ION TRANSPORT IN DIPOLAR MEDIUM I: A LOCAL DIELECTRIC POISSON--NERNST--PLANCK/POISSON--BOLTZMANN MODEL

被引：0
作者：
Gui, Sheng [1 ,2 ]
Lu, Benzhuo [1 ,2 ]
Yu, Weilin [3 ,4 ]
机构：
[1] Chinese Acad Sci, Acad Math & Syst Sci, LSEC, NCMIS, Beijing 100190, Peoples R China
[2] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
[3] Jiangxi Normal Univ, Sch Math & Stat, Nanchang 330022, Jiangxi, Peoples R China
[4] Jiangxi Normal Univ, Jiangxi Prov Ctr Appl Math, Nanchang 330022, Jiangxi, Peoples R China
来源：
SIAM JOURNAL ON APPLIED MATHEMATICS | 2024年 / 84卷 / 05期
基金：
中国博士后科学基金; 中国国家自然科学基金;
关键词：
dipolar media; local dielectric Poisson-Nernst-Planck (LDPNP) model; local dielectric Poisson--Boltzmann (LDPB) model; PLANCK EQUATIONS; ELECTROSTATIC PROPERTIES; COMPUTER-SIMULATIONS; MOLECULAR-DYNAMICS; POTASSIUM CHANNEL; CYTOCHROME-C; WATER; CONSTANT; RELAXATION; CHARGE;
D O I：
10.1137/24M1633959
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, an energetic variational method is employed to derive a set of ion transportation and electrostatic models of general electrolyte solution with a locally and mathematically rigorously determined dielectric permittivity of the dipolar solvent under certain assumptions. The model could be called the local dielectric Poisson--Nernst--Planck (LDPNP)/Poisson--Boltzmann (LDPB) model, which couples the Poisson--Nernst--Planck and Poisson--Boltzmann equations with a novel moment equation of dipolar molecules. A feature of this new model is that the system consistently determines the dipole moment distribution, thereby the local dielectric permittivity of the ionic aqueous solution, whereas this information is lacking and a constant assumption is usually adopted for the dielectric permittivity in traditional PNP simulations. We investigate the energy dissipation law of the derived LDPNP equations. For a planar bounded radially symmetric domain, we prove the existence and uniqueness of the equilibrium solution of LDPNP equations.
引用
收藏
页码：2110 / 2131
页数：22
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