Mathematical Analysis on Current–Voltage Relations via Classical Poisson–Nernst–Planck Systems with Nonzero Permanent Charges under Relaxed Electroneutrality Boundary Conditions
We focus on a quasi-one-dimensional Poisson–Nernst–Planck model with small permanent charges for ionic flows of two oppositely charged ion species through an ion channel. Of particular interest is to examine the dynamics of ionic flows in terms of I–V (current–voltage) relations with boundary layers...
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MDPI AG
2023-01-01
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| Series: | Membranes |
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| Online Access: | https://www.mdpi.com/2077-0375/13/2/131 |
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| author | Yiwei Wang Lijun Zhang Mingji Zhang |
| author_facet | Yiwei Wang Lijun Zhang Mingji Zhang |
| author_sort | Yiwei Wang |
| collection | DOAJ |
| description | We focus on a quasi-one-dimensional Poisson–Nernst–Planck model with small permanent charges for ionic flows of two oppositely charged ion species through an ion channel. Of particular interest is to examine the dynamics of ionic flows in terms of I–V (current–voltage) relations with boundary layers due to the relaxation of neutral conditions on boundary concentrations. This is achieved by employing the regular perturbation analysis on the solutions established through geometric singular perturbation analysis. Rich dynamics are observed, particularly, the nonlinear interplays among different physical parameters are characterized. Critical potentials are identified, which play critical roles in the study of ionic flows and can be estimated experimentally. Numerical simulations are performed to further illustrate and provide more intuitive understandings of our analytical results. |
| first_indexed | 2024-03-11T08:27:53Z |
| format | Article |
| id | doaj.art-e6efc5e07c5e4326b6d3d9a814d49707 |
| institution | Directory Open Access Journal |
| issn | 2077-0375 |
| language | English |
| last_indexed | 2024-03-11T08:27:53Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Membranes |
| spelling | doaj.art-e6efc5e07c5e4326b6d3d9a814d497072023-11-16T22:01:47ZengMDPI AGMembranes2077-03752023-01-0113213110.3390/membranes13020131Mathematical Analysis on Current–Voltage Relations via Classical Poisson–Nernst–Planck Systems with Nonzero Permanent Charges under Relaxed Electroneutrality Boundary ConditionsYiwei Wang0Lijun Zhang1Mingji Zhang2College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaWe focus on a quasi-one-dimensional Poisson–Nernst–Planck model with small permanent charges for ionic flows of two oppositely charged ion species through an ion channel. Of particular interest is to examine the dynamics of ionic flows in terms of I–V (current–voltage) relations with boundary layers due to the relaxation of neutral conditions on boundary concentrations. This is achieved by employing the regular perturbation analysis on the solutions established through geometric singular perturbation analysis. Rich dynamics are observed, particularly, the nonlinear interplays among different physical parameters are characterized. Critical potentials are identified, which play critical roles in the study of ionic flows and can be estimated experimentally. Numerical simulations are performed to further illustrate and provide more intuitive understandings of our analytical results.https://www.mdpi.com/2077-0375/13/2/131PNPpermanent chargesI–V relationscritical potentialsboundary layers |
| spellingShingle | Yiwei Wang Lijun Zhang Mingji Zhang Mathematical Analysis on Current–Voltage Relations via Classical Poisson–Nernst–Planck Systems with Nonzero Permanent Charges under Relaxed Electroneutrality Boundary Conditions Membranes PNP permanent charges I–V relations critical potentials boundary layers |
| title | Mathematical Analysis on Current–Voltage Relations via Classical Poisson–Nernst–Planck Systems with Nonzero Permanent Charges under Relaxed Electroneutrality Boundary Conditions |
| title_full | Mathematical Analysis on Current–Voltage Relations via Classical Poisson–Nernst–Planck Systems with Nonzero Permanent Charges under Relaxed Electroneutrality Boundary Conditions |
| title_fullStr | Mathematical Analysis on Current–Voltage Relations via Classical Poisson–Nernst–Planck Systems with Nonzero Permanent Charges under Relaxed Electroneutrality Boundary Conditions |
| title_full_unstemmed | Mathematical Analysis on Current–Voltage Relations via Classical Poisson–Nernst–Planck Systems with Nonzero Permanent Charges under Relaxed Electroneutrality Boundary Conditions |
| title_short | Mathematical Analysis on Current–Voltage Relations via Classical Poisson–Nernst–Planck Systems with Nonzero Permanent Charges under Relaxed Electroneutrality Boundary Conditions |
| title_sort | mathematical analysis on current voltage relations via classical poisson nernst planck systems with nonzero permanent charges under relaxed electroneutrality boundary conditions |
| topic | PNP permanent charges I–V relations critical potentials boundary layers |
| url | https://www.mdpi.com/2077-0375/13/2/131 |
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