Cubic-like Features of I–V Relations via Classical Poisson–Nernst–Planck Systems Under Relaxed Electroneutrality Boundary Conditions
Abstract
1. Introduction
1.1. Poisson–Nernst– Planck Model for Ionic Flows
1.2. Electroneutrality Boundary Conditions vs. Boundary Layers
2. Mathematical Methods
2.1. Previous Results and Assumptions
2.2. Approximation of as
3. Results
- (i)
- has three distinct real roots if one of the following conditions holds:
- (i1)
- ;
- (i2)
- and ;
- (i3)
- and ;
- (i4)
- ;
- (i5)
- ;
- (i6)
- .
- (ii)
- has a unique real root with multiplicity 3 if one the the following conditions holds:
- (ii1)
- and ;
- (ii2)
- and ;
- (ii3)
- ;
- (ii4)
- ;
- (ii5)
- .
4. Discussion
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
PNP | Poisson–Nernst–Planck |
I–V | Current–voltage |
Appendix A
- Inner solution expansions
- –
- Zeroth order inner solution expansions
- *
- At the boundary with
- *
- At the boundary with ,
- –
- First order inner solution expansion
- *
- At the boundary
- *
- At the boundary ,
- Outer solution expansions
- –
- Zeroth order outer solution expansion
- –
- First order outer solution expansion
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Li, H.; Li, Z.; Pan, C.; Song, J.; Zhang, M. Cubic-like Features of I–V Relations via Classical Poisson–Nernst–Planck Systems Under Relaxed Electroneutrality Boundary Conditions. Axioms 2024, 13, 790. https://doi.org/10.3390/axioms13110790
Li H, Li Z, Pan C, Song J, Zhang M. Cubic-like Features of I–V Relations via Classical Poisson–Nernst–Planck Systems Under Relaxed Electroneutrality Boundary Conditions. Axioms. 2024; 13(11):790. https://doi.org/10.3390/axioms13110790
Chicago/Turabian StyleLi, Hong, Zhantao Li, Chaohong Pan, Jie Song, and Mingji Zhang. 2024. "Cubic-like Features of I–V Relations via Classical Poisson–Nernst–Planck Systems Under Relaxed Electroneutrality Boundary Conditions" Axioms 13, no. 11: 790. https://doi.org/10.3390/axioms13110790
APA StyleLi, H., Li, Z., Pan, C., Song, J., & Zhang, M. (2024). Cubic-like Features of I–V Relations via Classical Poisson–Nernst–Planck Systems Under Relaxed Electroneutrality Boundary Conditions. Axioms, 13(11), 790. https://doi.org/10.3390/axioms13110790