Implementing contact angle boundary conditions for second-order Phase-Field models of wall-bounded multiphase flows

Huang, Ziyang; Lin, Guang; Ardekani, Arezoo M.

doi:10.1016/j.jcp.2022.111619

Implementing contact angle boundary conditions for second-order Phase-Field models of wall-bounded multiphase flows

Journal Article · Thu Sep 15 00:00:00 EDT 2022 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2022.111619· OSTI ID:2421761

^[1]; ^[2]; Ardekani, Arezoo M. ^[2]

Univ. of Michigan, Ann Arbor, MI (United States); OSTI
Purdue Univ., West Lafayette, IN (United States)

In the present work, a general formulation is proposed to implement the contact angle boundary conditions for the second-order Phase-Field models, which is applicable to N-phase (N ≥ 2) moving contact line problems. To remedy the issue of mass change due to the contact angle boundary condition, a source term or Lagrange multiplier is added to the original second-order Phase-Field models, which is determined by the consistent and conservative volume distribution algorithm so that the summation of the order parameters and the consistency of reduction are not influenced. To physically couple the proposed formulation to the hydrodynamics, especially for large-density-ratio problems, the consistent formulation is employed. The reduction-consistent conservative Allen-Cahn models are chosen as examples to illustrate the application of the proposed formulation. The numerical scheme that preserves the consistency and conservation of the proposed formulation is employed to demonstrate its effectiveness. Results produced by the proposed formulation are in good agreement with the exact and/or asymptotic solutions. The proposed method captures complex dynamics of moving contact line problems having large density ratios.

View Accepted Manuscript (DOE)

Research Organization:: Purdue Univ., West Lafayette, IN (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: SC0021142

OSTI ID:: 2421761

Alternate ID(s):: OSTI ID: 1960865

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 471; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (71)

Calculation of Two-Phase Navier–Stokes Flows Using Phase-Field Modeling Jacqmin, David Journal of Computational Physics, Vol. 155, Issue 1 https://doi.org/10.1006/jcph.1999.6332	journal	October 1999
A Front-Tracking Method for the Computations of Multiphase Flow Tryggvason, G.; Bunner, B.; Esmaeeli, A. Journal of Computational Physics, Vol. 169, Issue 2 https://doi.org/10.1006/jcph.2001.6726	journal	May 2001
Numerical Simulation of Moving Contact Line Problems Using a Volume-of-Fluid Method Renardy, Michael; Renardy, Yuriko; Li, Jie Journal of Computational Physics, Vol. 171, Issue 1 https://doi.org/10.1006/jcph.2001.6785	journal	July 2001
Moving contact lines in the Cahn-Hilliard theory Seppecher, Pierre International Journal of Engineering Science, Vol. 34, Issue 9 https://doi.org/10.1016/0020-7225(95)00141-7	journal	July 1996
A front-tracking method for computational modeling of impact and spreading of viscous droplets on solid walls Muradoglu, Metin; Tasoglu, Savas Computers & Fluids, Vol. 39, Issue 4 https://doi.org/10.1016/j.compfluid.2009.10.009	journal	April 2010
A level-set approach for simulations of flows with multiple moving contact lines with hysteresis Spelt, Peter D. M. Journal of Computational Physics, Vol. 207, Issue 2 https://doi.org/10.1016/j.jcp.2005.01.016	journal	August 2005
A conservative level set method for two phase flow Olsson, Elin; Kreiss, Gunilla Journal of Computational Physics, Vol. 210, Issue 1 https://doi.org/10.1016/j.jcp.2005.04.007	journal	November 2005
A conservative level set method for two phase flow II Olsson, Elin; Kreiss, Gunilla; Zahedi, Sara Journal of Computational Physics, Vol. 225, Issue 1 https://doi.org/10.1016/j.jcp.2006.12.027	journal	July 2007
A conservative level set method for contact line dynamics Zahedi, Sara; Gustavsson, Katarina; Kreiss, Gunilla Journal of Computational Physics, Vol. 228, Issue 17 https://doi.org/10.1016/j.jcp.2009.05.043	journal	September 2009
Contact-line dynamics of a diffuse fluid interface Jacqmin, David Journal of Fluid Mechanics, Vol. 402 https://doi.org/10.1017/s0022112099006874	journal	January 2000
Direct Numerical Simulation of Free-Surface and Interfacial flow Scardovelli, Ruben; Zaleski, Stéphane Annual Review of Fluid Mechanics, Vol. 31, Issue 1 https://doi.org/10.1146/annurev.fluid.31.1.567	journal	January 1999
Short time dynamics of viscous drop spreading Eddi, Antonin; Winkels, Koen G.; Snoeijer, Jacco H. arXiv https://doi.org/10.48550/arxiv.1209.6150	text	January 2012
A modified phase field approximation for mean curvature flow with conservation of the volume Brassel, M.; Bretin, E. Mathematical Methods in the Applied Sciences, Vol. 34, Issue 10 https://doi.org/10.1002/mma.1426	journal	March 2011
Efficient Implementation of Weighted ENO Schemes Jiang, Guang-Shan; Shu, Chi-Wang Journal of Computational Physics, Vol. 126, Issue 1 https://doi.org/10.1006/jcph.1996.0130	journal	June 1996
Modeling and simulation of dynamics of three-component flows on solid surface Shi, Yi; Wang, Xiao-Ping Japan Journal of Industrial and Applied Mathematics, Vol. 31, Issue 3 https://doi.org/10.1007/s13160-014-0151-7	journal	October 2014
A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening Allen, Samuel M.; Cahn, John W. Acta Metallurgica, Vol. 27, Issue 6 https://doi.org/10.1016/0001-6160(79)90196-2	journal	June 1979
Volume of fluid (VOF) method for the dynamics of free boundaries Hirt, C. W.; Nichols, B. D. Journal of Computational Physics, Vol. 39, Issue 1 https://doi.org/10.1016/0021-9991(81)90145-5	journal	January 1981
Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations Osher, Stanley; Sethian, James A. Journal of Computational Physics, Vol. 79, Issue 1 https://doi.org/10.1016/0021-9991(88)90002-2	journal	November 1988
A continuum method for modeling surface tension Brackbill, J. U.; Kothe, D. B.; Zemach, C. Journal of Computational Physics, Vol. 100, Issue 2 https://doi.org/10.1016/0021-9991(92)90240-Y	journal	June 1992
A front-tracking method for viscous, incompressible, multi-fluid flows Unverdi, Salih Ozen; Tryggvason, Grétar Journal of Computational Physics, Vol. 100, Issue 1 https://doi.org/10.1016/0021-9991(92)90307-K	journal	May 1992
A consistent and conservative Phase-Field method for multiphase incompressible flows Huang, Ziyang; Lin, Guang; Ardekani, Arezoo M. Journal of Computational and Applied Mathematics, Vol. 408 https://doi.org/10.1016/j.cam.2022.114116	journal	July 2022
On imposing dynamic contact-angle boundary conditions for wall-bounded liquid–gas flows Dong, S. Computer Methods in Applied Mechanics and Engineering, Vol. 247-248 https://doi.org/10.1016/j.cma.2012.07.023	journal	November 2012
A variational approach to the contact angle dynamics of spreading droplets Manservisi, S.; Scardovelli, R. Computers & Fluids, Vol. 38, Issue 2 https://doi.org/10.1016/j.compfluid.2008.05.001	journal	February 2009
Accurate contact angle boundary conditions for the Cahn–Hilliard equations Lee, Hyun Geun; Kim, Junseok Computers & Fluids, Vol. 44, Issue 1 https://doi.org/10.1016/j.compfluid.2010.12.031	journal	May 2011
Conservative Allen–Cahn–Navier–Stokes system for incompressible two-phase fluid flows Jeong, Darae; Kim, Junseok Computers & Fluids, Vol. 156 https://doi.org/10.1016/j.compfluid.2017.07.009	journal	October 2017
Multi-phase-field modeling using a conservative Allen–Cahn equation for multiphase flow Aihara, Shintaro; Takaki, Tomohiro; Takada, Naoki Computers & Fluids, Vol. 178 https://doi.org/10.1016/j.compfluid.2018.08.023	journal	January 2019
A new conservative vector-valued Allen–Cahn equation and its fast numerical method Kim, Junseok; Lee, Hyun Geun Computer Physics Communications, Vol. 221 https://doi.org/10.1016/j.cpc.2017.08.006	journal	December 2017
A conservative Allen–Cahn equation with a space–time dependent Lagrange multiplier Kim, Junseok; Lee, Seunggyu; Choi, Yongho International Journal of Engineering Science, Vol. 84 https://doi.org/10.1016/j.ijengsci.2014.06.004	journal	November 2014
Three dimensional phase-field investigation of droplet formation in microfluidic flow focusing devices with experimental validation Bai, Feng; He, Xiaoming; Yang, Xiaofeng International Journal of Multiphase Flow, Vol. 93 https://doi.org/10.1016/j.ijmultiphaseflow.2017.04.008	journal	July 2017
Generalized conservative phase field model and its lattice Boltzmann scheme for multicomponent multiphase flows Hu, Yang; Li, Decai; He, Qiang International Journal of Multiphase Flow, Vol. 132 https://doi.org/10.1016/j.ijmultiphaseflow.2020.103432	journal	November 2020
A consistent and conservative volume distribution algorithm and its applications to multiphase flows using Phase-Field models Huang, Ziyang; Lin, Guang; Ardekani, Arezoo M. International Journal of Multiphase Flow, Vol. 142 https://doi.org/10.1016/j.ijmultiphaseflow.2021.103727	journal	September 2021
A mesh-dependent model for applying dynamic contact angles to VOF simulations Afkhami, S.; Zaleski, S.; Bussmann, M. Journal of Computational Physics, Vol. 228, Issue 15 https://doi.org/10.1016/j.jcp.2009.04.027	journal	August 2009
A conservative phase field method for solving incompressible two-phase flows Chiu, Pao-Hsiung; Lin, Yan-Ting Journal of Computational Physics, Vol. 230, Issue 1 https://doi.org/10.1016/j.jcp.2010.09.021	journal	January 2011
A new contact line treatment for a conservative level set method Sato, Yohei; Ničeno, Bojan Journal of Computational Physics, Vol. 231, Issue 10 https://doi.org/10.1016/j.jcp.2012.01.034	journal	May 2012
A time-stepping scheme involving constant coefficient matrices for phase-field simulations of two-phase incompressible flows with large density ratios Dong, S.; Shen, J. Journal of Computational Physics, Vol. 231, Issue 17 https://doi.org/10.1016/j.jcp.2012.04.041	journal	July 2012
Efficient energy stable numerical schemes for a phase field moving contact line model Shen, Jie; Yang, Xiaofeng; Yu, Haijun Journal of Computational Physics, Vol. 284 https://doi.org/10.1016/j.jcp.2014.12.046	journal	March 2015
Diffuse interface simulation of ternary fluids in contact with solid Zhang, Chun-Yu; Ding, Hang; Gao, Peng Journal of Computational Physics, Vol. 309 https://doi.org/10.1016/j.jcp.2015.12.054	journal	March 2016
Phase field modeling and simulation of three-phase flow on solid surfaces Zhang, Qian; Wang, Xiao-Ping Journal of Computational Physics, Vol. 319 https://doi.org/10.1016/j.jcp.2016.05.016	journal	August 2016
Wall-bounded multiphase flows of N immiscible incompressible fluids: Consistency and contact-angle boundary condition Dong, S. Journal of Computational Physics, Vol. 338 https://doi.org/10.1016/j.jcp.2017.02.048	journal	June 2017
A positivity preserving and conservative variational scheme for phase-field modeling of two-phase flows Joshi, Vaibhav; Jaiman, Rajeev K. Journal of Computational Physics, Vol. 360 https://doi.org/10.1016/j.jcp.2018.01.028	journal	May 2018
Multiphase flows of N immiscible incompressible fluids: A reduction-consistent and thermodynamically-consistent formulation and associated algorithm Dong, S. Journal of Computational Physics, Vol. 361 https://doi.org/10.1016/j.jcp.2018.01.041	journal	May 2018
An adaptive variational procedure for the conservative and positivity preserving Allen–Cahn phase-field model Joshi, Vaibhav; Jaiman, Rajeev K. Journal of Computational Physics, Vol. 366 https://doi.org/10.1016/j.jcp.2018.04.022	journal	August 2018
A conservative diffuse interface method for two-phase flows with provable boundedness properties Mirjalili, Shahab; Ivey, Christopher B.; Mani, Ali Journal of Computational Physics, Vol. 401 https://doi.org/10.1016/j.jcp.2019.109006	journal	January 2020
A phase-field moving contact line model with soluble surfactants Zhu, Guangpu; Kou, Jisheng; Yao, Jun Journal of Computational Physics, Vol. 405 https://doi.org/10.1016/j.jcp.2019.109170	journal	March 2020
An energy stable C0 finite element scheme for a quasi-incompressible phase-field model of moving contact line with variable density Shen, Lingyue; Huang, Huaxiong; Lin, Ping Journal of Computational Physics, Vol. 405 https://doi.org/10.1016/j.jcp.2019.109179	journal	March 2020
Consistent, essentially conservative and balanced-force Phase-Field method to model incompressible two-phase flows Huang, Ziyang; Lin, Guang; Ardekani, Arezoo M. Journal of Computational Physics, Vol. 406 https://doi.org/10.1016/j.jcp.2019.109192	journal	April 2020
A level-set method for moving contact lines with contact angle hysteresis Zhang, Jiaqi; Yue, Pengtao Journal of Computational Physics, Vol. 418 https://doi.org/10.1016/j.jcp.2020.109636	journal	October 2020
Consistent and conservative scheme for incompressible two-phase flows using the conservative Allen-Cahn model Huang, Ziyang; Lin, Guang; Ardekani, Arezoo M. Journal of Computational Physics, Vol. 420 https://doi.org/10.1016/j.jcp.2020.109718	journal	November 2020
Consistent, energy-conserving momentum transport for simulations of two-phase flows using the phase field equations Mirjalili, Shahab; Mani, Ali Journal of Computational Physics, Vol. 426 https://doi.org/10.1016/j.jcp.2020.109918	journal	February 2021
A consistent and conservative model and its scheme for N-phase-M-component incompressible flows Huang, Ziyang; Lin, Guang; Ardekani, Arezoo M. Journal of Computational Physics, Vol. 434 https://doi.org/10.1016/j.jcp.2021.110229	journal	June 2021
A consistent and conservative Phase-Field model for thermo-gas-liquid-solid flows including liquid-solid phase change Huang, Ziyang; Lin, Guang; Ardekani, Arezoo M. Journal of Computational Physics, Vol. 449 https://doi.org/10.1016/j.jcp.2021.110795	journal	January 2022
Comparison study of the conservative Allen–Cahn and the Cahn–Hilliard equations Lee, Dongsun; Kim, Junseok Mathematics and Computers in Simulation, Vol. 119 https://doi.org/10.1016/j.matcom.2015.08.018	journal	January 2016
A variational approach to moving contact line hydrodynamics Qian, Tiezheng; Wang, Xiao-Ping; Sheng, Ping Journal of Fluid Mechanics, Vol. 564 https://doi.org/10.1017/S0022112006001935	journal	September 2006
Sharp-interface limit of the Cahn–Hilliard model for moving contact lines Yue, Pengtao; Zhou, Chunfeng; Feng, James J. Journal of Fluid Mechanics, Vol. 645 https://doi.org/10.1017/S0022112009992679	journal	February 2010
The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow Cox, R. G. Journal of Fluid Mechanics, Vol. 168, Issue -1 https://doi.org/10.1017/S0022112086000332	journal	July 1986
Contact-line dynamics of a diffuse fluid interface Jacqmin, David Journal of Fluid Mechanics, Vol. 402 https://doi.org/10.1017/S0022112099006874	journal	January 2000
Sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for moving contact lines Xu, Xianmin; Di, Yana; Yu, Haijun Journal of Fluid Mechanics, Vol. 849 https://doi.org/10.1017/jfm.2018.428	journal	June 2018
Thermodynamically consistent phase-field modelling of contact angle hysteresis Yue, Pengtao Journal of Fluid Mechanics, Vol. 899 https://doi.org/10.1017/jfm.2020.465	journal	July 2020
Numerical studies of droplet splashing on a dry surface: triggering a splash with the dynamic contact angle Yokoi, Kensuke Soft Matter, Vol. 7, Issue 11 https://doi.org/10.1039/c1sm05336a	journal	January 2011
Free Energy of a Nonuniform System. I. Interfacial Free Energy Cahn, John W.; Hilliard, John E. The Journal of Chemical Physics, Vol. 28, Issue 2 https://doi.org/10.1063/1.1744102	journal	February 1958
Wall energy relaxation in the Cahn–Hilliard model for moving contact lines Yue, Pengtao; Feng, James J. Physics of Fluids, Vol. 23, Issue 1 https://doi.org/10.1063/1.3541806	journal	January 2011
Short time dynamics of viscous drop spreading Eddi, A.; Winkels, K. G.; Snoeijer, J. H. Physics of Fluids, Vol. 25, Issue 1 https://doi.org/10.1063/1.4788693	journal	January 2013
Wetting condition in diffuse interface simulations of contact line motion Ding, Hang; Spelt, Peter D. M. Physical Review E, Vol. 75, Issue 4 https://doi.org/10.1103/PhysRevE.75.046708	journal	April 2007
XSEDE: Accelerating Scientific Discovery Towns, John; Cockerill, Timothy; Dahan, Maytal Computing in Science & Engineering, Vol. 16, Issue 5 https://doi.org/10.1109/MCSE.2014.80	journal	September 2014
Drag force on a particle straddling a fluid interface: Influence of interfacial deformations Loudet, J. -C.; Qiu, M.; Hemauer, J. The European Physical Journal E, Vol. 43, Issue 2 https://doi.org/10.1140/epje/i2020-11936-1	journal	February 2020
Steady moving contact line of water over a no-slip substrate Lācis, Uǧis; Johansson, Petter; Fullana, Tomas The European Physical Journal Special Topics, Vol. 229, Issue 10 https://doi.org/10.1140/epjst/e2020-900280-9	journal	September 2020
Thermodynamically Consistent, Frame Indifferent Diffuse Interface Models for Incompressible Two-Phase Flows with Different Densities Abels, Helmut; Garcke, Harald; GrÜN, GÜNther Mathematical Models and Methods in Applied Sciences, Vol. 22, Issue 03 https://doi.org/10.1142/S0218202511500138	journal	March 2012
Hierarchy of consistent n-component Cahn–Hilliard systems Boyer, Franck; Minjeaud, Sebastian Mathematical Models and Methods in Applied Sciences, Vol. 24, Issue 14 https://doi.org/10.1142/S0218202514500407	journal	October 2014
Numerical Simulations of Flows with Moving Contact Lines Sui, Yi; Ding, Hang; Spelt, Peter D. M. Annual Review of Fluid Mechanics, Vol. 46, Issue 1 https://doi.org/10.1146/annurev-fluid-010313-141338	journal	January 2014
Diffuse-Interface Methods in Fluid Mechanics Anderson, D. M.; McFadden, G. B.; Wheeler, A. A. Annual Review of Fluid Mechanics, Vol. 30, Issue 1 https://doi.org/10.1146/annurev.fluid.30.1.139	journal	January 1998
L EVEL S ET M ETHODS FOR F LUID I NTERFACES Sethian, J. A.; Smereka, Peter Annual Review of Fluid Mechanics, Vol. 35, Issue 1 https://doi.org/10.1146/annurev.fluid.35.101101.161105	journal	January 2003

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97 MATHEMATICS AND COMPUTING
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Implementing contact angle boundary conditions for second-order Phase-Field models of wall-bounded multiphase flows

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