Variational multiscale models for charge transport.
Variational multiscale models for charge transport.
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DOI：
10.1137/110845690
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Xia K
中科院分区：
文献类型：
--
作者：
Wei GW;Zheng Q;Chen Z;Xia K
这项工作提出了一些复杂的物理、化学和生物系统和工程设备（如燃料电池、太阳能电池、电池、纳米流体、晶体管和离子通道）中电荷输运的变分多尺度模型。早期的一篇论文（Bulletin of Mathematical Biology, 72, 1562-1622, 2010）介绍了当前模型的一个重要组成部分，即利用曲面的微分几何理论作为一种自然手段，从几何上分离宏观领域和微观领域，同时动态耦合离散和连续体描述。我们的主要策略是构建包含极性和非极性溶剂化自由能以及化学势相关能的电荷输运系统的总能量泛函。利用欧拉-拉格朗日变分，导出了Laplace-Beltrami和泊松-能斯特-普朗克（LB-PNP）耦合方程。LB-PNP方程的解导致了总自由能的最小化，以及静电势和电荷密度的显式分布。为了进一步降低计算复杂度，利用泊松-玻尔兹曼（PB）方程得到的玻尔兹曼分布来表示某些电荷种的密度，从而避免了某些能思-普朗克（NP）方程的计算开销。因此，提出了非均相系统中电荷输运的拉普拉斯-贝尔特拉米和泊松-玻尔兹曼-能斯特-普朗克耦合方程。本公式的一个主要重点是平衡LB-PB理论和非平衡LB-PNP理论在平衡状态下的一致性。另一个重点是简化LB-PBNP模型在非平衡设置下完全恢复LB-PNP模型预测的能力。为了解释流体对电荷输运的影响，我们从化学-电-流体系统的变分原理推导出耦合的拉普拉斯-贝尔特拉米方程、泊松-能-普朗克方程和纳维-斯托克斯方程。为了有效地实现所提出的新变分多尺度模型，开发了许多计算算法。使用一组10个蛋白质分子和一个现实的离子通道Gramicidin A来确认一致性和验证能力。设计了大量的数值实验来验证所提出的变分多尺度模型。我们的模型预测和实验测量的电流-电压曲线在Gramicidin A通道输运中有很好的定量一致性。本文还提供了该领域的简要回顾。
This work presents a few variational multiscale models for charge transport in complex physical, chemical and biological systems and engineering devices, such as fuel cells, solar cells, battery cells, nanofluidics, transistors and ion channels. An essential ingredient of the present models, introduced in an earlier paper (Bulletin of Mathematical Biology, 72, 1562-1622, 2010), is the use of differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain from the microscopic domain, meanwhile, dynamically couple discrete and continuum descriptions. Our main strategy is to construct the total energy functional of a charge transport system to encompass the polar and nonpolar free energies of solvation, and chemical potential related energy. By using the Euler-Lagrange variation, coupled Laplace-Beltrami and Poisson-Nernst-Planck (LB-PNP) equations are derived. The solution of the LB-PNP equations leads to the minimization of the total free energy, and explicit profiles of electrostatic potential and densities of charge species. To further reduce the computational complexity, the Boltzmann distribution obtained from the Poisson-Boltzmann (PB) equation is utilized to represent the densities of certain charge species so as to avoid the computationally expensive solution of some Nernst-Planck (NP) equations. Consequently, the coupled Laplace-Beltrami and Poisson-Boltzmann-Nernst-Planck (LB-PBNP) equations are proposed for charge transport in heterogeneous systems. A major emphasis of the present formulation is the consistency between equilibrium LB-PB theory and non-equilibrium LB-PNP theory at equilibrium. Another major emphasis is the capability of the reduced LB-PBNP model to fully recover the prediction of the LB-PNP model at non-equilibrium settings. To account for the fluid impact on the charge transport, we derive coupled Laplace-Beltrami, Poisson-Nernst-Planck and Navier-Stokes equations from the variational principle for chemo-electro-fluid systems. A number of computational algorithms is developed to implement the proposed new variational multiscale models in an efficient manner. A set of ten protein molecules and a realistic ion channel, Gramicidin A, are employed to confirm the consistency and verify the capability. Extensive numerical experiment is designed to validate the proposed variational multiscale models. A good quantitative agreement between our model prediction and the experimental measurement of current-voltage curves is observed for the Gramicidin A channel transport. This paper also provides a brief review of the field.
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DOI：
10.1002/cnm.1458
发表时间：
2012-01
影响因子：
2.1
作者：
Chen D;Chen Z;Wei GW
通讯作者：
Wei GW
影响因子：
3.4
作者：
Cárdenas, AE;Coalson, RD;Kurnikova, MG
通讯作者：
Kurnikova, MG
影响因子：
3.2
作者：
Andrei, P;Mayergoyz, I
通讯作者：
Mayergoyz, I
影响因子：
12.6
作者：
Belgrader, P;Okuzumi, M;Northrup, MA
通讯作者：
Northrup, MA
影响因子：
10.8
作者：
Burch, Damian;Bazant, Martin Z.
通讯作者：
Bazant, Martin Z.