论文标题
在Poisson-Nernst-Nernst-Nernst-Planck-Bikermann模型的平衡上，配备了空间和相关效果
On the equilibrium of the Poisson-Nernst-Planck-Bikermann model equipping with the steric and correlation effects
论文作者
论文摘要
Poisson-nernst-Planck-Bikermann（PNPB）模型，其中将离子和水分子视为具有不同大小的不同物种，具有间隙空隙的物种，可以描述由Poisson-Nernst-Nernst-Planck和Poisson-Boltzmann conforsion consection the pointert-nernst-boltzmann与Pointers-nernst-boltzmann taperiory consect and the Inotial voids的变态和相关效应。在PNPB模型中，电势由四阶泊松型摩托车（4pbik）方程而不是泊松方程来控制，以便它可以描述相关效应。更重要的是，空间电势包括在离子和水通量中，以及平衡的类似费米样的分布，这些分布量化了空间效应的特征。 在这项工作中，在执行了非量化步骤之后，我们分析了4PBIK方程的四阶操作员的自我偶和性和内核。此外，我们还显示了空隙体积函数的阳性和自由能的凸度。遵循这些特性，给出了平衡中PNPB模型的良好性。此外，由于PNPB模型具有耗能的结构，因此我们采用有限的体积方案，该方案将能量消散的特性保留在半污垢水平上。之后，进行了各种数值研究，以显示空间效应对稳态的参数依赖性。
The Poisson-Nernst-Planck-Bikermann (PNPB) model, in which the ions and water molecules are treated as different species with non-uniform sizes and valences with interstitial voids, can describe the steric and correlation effects in ionic solution neglected by the Poisson-Nernst-Planck and Poisson-Boltzmann theories with point charge assumption. In the PNPB model, the electric potential is governed by the fourth-order Poisson-Bikermann (4PBik) equation instead of the Poisson equation so that it can describe the correlation effect. What's more, the steric potential is included in the ionic and water fluxes as well as the equilibrium Fermi-like distributions which characterizes the steric effect quantitatively. In this work, after doing a nondimensionalization step, we analyze the self-adjointness and the kernel of the fourth-order operator of the 4PBik equation. Also, we show the positivity of the void volume function and the convexity of the free energy. Following these properties, the well-posedness of the PNPB model in equilibrium is given. Furthermore, because the PNPB model has an energy dissipated structure, we adopt a finite volume scheme which preserves the energy dissipated property at the semi-discrete level. After that, various numerical investigations are given to show the parameter dependence of the steric effect to the steady state.
