1
|
Luo K, Zhang Y, Wu J, Yi HL, Tan HP. Lattice Boltzmann modeling of two-phase electrohydrodynamic flows under unipolar charge injection. Phys Rev E 2022; 105:065304. [PMID: 35854602 DOI: 10.1103/physreve.105.065304] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2022] [Accepted: 06/01/2022] [Indexed: 06/15/2023]
Abstract
In this work, a two-dimensional droplet confined between two parallel electrodes under the combined effects of a nonuniform electric field and unipolar charge injection is numerically investigated using the lattice Boltzmann method (LBM). Under the non-Ohmic regime, the interfacial tension and electric forces at the droplet surface cooperate with the volumetric Coulomb force, leading to complex deformation and motion of the droplet while at the same time inducing a bulk electroconvective flow. After we validate the model by comparing with analytical solutions at the hydrostatic state, we perform a quantitative analysis on the droplet deformation factor D and bulk flow stability criteria T_{c} under different parameters, including the electric capillary number Ca, the electric Rayleigh number T, the permittivity ratio ɛ_{r}, and the mobility ratio K_{r}. It is found that the bulk flow significantly modifies the magnitude of D, which in turn decreases T_{c} of the electroconvective flow. For a droplet repelled by the anode, ɛ_{r}>1, an interesting linear relationship can be observed in the D-Ca curves. However, for a droplet attracted to the anode, ɛ_{r}<1, the system is potentially unstable. After first evolving into a quasisteady state, the droplet successively experiences steady flow, periodic flow, second steady flow, and oscillatory flow with increasing T. Moreover, discontinuities can be observed in the D-T curves due to the transitions of bulk flow.
Collapse
Affiliation(s)
- Kang Luo
- School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150 001, People's Republic of China and Key Laboratory of Aerospace Thermophysics, Harbin Institute of Technology, Harbin 150 001, People's Republic of China
| | - Yu Zhang
- School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150 001, People's Republic of China and Key Laboratory of Aerospace Thermophysics, Harbin Institute of Technology, Harbin 150 001, People's Republic of China
| | - Jian Wu
- School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150 001, People's Republic of China and Key Laboratory of Aerospace Thermophysics, Harbin Institute of Technology, Harbin 150 001, People's Republic of China
| | - Hong-Liang Yi
- School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150 001, People's Republic of China and Key Laboratory of Aerospace Thermophysics, Harbin Institute of Technology, Harbin 150 001, People's Republic of China
| | - He-Ping Tan
- School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150 001, People's Republic of China and Key Laboratory of Aerospace Thermophysics, Harbin Institute of Technology, Harbin 150 001, People's Republic of China
| |
Collapse
|
2
|
Yue L, Chai Z, Wang H, Shi B. Improved phase-field-based lattice Boltzmann method for thermocapillary flow. Phys Rev E 2022; 105:015314. [PMID: 35193195 DOI: 10.1103/physreve.105.015314] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2021] [Accepted: 01/06/2022] [Indexed: 06/14/2023]
Abstract
In this paper, we present an improved phase-field-based lattice Boltzmann (LB) method for thermocapillary flows with large density, viscosity, and thermal conductivity ratios. The present method uses three LB models to solve the conservative Allen-Cahn equation, the incompressible Navier-Stokes equations, and the temperature equation. To overcome the difficulty caused by the convection term in solving the convection-diffusion equation for the temperature field, we first rewrite the temperature equation as a diffuse equation where the convection term is regarded as the source term and then construct an improved LB model for the diffusion equation. The macroscopic governing equations can be recovered correctly from the present LB method; moreover, the present LB method is much simpler and more efficient. In order to test the accuracy of this LB method, several numerical examples are considered, including the planar thermal Poiseuille flow of two immiscible fluids, the two-phase thermocapillary flow in a nonuniformly heated channel, and the thermocapillary Marangoni flow of a deformable bubble. It is found that the numerical results obtained from the present LB method are consistent with the theoretical prediction and available numerical data, which indicates that the present LB method is an effective approach for the thermocapillary flows.
Collapse
Affiliation(s)
- Liqing Yue
- 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
| | - Huili Wang
- School of Mathematical and Computer Sciences, Wuhan Textile University, 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
| |
Collapse
|
3
|
Li D, Lai H, Lin C. Mesoscopic Simulation of the Two-Component System of Coupled Sine-Gordon Equations with Lattice Boltzmann Method. ENTROPY (BASEL, SWITZERLAND) 2019; 21:E542. [PMID: 33267256 PMCID: PMC7515031 DOI: 10.3390/e21060542] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/29/2019] [Revised: 05/22/2019] [Accepted: 05/25/2019] [Indexed: 02/01/2023]
Abstract
In this paper, a new lattice Boltzmann model for the two-component system of coupled sine-Gordon equations is presented by using the coupled mesoscopic Boltzmann equations. Via the Chapman-Enskog multiscale expansion, the macroscopical governing evolution system can be recovered correctly by selecting suitable discrete equilibrium distribution functions and the amending functions. The mesoscopic model has been validated by several related issues where analytic solutions are available. The experimental results show that the numerical results are consistent with the analytic solutions. From the mesoscopic point of view, the present approach provides a new way for studying the complex nonlinear partial differential equations arising in natural nonlinear phenomena of engineering and science.
Collapse
Affiliation(s)
- Demei Li
- College of Mathematics and Informatics, FJKLMAA, Fujian Normal University, Fuzhou 350007, China
| | - Huilin Lai
- College of Mathematics and Informatics, FJKLMAA, Fujian Normal University, Fuzhou 350007, China
| | - Chuandong Lin
- Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-Sen University, Zhuhai 519082, China
| |
Collapse
|
4
|
Qin F, Mazloomi Moqaddam A, Del Carro L, Kang Q, Brunschwiler T, Derome D, Carmeliet J. Tricoupled hybrid lattice Boltzmann model for nonisothermal drying of colloidal suspensions in micropore structures. Phys Rev E 2019; 99:053306. [PMID: 31212433 DOI: 10.1103/physreve.99.053306] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2019] [Indexed: 06/09/2023]
Abstract
A tricoupled hybrid lattice Boltzmann model (LBM) is developed to simulate colloidal liquid evaporation and colloidal particle deposition during the nonisothermal drying of colloidal suspensions in micropore structures. An entropic multiple-relaxation-time multirange pseudopotential two-phase LBM for isothermal interfacial flow is first coupled to an extended temperature equation for simulating nonisothermal liquid drying. Then the coupled model is further coupled with a modified convection diffusion equation to consider the nonisothermal drying of colloidal suspensions. Two drying examples are considered. First, drying of colloidal suspensions in a two-pillar micropore structure is simulated in two dimensions (2D), and the final configuration of colloidal particles is compared with the experimental one. Good agreement is observed. Second, at the temperature of 343.15 K (70^{∘}C), drying of colloidal suspensions in a complex spiral-shaped micropore structure containing 220 pillars is simulated (also in 2D). The drying pattern follows the designed spiral shape due to capillary pumping, i.e., transport of the liquid from larger pores to smaller ones by capillary pressure difference. Since the colloidal particles are passively carried with liquid, they accumulate at the small menisci as drying proceeds. As liquid evaporates at the small menisci, colloidal particles are deposited, eventually forming solid structures between the pillars (primarily), and at the base of the pillars (secondarily). As a result, the particle deposition conforms to the spiral route. Qualitatively, the simulated liquid and particle configurations agree well with the experimental ones during the entire drying process. Quantitatively, the model demonstrates that the evaporation rate and the particle accumulation rate slowly decrease during drying, similar to what is seen in the experimental results, which is due to the reduction of the liquid-vapor interfacial area. In conclusion, the hybrid model shows the capability and accuracy for simulating nonisothermal drying of colloidal suspensions in a complex micropore structure both qualitatively and quantitatively, as it includes all the required physics and captures all the complex features observed experimentally. Such a tricoupled LBM has a high potential to become an efficient numerical tool for further investigation of real and complex engineering problems incorporating drying of colloidal suspensions in porous media.
Collapse
Affiliation(s)
- Feifei Qin
- Chair of Building Physics, Department of Mechanical and Process Engineering, ETH Zürich (Swiss Federal Institute of Technology in Zürich), Zürich 8093, Switzerland
- Laboratory of Multiscale Studies in Building Physics, Empa (Swiss Federal Laboratories for Materials Science and Technology), Dübendorf 8600, Switzerland
| | - Ali Mazloomi Moqaddam
- Laboratory of Multiscale Studies in Building Physics, Empa (Swiss Federal Laboratories for Materials Science and Technology), Dübendorf 8600, Switzerland
| | - Luca Del Carro
- Smart System Integration, IBM Research-Zürich, Saumerstrasse 4, 8803 Rüschlikon, Switzerland
| | - Qinjun Kang
- Earth and Environment Sciences Division (EES-16), Los Alamos National Laboratory (LANL), Los Alamos, New Mexico 87545, USA
| | - Thomas Brunschwiler
- Smart System Integration, IBM Research-Zürich, Saumerstrasse 4, 8803 Rüschlikon, Switzerland
| | - Dominique Derome
- Laboratory of Multiscale Studies in Building Physics, Empa (Swiss Federal Laboratories for Materials Science and Technology), Dübendorf 8600, Switzerland
| | - Jan Carmeliet
- Chair of Building Physics, Department of Mechanical and Process Engineering, ETH Zürich (Swiss Federal Institute of Technology in Zürich), Zürich 8093, Switzerland
| |
Collapse
|
5
|
Kupershtokh AL, Medvedev DA, Gribanov II. Thermal lattice Boltzmann method for multiphase flows. Phys Rev E 2018; 98:023308. [PMID: 30253592 DOI: 10.1103/physreve.98.023308] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2017] [Indexed: 04/25/2023]
Abstract
An alternative method to simulate heat transport in the multiphase lattice Boltzmann (LB) method is proposed. To solve the energy transport equation when phase boundaries are present, the method of a passive scalar is considerably modified. The internal energy is represented by an additional set of distribution functions, which evolve according to an LB-like equation simulating the transport of a passive scalar. Parasitic heat diffusion near boundaries with a large density gradient is suppressed by using special "pseudoforces" which prevent the spreading of energy. The compression work and heat diffusion are calculated by finite differences. A new method to take into account the latent heat of a phase transition Q(T) is realized. The latent heat is released or absorbed continuously inside a thin transition layer in a certain range of density, ρ_{1}<ρ<ρ_{2}. This allows one to avoid interface tracking. Several tests were carried out concerning all aspects of the processes. It is shown that the Galilean invariance and the scaling of the thermal conduction process hold, as well as the correct dependence of the sound speed on the heat capacity ratio. The method proposed has low scheme diffusion of the internal energy, and it can be applied to modeling a wide range of multiphase flows with heat and mass transfer even for high density ratios of liquid and vapor phases.
Collapse
Affiliation(s)
- Alexander L Kupershtokh
- Lavrentyev Institute of Hydrodynamics, Siberian Branch of Russian Academy of Sciences, Lavrentyev prosp. 15, 630090 Novosibirsk, Russia
| | - Dmitry A Medvedev
- Lavrentyev Institute of Hydrodynamics, Siberian Branch of Russian Academy of Sciences, Lavrentyev prosp. 15, 630090 Novosibirsk, Russia
- Novosibirsk State University, Pirogova str. 2, 630090 Novosibirsk, Russia
| | - Igor I Gribanov
- Lavrentyev Institute of Hydrodynamics, Siberian Branch of Russian Academy of Sciences, Lavrentyev prosp. 15, 630090 Novosibirsk, Russia
| |
Collapse
|
6
|
Li Q, Zhou P, Yan HJ. Improved thermal lattice Boltzmann model for simulation of liquid-vapor phase change. Phys Rev E 2017; 96:063303. [PMID: 29347407 DOI: 10.1103/physreve.96.063303] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2017] [Indexed: 06/07/2023]
Abstract
In this paper, an improved thermal lattice Boltzmann (LB) model is proposed for simulating liquid-vapor phase change, which is aimed at improving an existing thermal LB model for liquid-vapor phase change [S. Gong and P. Cheng, Int. J. Heat Mass Transfer 55, 4923 (2012)10.1016/j.ijheatmasstransfer.2012.04.037]. First, we emphasize that the replacement of ∇·(λ∇T)/∇·(λ∇T)ρc_{V}ρc_{V} with ∇·(χ∇T) is an inappropriate treatment for diffuse interface modeling of liquid-vapor phase change. Furthermore, the error terms ∂_{t_{0}}(Tv)+∇·(Tvv), which exist in the macroscopic temperature equation recovered from the previous model, are eliminated in the present model through a way that is consistent with the philosophy of the LB method. Moreover, the discrete effect of the source term is also eliminated in the present model. Numerical simulations are performed for droplet evaporation and bubble nucleation to validate the capability of the model for simulating liquid-vapor phase change. It is shown that the numerical results of the improved model agree well with those of a finite-difference scheme. Meanwhile, it is found that the replacement of ∇·(λ∇T)/∇·(λ∇T)ρc_{V}ρc_{V} with ∇·(χ∇T) leads to significant numerical errors and the error terms in the recovered macroscopic temperature equation also result in considerable errors.
Collapse
Affiliation(s)
- Qing Li
- School of Energy Science and Engineering, Central South University, Changsha 410083, China
| | - P Zhou
- School of Energy Science and Engineering, Central South University, Changsha 410083, China
| | - H J Yan
- School of Energy Science and Engineering, Central South University, Changsha 410083, China
| |
Collapse
|
7
|
Zarghami A, Van den Akker HEA. Thermohydrodynamics of an evaporating droplet studied using a multiphase lattice Boltzmann method. Phys Rev E 2017; 95:043310. [PMID: 28505732 DOI: 10.1103/physreve.95.043310] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2016] [Indexed: 11/07/2022]
Abstract
In this paper, the thermohydrodynamics of an evaporating droplet is investigated by using a single-component pseudopotential lattice Boltzmann model. The phase change is applied to the model by adding source terms to the thermal lattice Boltzmann equation in such a way that the macroscopic energy equation of multiphase flows is recovered. In order to gain an exhaustive understanding of the complex hydrodynamics during evaporation, a single droplet is selected as a case study. At first, some tests for a stationary (non-)evaporating droplet are carried out to validate the method. Then the model is used to study the thermohydrodynamics of a falling evaporating droplet. The results show that the model is capable of reproducing the flow dynamics and transport phenomena of a stationary evaporating droplet quite well. Of course, a moving droplet evaporates faster than a stationary one due to the convective transport. Our study shows that our single-component model for simulating a moving evaporating droplet is limited to low Reynolds numbers.
Collapse
Affiliation(s)
- Ahad Zarghami
- Department of Process and Energy, TU Delft, Netherlands
| | - Harry E A Van den Akker
- Transport Phenomena Group, Department of Chemical Engineering, TU Delft, Netherlands.,Bernal Institute, School of Engineering, University of Limerick, Ireland
| |
Collapse
|