Poisson–Nernst–Planck (PNP) model has been extensively used for the study of channel flow under the influence of electrochemical gradients. PNP theory is a continuum description of ion flow where ionic distributions are described in terms of concentrations. Nonionic interparticle interactions are not considered in this theory as in continuum framework, their impact on the solution is minimal. This theory holds true for dilute flows or flows where channel radius is significantly larger than ion radius. However, for ion channel flows, where channel dimensions and ionic radius are of similar magnitude, nonionic interactions, particularly related to the size of the ions (steric effect), play an important role in defining the selectivity of the channel, concentration distribution of ionic species, and current across the channel, etc. To account for the effect of size of ions, several modifications to PNP equations have been proposed. One such approach is the introduction of Lennard-Jones potential to the energy variational formulation of PNP system. This study focuses on understanding the role of steric effect on flow properties. To discretize the system, Lattice Boltzmann method has been used. The system is defined by modified PNP equations where the steric effect is described by Lennard-Jones potential. In addition, boundary conditions for the complex channel geometry have been treated using immersed boundary method.

中文翻译：

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使用浸入式边界格子 Boltzmann 方法求解离子通道流。

Poisson-Nernst-Planck (PNP) 模型已广泛用于研究电化学梯度影响下的通道流动。PNP 理论是对离子流的连续描述，其中离子分布是根据浓度来描述的。在该理论中不考虑非离子粒子间相互作用，因为在连续框架中，它们对解决方案的影响很小。该理论适用于稀流或通道半径明显大于离子半径的流。然而，对于离子通道流动，通道尺寸和离子半径具有相似的幅度，非离子相互作用，特别是与离子大小（空间效应）相关的非离子相互作用，在定义通道的选择性、离子浓度分布方面起着重要作用。物种，以及穿过海峡的电流等。为了考虑离子大小的影响，已经提出了对 PNP 方程的几种修改。其中一种方法是将 Lennard-Jones 势引入 PNP 系统的能量变分公式。本研究侧重于了解空间效应对流动特性的作用。为了离散化系统，已使用格子玻尔兹曼方法。该系统由修正的 PNP 方程定义，其中空间效应由 Lennard-Jones 势描述。此外，复杂通道几何的边界条件已使用浸入边界方法处理。本研究侧重于了解空间效应对流动特性的作用。为了离散化系统，已使用格子玻尔兹曼方法。该系统由修正的 PNP 方程定义，其中空间效应由 Lennard-Jones 势描述。此外，复杂通道几何的边界条件已使用浸入边界方法处理。本研究侧重于了解空间效应对流动特性的作用。为了离散化系统，已使用格子玻尔兹曼方法。该系统由修正的 PNP 方程定义，其中空间效应由 Lennard-Jones 势描述。此外，复杂通道几何的边界条件已使用浸入边界方法处理。