An OpenFOAM-integrated Numerical Solver for Electroconvective Flow
Main Article Content
Abstract
In this work, we developed a numerical solver, integrated in OpenFOAM platform, for modeling electroconvective. The solver deals with the system of Poisson-Nernst-Planck-Navier-Stokes equations. The finite volume schemes functioned in OpenFOAM was used for discretisation of the Poisson-Nernst-Planck equations. The Newton method was employed to solve the nonlinear Poisson-Nernst-Planck equations in a coupled manner. The validation shows that the high accuracy of our solver. It is used to investigate ion conduction in the electrodialysis cell. The simulation results have allowed to examine the flow’s profile, ion distribution in different regimes of the system. Especially, the mechanisms behind the voxtex formation in the channel can be explained by these results. This solver developed on OpenFoam open-source code provides the research community with a valuable tool for the study of the electrochemical problems.
Keywords
Poisson-Nernst-Planck-Navier-Stokes, electrokinetic, ion concentration polarization
Article Details

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References
[1] V.-B. Nguyen and V.-S. Pham, Study and modeling
DNA-preconcentration microfluidic device, J. Sci.
Technol, vol. 143, no. 1, pp. 1–6. 2020.
[2] V. S. Pham, Z. Li, K. M. Lim, J. K. White, and J. Han,
Direct numerical simulation of electroconvective
instability and hysteretic current-voltage response of a
permselective membrane, Phys. Rev. E - Stat.
Nonlinear, Soft Matter Phys., vol. 86, no. 4. 2012.
https://doi.org/10.1103/PhysRevE.86.046310.
[3] R. J. Hunter, Zeta Potential In Colloid Science, San
Diego: Academic press Inc, 1981.
[4] I. Rubinstein and B. Zaltzman, Electro-osmotically
induced convection at a permselective membrane,
Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat.
Interdiscip. Top, vol. 62, no. 2, pp. 2238–2251. 2000.
https://doi.org/10.1103/PhysRevE.62.2238.
[5] S. R. Mathur and J. Y. Murthy, A multigrid method for
the Poisson – Nernst – Planck equations, Int. J. Heat
Mass Transf, vol. 52, no. 17–18, pp. 4031–4039. 2009.
https://doi.org/10.1016/j.ijheatmasstransfer.2009.03.0
40.
[6] H. Daiguji, P. Yang, and A. Majumdar, Ion transport in
nanofluidic channels, Nano Letters, 2004 4 (1),
pp. 137-142.
https://doi.org/10.1021/nl0348185
[7] H. J. Kwon, B. Kim, G. Lim, and J. Han, A multiscalepore ion exchange membrane for better energy
efficiency, J. Mater. Chem. A, vol. 6, no. 17, pp. 7714–
7723. 2018.
https://doi.org/10.1039/c7ta10570c.
[8] J. Yoon, V. Q. Do, V. S. Pham, and J. Han, Return flow
ion concentration polarization desalination: A new way
to enhance electromembrane desalination, Water Res,
vol. 159, pp. 501–510. 2019
https://doi.org/10.1016/j.watres.2019.05.042.
[9] V. S. Pham, Z. Li, K. M. Lim, J. K. White, and J. Han,
Direct numerical simulation of electroconvective
instability and hysteretic current-voltage response of a
permselective membrane, Phys. Rev. E-Stat.
Nonlinear, Soft Matter Phys, vol. 86, no. 4, pp. 1–11.
2012.
https://doi.org/10.1103/PhysRevE.86.046310.
[10] S. V. Pham, H. Kwon, B. Kim, J. K. White, G. Lim, and
J. Han, Helical vortex formation in three-dimensional
electrochemical systems with ion-selective
membranes, Phys. Rev. E, vol. 93, no. 3. 2016.
https://doi.org/10.1103/PhysRevE.93.033114.
[11] C. L. Druzgalski, M. B. Andersen, and A. Mani, Direct
numerical simulation of electroconvective instability
and hydrodynamic chaos near an ion-selective surface,
Phys. Fluids, vol. 25, no. 11. 2013.
https://doi.org/10.1063/1.4818995.
[12] H. C. Chang and G. Yossifon, Understanding
electrokinetics at the nanoscale: A perspective,
Biomicrofluidics, vol. 3, no. 1, pp. 1–16. 2009.
https://doi.org/10.1063/1.305604
DNA-preconcentration microfluidic device, J. Sci.
Technol, vol. 143, no. 1, pp. 1–6. 2020.
[2] V. S. Pham, Z. Li, K. M. Lim, J. K. White, and J. Han,
Direct numerical simulation of electroconvective
instability and hysteretic current-voltage response of a
permselective membrane, Phys. Rev. E - Stat.
Nonlinear, Soft Matter Phys., vol. 86, no. 4. 2012.
https://doi.org/10.1103/PhysRevE.86.046310.
[3] R. J. Hunter, Zeta Potential In Colloid Science, San
Diego: Academic press Inc, 1981.
[4] I. Rubinstein and B. Zaltzman, Electro-osmotically
induced convection at a permselective membrane,
Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat.
Interdiscip. Top, vol. 62, no. 2, pp. 2238–2251. 2000.
https://doi.org/10.1103/PhysRevE.62.2238.
[5] S. R. Mathur and J. Y. Murthy, A multigrid method for
the Poisson – Nernst – Planck equations, Int. J. Heat
Mass Transf, vol. 52, no. 17–18, pp. 4031–4039. 2009.
https://doi.org/10.1016/j.ijheatmasstransfer.2009.03.0
40.
[6] H. Daiguji, P. Yang, and A. Majumdar, Ion transport in
nanofluidic channels, Nano Letters, 2004 4 (1),
pp. 137-142.
https://doi.org/10.1021/nl0348185
[7] H. J. Kwon, B. Kim, G. Lim, and J. Han, A multiscalepore ion exchange membrane for better energy
efficiency, J. Mater. Chem. A, vol. 6, no. 17, pp. 7714–
7723. 2018.
https://doi.org/10.1039/c7ta10570c.
[8] J. Yoon, V. Q. Do, V. S. Pham, and J. Han, Return flow
ion concentration polarization desalination: A new way
to enhance electromembrane desalination, Water Res,
vol. 159, pp. 501–510. 2019
https://doi.org/10.1016/j.watres.2019.05.042.
[9] V. S. Pham, Z. Li, K. M. Lim, J. K. White, and J. Han,
Direct numerical simulation of electroconvective
instability and hysteretic current-voltage response of a
permselective membrane, Phys. Rev. E-Stat.
Nonlinear, Soft Matter Phys, vol. 86, no. 4, pp. 1–11.
2012.
https://doi.org/10.1103/PhysRevE.86.046310.
[10] S. V. Pham, H. Kwon, B. Kim, J. K. White, G. Lim, and
J. Han, Helical vortex formation in three-dimensional
electrochemical systems with ion-selective
membranes, Phys. Rev. E, vol. 93, no. 3. 2016.
https://doi.org/10.1103/PhysRevE.93.033114.
[11] C. L. Druzgalski, M. B. Andersen, and A. Mani, Direct
numerical simulation of electroconvective instability
and hydrodynamic chaos near an ion-selective surface,
Phys. Fluids, vol. 25, no. 11. 2013.
https://doi.org/10.1063/1.4818995.
[12] H. C. Chang and G. Yossifon, Understanding
electrokinetics at the nanoscale: A perspective,
Biomicrofluidics, vol. 3, no. 1, pp. 1–16. 2009.
https://doi.org/10.1063/1.305604