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Bao J, Guo Z. Phase-field lattice Boltzmann model with singular mobility for quasi-incompressible two-phase flows. Phys Rev E 2024; 109:025302. [PMID: 38491598 DOI: 10.1103/physreve.109.025302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2023] [Accepted: 01/05/2024] [Indexed: 03/18/2024]
Abstract
In this paper, a lattice Boltzmann for quasi-incompressible two-phase flows is proposed based on the Cahn-Hilliard phase-field theory, which can be viewed as an improved model of a previous one [Yang and Guo, Phys. Rev. E 93, 043303 (2016)2470-004510.1103/PhysRevE.93.043303]. The model is composed of two LBE's, one for the Cahn-Hilliard equation (CHE) with a singular mobility, and the other for the quasi-incompressible Navier-Stokes equations (qINSE). Particularly, the LBE for the CHE uses an equilibrium distribution function containing a free parameter associated with the gradient of chemical potential, such that the variable (and even zero) mobility can be handled. In addition, the LBE for the qINSE uses an equilibrium distribution function containing another free parameter associated with the local shear rate, such that the large viscosity ratio problems can be handled. Several tests are first carried out to test the capability of the proposed LBE for the CHE in capturing phase interface, and the results demonstrate that the proposed model outperforms the original LBE model in terms of accuracy and stability. Furthermore, by coupling the hydrodynamic equations, the tests of double-stationary droplets and droplets falling problems indicate that the proposed model can reduce numerical dissipation and produce physically acceptable results at large time scales. The results of droplets falling and phase separation of binary fluid problems show that the present model can handle two-phase flows with large viscosity ratio up to the magnitude of 10^{4}.
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Affiliation(s)
- Jin Bao
- State Key Laboratory of Coal Combustion, School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Zhaoli Guo
- Institute of Interdisciplinary Research for Mathematics and Applied Science, Huazhong University of Science and Technology, Wuhan 430074, China
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2
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Zhang C, Liang H, Guo Z, Wang LP. Discrete unified gas-kinetic scheme for the conservative Allen-Cahn equation. Phys Rev E 2022; 105:045317. [PMID: 35590655 DOI: 10.1103/physreve.105.045317] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2021] [Accepted: 04/07/2022] [Indexed: 06/15/2023]
Abstract
In this paper, two discrete unified gas-kinetic scheme (DUGKS) methods with piecewise-parabolic flux reconstruction are presented for the conservative Allen-Cahn equation (CACE). One includes a temporal derivative of the order parameter in the force term while the other does not include temporal derivative in the force term but results in a modified CACE with additional terms. In the context of DUGKS, the continuum equations recovered from the piecewise-linear and piecewise-parabolic reconstructions for the fluxes at cell faces are subsequently derived. It is proved that the resulting equation with the piecewise-linear reconstruction is a first-order approximation to the discrete velocity kinetic equation due to the presence of the force term and the nonconservation property of the momentum of the collision model. To guarantee second-order accuracy of DUGKS, the piecewise-parabolic reconstruction for numerical flux is proposed. To validate the accuracy of the present DUGKS with the proposed flux evaluation, several benchmark problems, including the diagonal translation of a circular interface, the rotation of a Zalesak disk and the deformation of a circular interface, have been simulated. Numerical results show that the accuracy of both proposed DUGKS methods is almost comparable and improved compared with the DUGKS with linear flux reconstruction scheme.
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Affiliation(s)
- Chunhua Zhang
- Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China
| | - Hong Liang
- Department of Physics, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Zhaoli Guo
- State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Lian-Ping Wang
- Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China
- Center for Complex Flows and Soft Matter Research, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China
- Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China
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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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Ruiz-Gutiérrez É, Edwards AMJ, McHale G, Newton MI, Wells GG, Brown CV, Ledesma-Aguilar R. Lattice Boltzmann Simulations of Multiphase Dielectric Fluids. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2021; 37:7328-7340. [PMID: 34101471 DOI: 10.1021/acs.langmuir.1c00606] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The dynamic effect of an electric field on dielectric liquids is called liquid dielectrophoresis. It is widely used in several industrial and scientific applications, including inkjet printing, microfabrication, and optical devices. Numerical simulations of liquid-dielectrophoresis are necessary to understand the fundamental physics of the phenomenon, but also to explore situations that might be difficult or expensive to implement experimentally. However, such modeling is challenging, as one needs to solve the electrostatic and fluid dynamics equations simultaneously. Here, we formulate a new lattice-Boltzmann method capable of modeling the dynamics of immiscible dielectric fluids coupled with electric fields within a single framework, thus eliminating the need of using separate algorithms to solve the electrostatic and fluid dynamics equations. We validate the numerical method by comparing it with analytical solutions and previously reported experimental results. Beyond the benchmarking of the method, we study the spreading of a droplet using a dielectrowetting setup and quantify the mechanism driving the variation of the apparent contact angle of the droplet with the applied voltage. Our method provides a useful tool to study liquid-dielectrophoresis and can be used to model dielectric fluids in general, such as liquid-liquid and liquid-gas systems.
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Affiliation(s)
- Élfego Ruiz-Gutiérrez
- Institute for Multiscale Thermofluids, School of Engineering, University of Edinburgh, The King's Buildings, Mayfield Road, Edinburgh EH9 3FB, U.K
| | - Andrew M J Edwards
- SOFT Group, School of Science and Technology, Nottingham Trent University, Clifton Lane, Nottingham NG11 8NS, U.K
| | - Glen McHale
- Institute for Multiscale Thermofluids, School of Engineering, University of Edinburgh, The King's Buildings, Mayfield Road, Edinburgh EH9 3FB, U.K
| | - Michael I Newton
- SOFT Group, School of Science and Technology, Nottingham Trent University, Clifton Lane, Nottingham NG11 8NS, U.K
| | - Gary G Wells
- Institute for Multiscale Thermofluids, School of Engineering, University of Edinburgh, The King's Buildings, Mayfield Road, Edinburgh EH9 3FB, U.K
| | - Carl V Brown
- SOFT Group, School of Science and Technology, Nottingham Trent University, Clifton Lane, Nottingham NG11 8NS, U.K
| | - Rodrigo Ledesma-Aguilar
- Institute for Multiscale Thermofluids, School of Engineering, University of Edinburgh, The King's Buildings, Mayfield Road, Edinburgh EH9 3FB, U.K
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Zhang C, Guo Z. Spontaneous shrinkage of droplet on a wetting surface in the phase-field model. Phys Rev E 2019; 100:061302. [PMID: 31962399 DOI: 10.1103/physreve.100.061302] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2019] [Indexed: 06/10/2023]
Abstract
Phase-field theory is widely used to model multiphase flow. The fact that a drop can shrink or grow spontaneously due to the redistribution of interface and bulk energies to minimize the system energy may produce ill effects on the simulation. In this Rapid Communication, the spontaneous behavior of a drop on a partially wetting surface is investigated. It is found that there exists a critical radius dependent on the contact angle, the domain size, and the interface width, below which the drop will eventually disappear. In particular, the critical radius can be very large when the surface becomes very hydrophilic. The theoretical prediction of the critical radius is verified numerically by simulating a drop on a surface with various contact angles, the domain sizes, and the interface widths.
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Affiliation(s)
- Chunhua Zhang
- State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Zhaoli Guo
- State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074, China
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