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Multiscale Model for Electrokinetic Transport in Networks of Pores, Part I: Model Derivation
Shima Alizadeh1,2, Ali Mani1,2
1Department of Mechanical Engineering, Flow Physics and Computational Engineering, Stanford University , Stanford, California 94305, United States.
Langmuir : the ACS Journal of Surfaces and Colloids
|May 13, 2017
Summary
We developed an efficient reduced-order model for simulating electrokinetic phenomena in porous media. This model accurately captures complex interactions in microfluidic systems, reducing computational cost.
Area of Science:
- Computational physics and chemistry
- Multiphysics modeling
- Porous media science
Background:
- Electrokinetic phenomena are crucial in applications like energy conversion and microfluidics.
- Simulating these phenomena in complex porous media using full multidimensional models is computationally prohibitive.
- Existing reduced-order models often face limitations in accuracy and stability.
Purpose of the Study:
- To present an efficient and robust reduced-order numerical model for simulating electrokinetic phenomena in porous media and microstructure networks.
- To overcome the computational expense of multidimensional simulations by employing a network of one-dimensional (1D) equations.
- To accurately account for cross-sectional variations in potential and ion concentration fields.
Main Methods:
- Derivation of a 1D reduced-order model based on the Poisson-Nernst-Planck-Stokes equations, assuming long and thin pores.
- Incorporation of cross-sectional non-uniformities using area-averaged coefficients derived from Poisson-Boltzmann equation solutions.
- Tabulation of coefficients against dimensionless surface charge and electric double layer (EDL) thickness for broad applicability.
Main Results:
- A fully conservative discretization scheme ensuring zero numerical leakage.
- Fully bounded area-averaged coefficients, avoiding singularities even for infinitely thick EDLs.
- Flux discretization that precisely preserves equilibrium conditions and extends to general pore networks.
Conclusions:
- The developed 1D reduced-order model offers a computationally efficient and accurate alternative for simulating complex electrokinetic phenomena.
- The model's robustness and ability to handle various microstructural complexities make it suitable for diverse applications.
- This framework provides a significant advancement for modeling deionization, energy conversion, and lab-on-a-chip systems.
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