Year: 2010
Communications in Computational Physics, Vol. 7 (2010), Iss. 2 : pp. 362–382
Abstract
The Cahn-Hilliard equation is often used to describe evolution of phase boundaries in phase field models for multiphase fluids. In this paper, we compare the use of the Cahn-Hilliard equation (of a constant mobility) for the phase variable with that of the singular or modified Cahn-Hilliard equation (of a variable mobility) in the context of physical derivation of the transport equation and numerical simulations of immiscible binary fluids. We show numerically that (i). both equations work fine for interfaces of small to moderate curvature in short to intermediate time scales; (ii) the Cahn-Hilliard equation renders strong dissipation in simulations of small droplets leading to dissolution of small droplets into the surrounding fluid and/or absorption of small droplets by larger droplets nearby, an artifact for immiscible binary fluids; whereas, the singular Cahn-Hilliard equation can significantly reduce the numerical dissipation around small droplets to yield physically acceptable results in intermediate time scales; (iii) the size of droplets that can be simulated by the Cahn-Hilliard equations scale inversely with the strength of the mixing free energy. Since the intermediate timescale is the time scale of interest in most transient fluid simulations, the singular Cahn-Hilliard equation proves to be the more accurate phase transporting equation for immiscible binary fluids.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.2009.09.016
Communications in Computational Physics, Vol. 7 (2010), Iss. 2 : pp. 362–382
Published online: 2010-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
-
Phase-field lattice Boltzmann model with singular mobility for quasi-incompressible two-phase flows
Bao, Jin | Guo, ZhaoliPhysical Review E, Vol. 109 (2024), Iss. 2
https://doi.org/10.1103/PhysRevE.109.025302 [Citations: 0] -
An interfacial profile-preserving approach for phase field modeling of incompressible two-phase flows
Hao, Haohao | Li, Xiangwei | Jiang, Chenglin | Tan, HuanshuInternational Journal of Multiphase Flow, Vol. 174 (2024), Iss. P.104750
https://doi.org/10.1016/j.ijmultiphaseflow.2024.104750 [Citations: 0] -
Phase-field-based lattice Boltzmann finite-difference model for simulating thermocapillary flows
Liu, Haihu | Valocchi, Albert J. | Zhang, Yonghao | Kang, QinjunPhysical Review E, Vol. 87 (2013), Iss. 1
https://doi.org/10.1103/PhysRevE.87.013010 [Citations: 102] -
A new approach for the numerical solution of diffusion equations with variable and degenerate mobility
Ceniceros, Hector D. | García-Cervera, Carlos J.Journal of Computational Physics, Vol. 246 (2013), Iss. P.1
https://doi.org/10.1016/j.jcp.2013.03.036 [Citations: 19] -
Investigations of spray breakup Rayleigh–Taylor instability via multiphase lattice Boltzmann flux solver
Wang, Yue | Gao, Shen-Yong | Zhao, Fei-Yang | Yang, Li-Ming | Yu, Wen-BinPhysics of Fluids, Vol. 35 (2023), Iss. 12
https://doi.org/10.1063/5.0176836 [Citations: 3] -
Three-dimensional coarsening dynamics of a conserved, nematic liquid crystal-isotropic fluid mixture
Nós, Rudimar L. | Roma, Alexandre M. | García-Cervera, Carlos J. | Ceniceros, Hector D.Journal of Non-Newtonian Fluid Mechanics, Vol. 248 (2017), Iss. P.62
https://doi.org/10.1016/j.jnnfm.2017.08.009 [Citations: 7] -
Ordering kinetics of a conserved binary mixture with a nematic liquid crystal component
Mata, Matthew | García-Cervera, Carlos J. | Ceniceros, Hector D.Journal of Non-Newtonian Fluid Mechanics, Vol. 212 (2014), Iss. P.18
https://doi.org/10.1016/j.jnnfm.2014.08.003 [Citations: 9] -
A Class of Conservative Phase Field Models for Multiphase Fluid Flows
Li, Jun | Wang, QiJournal of Applied Mechanics, Vol. 81 (2014), Iss. 2
https://doi.org/10.1115/1.4024404 [Citations: 21] -
A hybrid lattice Boltzmann and finite difference method for two-phase flows with soluble surfactants
Ba, Yan | Liu, Haihu | Li, Wenqiang | Yang, WenjingComputers & Mathematics with Applications, Vol. 174 (2024), Iss. P.325
https://doi.org/10.1016/j.camwa.2024.09.022 [Citations: 0] -
A second order in time, uniquely solvable, unconditionally stable numerical scheme for Cahn–Hilliard–Navier–Stokes equation
Han, Daozhi | Wang, XiaomingJournal of Computational Physics, Vol. 290 (2015), Iss. P.139
https://doi.org/10.1016/j.jcp.2015.02.046 [Citations: 154] -
The Cahn-Hilliard Equation with Logarithmic Potentials
Cherfils, Laurence | Miranville, Alain | Zelik, SergeyMilan Journal of Mathematics, Vol. 79 (2011), Iss. 2 P.561
https://doi.org/10.1007/s00032-011-0165-4 [Citations: 136] -
Modeling of three-phase displacement in three-dimensional irregular geometries using a lattice Boltzmann method
Li, Sheng | Liu, Haihu | Zhang, Jinggang | Jiang, Fei | Xi, GuangPhysics of Fluids, Vol. 33 (2021), Iss. 12
https://doi.org/10.1063/5.0068759 [Citations: 15] -
On the Cahn-Hilliard-Oono-Navier-Stokes equations with singular potentials
Miranville, Alain | Temam, RogerApplicable Analysis, Vol. 95 (2016), Iss. 12 P.2609
https://doi.org/10.1080/00036811.2015.1102893 [Citations: 18] -
Mass and Volume Conservation in Phase Field Models for Binary Fluids
Shen, Jie | Yang, Xiaofeng | Wang, QiCommunications in Computational Physics, Vol. 13 (2013), Iss. 4 P.1045
https://doi.org/10.4208/cicp.300711.160212a [Citations: 69] -
COMPARISON OF DIFFERENT NUMERICAL SCHEMES FOR THE CAHN-HILLIARD EQUATION
Lee, Seunggyu | Lee, Chaeyoung | Lee, Hyun Geun | Kim, JunseokJournal of the Korea Society for Industrial and Applied Mathematics, Vol. 17 (2013), Iss. 3 P.197
https://doi.org/10.12941/jksiam.2013.17.197 [Citations: 7] -
Influence of Adding Carbonaceous Fuels to Ionic Liquids on Propellant Properties
Gao, Xuyao | Gao, Zhongquan | Tan, Yonghua | Chen, Pengfei | Du, Zenghui | Li, YutongACS Omega, Vol. 7 (2022), Iss. 48 P.43582
https://doi.org/10.1021/acsomega.2c04386 [Citations: 1] -
A hybrid lattice Boltzmann and finite difference method for droplet dynamics with insoluble surfactants
Liu, Haihu | Ba, Yan | Wu, Lei | Li, Zhen | Xi, Guang | Zhang, YonghaoJournal of Fluid Mechanics, Vol. 837 (2018), Iss. P.381
https://doi.org/10.1017/jfm.2017.859 [Citations: 93] -
Effect of Wettability and Permeability on Pore-Scale of CH4–Water Two-Phase Displacement Behavior in the Phase Field Model
Wang, Zedong | Guo, Chang | Liu, Nan | Fan, Kai | Zhang, Xiangliang | Liu, TingApplied Sciences, Vol. 14 (2024), Iss. 15 P.6815
https://doi.org/10.3390/app14156815 [Citations: 0] -
Multiphase lattice Boltzmann simulations for porous media applications
Liu, Haihu | Kang, Qinjun | Leonardi, Christopher R. | Schmieschek, Sebastian | Narváez, Ariel | Jones, Bruce D. | Williams, John R. | Valocchi, Albert J. | Harting, JensComputational Geosciences, Vol. 20 (2016), Iss. 4 P.777
https://doi.org/10.1007/s10596-015-9542-3 [Citations: 336]