Abstract An integral equation method is presented for the 1D steady-state Poisson-Nernst-Planck equations modeling ion transport through membrane channels. The differential equations are recast as integral equations using Green’s 3rd identity yielding a fixed-point problem for the electric potential gradient and ion concentrations. The integrals are discretized by a combination of midpoint and trapezoid rules, and the resulting algebraic equations are solved by Gummel iteration. Numerical tests for electroneutral and non-electroneutral systems demonstrate the method’s 2nd order accuracy and ability to resolve sharp boundary layers. The method is applied to a 1D model of the K$$^+$$ ion channel with a fixed charge density that ensures cation selectivity. In these tests, the proposed integral equation method yields potential and concentration profiles in good agreement with published results.
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Smoothed Particle Hydrodynamics Modeling of Electrodeposition and Dendritic Growth Under Migration- and Diffusion-Controlled Mass Transport
Abstract In many electrochemical processes, the transport of charged species is governed by the Nernst–Planck equation, which includes terms for both diffusion and electrochemical migration. In this work, a multi-physics, multi-species model based on the smoothed particle hydrodynamics (SPH) method is presented to model the Nernst–Planck equation in systems with electrodeposition. Electrodeposition occurs when ions are deposited onto an electrode. These deposits create complex boundary geometries, which can be challenging for numerical methods to resolve. SPH is a particularly effective numerical method for systems with moving and deforming boundaries due to its particle nature. This paper discusses the SPH implementation of the Nernst–Planck equations with electrodeposition and verifies the model with an analytical solution and a numerical integrator. A convergence study of migration and precipitation is presented to illustrate the model’s accuracy, along with comparisons of the deposition growth front to experimental results.
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- Award ID(s):
- 2034154
- PAR ID:
- 10465720
- Date Published:
- Journal Name:
- Journal of Electrochemical Energy Conversion and Storage
- Volume:
- 20
- Issue:
- 4
- ISSN:
- 2381-6872
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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