface using a three dimensional color-gradient lattice Boltzmann model. SOFT MATTER 2018; 14:837-847. [PMID: 29308826 DOI: 10.1039/c7sm02078c] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Inspired by the experimental work of Raj et al. (high-resolution liquid patterns via three-dimensional droplet shape control), in the present study, a three-dimensional multiphase color-gradient lattice Boltzmann model developed previously by some of the authors is used to simulate droplet dynamic behaviors with different surface micro-pillar arrays. To facilitate the present simulation, wetting boundary conditions are used and the accuracy of color gradient prediction at boundary nodes is enhanced. The experimental findings are confirmed and non-circular contact lines are reproduced numerically for the first time. To justify the existing contact angle formula proposed based on the Wenzel model, a systematic parametric study is conducted, based on which the pillar density is redefined to allow for the influence of pillar height, and then it is used to modify the contact angle. In addition, the evolution of the contact line motion for various droplet shapes is investigated systematically, and both circular and non-circular contact characteristics are well-depicted for different surface micro-pillar arrays.
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Affiliation(s)
- Zihao Cheng
- School of Energy and Power Engineering, Xi'an Jiaotong University, 28 West Xianning Road, Xi'an, 710049, China.
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32
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Fakhari A, Mitchell T, Leonardi C, Bolster D. Improved locality of the phase-field lattice-Boltzmann model for immiscible fluids at high density ratios. Phys Rev E 2017; 96:053301. [PMID: 29347689 DOI: 10.1103/physreve.96.053301] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2017] [Indexed: 06/07/2023]
Abstract
Based on phase-field theory, we introduce a robust lattice-Boltzmann equation for modeling immiscible multiphase flows at large density and viscosity contrasts. Our approach is built by modifying the method proposed by Zu and He [Phys. Rev. E 87, 043301 (2013)PLEEE81539-375510.1103/PhysRevE.87.043301] in such a way as to improve efficiency and numerical stability. In particular, we employ a different interface-tracking equation based on the so-called conservative phase-field model, a simplified equilibrium distribution that decouples pressure and velocity calculations, and a local scheme based on the hydrodynamic distribution functions for calculation of the stress tensor. In addition to two distribution functions for interface tracking and recovery of hydrodynamic properties, the only nonlocal variable in the proposed model is the phase field. Moreover, within our framework there is no need to use biased or mixed difference stencils for numerical stability and accuracy at high density ratios. This not only simplifies the implementation and efficiency of the model, but also leads to a model that is better suited to parallel implementation on distributed-memory machines. Several benchmark cases are considered to assess the efficacy of the proposed model, including the layered Poiseuille flow in a rectangular channel, Rayleigh-Taylor instability, and the rise of a Taylor bubble in a duct. The numerical results are in good agreement with available numerical and experimental data.
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Affiliation(s)
- Abbas Fakhari
- Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, Indiana 46556, USA
- Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Pennsylvania 19104, USA
| | - Travis Mitchell
- School of Mechanical and Mining Engineering, The University of Queensland, St Lucia, QLD 4072, Australia
| | - Christopher Leonardi
- School of Mechanical and Mining Engineering, The University of Queensland, St Lucia, QLD 4072, Australia
| | - Diogo Bolster
- Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, Indiana 46556, USA
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33
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Saito S, Abe Y, Koyama K. Lattice Boltzmann modeling and simulation of liquid jet breakup. Phys Rev E 2017; 96:013317. [PMID: 29347180 DOI: 10.1103/physreve.96.013317] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2017] [Indexed: 06/07/2023]
Abstract
A three-dimensional color-fluid lattice Boltzmann model for immiscible two-phase flows is developed in the framework of a three-dimensional 27-velocity (D3Q27) lattice. The collision operator comprises the D3Q27 versions of three suboperators: a multiple-relaxation-time (MRT) collision operator, a generalized Liu-Valocchi-Kang perturbation operator, and a Latva-Kokko-Rothman recoloring operator. A D3Q27 version of an enhanced equilibrium distribution function is also incorporated into this model to improve the Galilean invariance. Three types of numerical tests, namely, a static droplet, an oscillating droplet, and the Rayleigh-Taylor instability, show a good agreement with analytical solutions and numerical simulations. Following these numerical tests, this model is applied to liquid-jet-breakup simulations. The simulation conditions are matched to the conditions of the previous experiments. In this case, numerical stability is maintained throughout the simulation, although the kinematic viscosity for the continuous phase is set as low as 1.8×10^{-4}, in which case the corresponding Reynolds number is 3.4×10^{3}; the developed lattice Boltzmann model based on the D3Q27 lattice enables us to perform the simulation with parameters directly matched to the experiments. The jet's liquid column transitions from an asymmetrical to an axisymmetrical shape, and entrainment occurs from the side of the jet. The measured time history of the jet's leading-edge position shows a good agreement with the experiments. Finally, the reproducibility of the regime map for liquid-liquid systems is assessed. The present lattice Boltzmann simulations well reproduce the characteristics of predicted regimes, including varicose breakup, sinuous breakup, and atomization.
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Affiliation(s)
- Shimpei Saito
- Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba 305-8573, Japan
| | - Yutaka Abe
- Faculty of Engineering, Information and Systems, University of Tsukuba, Tsukuba 305-8573, Japan
| | - Kazuya Koyama
- Reactor Core and Safety Design Department, Mitsubishi FBR Systems, Inc., Shibuya, Tokyo 150-0001, Japan
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Leclaire S, Parmigiani A, Malaspinas O, Chopard B, Latt J. Generalized three-dimensional lattice Boltzmann color-gradient method for immiscible two-phase pore-scale imbibition and drainage in porous media. Phys Rev E 2017; 95:033306. [PMID: 28415302 DOI: 10.1103/physreve.95.033306] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2016] [Indexed: 05/24/2023]
Abstract
This article presents a three-dimensional numerical framework for the simulation of fluid-fluid immiscible compounds in complex geometries, based on the multiple-relaxation-time lattice Boltzmann method to model the fluid dynamics and the color-gradient approach to model multicomponent flow interaction. New lattice weights for the lattices D3Q15, D3Q19, and D3Q27 that improve the Galilean invariance of the color-gradient model as well as for modeling the interfacial tension are derived and provided in the Appendix. The presented method proposes in particular an approach to model the interaction between the fluid compound and the solid, and to maintain a precise contact angle between the two-component interface and the wall. Contrarily to previous approaches proposed in the literature, this method yields accurate solutions even in complex geometries and does not suffer from numerical artifacts like nonphysical mass transfer along the solid wall, which is crucial for modeling imbibition-type problems. The article also proposes an approach to model inflow and outflow boundaries with the color-gradient method by generalizing the regularized boundary conditions. The numerical framework is first validated for three-dimensional (3D) stationary state (Jurin's law) and time-dependent (Washburn's law and capillary waves) problems. Then, the usefulness of the method for practical problems of pore-scale flow imbibition and drainage in porous media is demonstrated. Through the simulation of nonwetting displacement in two-dimensional random porous media networks, we show that the model properly reproduces three main invasion regimes (stable displacement, capillary fingering, and viscous fingering) as well as the saturating zone transition between these regimes. Finally, the ability to simulate immiscible two-component flow imbibition and drainage is validated, with excellent results, by numerical simulations in a Berea sandstone, a frequently used benchmark case used in this field, using a complex geometry that originates from a 3D scan of a porous sandstone. The methods presented in this article were implemented in the open-source PALABOS library, a general C++ matrix-based library well adapted for massive fluid flow parallel computation.
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Affiliation(s)
- Sébastien Leclaire
- Department of Computer Science, University of Geneva, 7 route de Drize, 1227 Carouge, Switzerland and Department of Chemical Engineering, Polytechnique Montréal, 2500, chemin de Polytechnique, Montreal, H3T 1J4, Canada
| | - Andrea Parmigiani
- Department of Earth Sciences, Institute of Geochemistry and Petrology, ETH Zurich, Clausiusstrasse 25, 8092 Zürich, Switzerland
| | - Orestis Malaspinas
- Department of Computer Science, University of Geneva, 7 route de Drize, 1227 Carouge, Switzerland
| | - Bastien Chopard
- Department of Computer Science, University of Geneva, 7 route de Drize, 1227 Carouge, Switzerland
| | - Jonas Latt
- Department of Computer Science, University of Geneva, 7 route de Drize, 1227 Carouge, Switzerland and FlowKit Sàrl, Route d'Oron 2, 1010 Lausanne, Switzerland
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