The electroosmotic flow (EOF) and ion transport within a hydrophobic conical nanopore connecting reservoirs are studied numerically. The ion transport equation is modified to consider the ion steric effect for a finite ion size. The continuum-based model compiled with the modified Poisson–Nernst–Planck and Navier–Stokes equations are adopted for analyzing the hydrodynamics and electric field. The governing equations in their full form are solved in a coupled manner through a control volume approach over a nonuniform staggered grid arrangement. Analytic solutions for the EOF in the hydrophobic nanopore with large membrane thickness is obtained by including the volume exclusion effects in the electrochemical potential of the ionic species. The analytic solutions are obtained by considering the steric interactions based on either the Bikerman model or the Carnahan-Starling (CS) model. However, the numerical solutions are presented based on the CS model for steric interactions. The present numerical results for the hydrophobic nanopore with large pore length are validated with these analytic solutions and existing correlations based on experimental data. The fluid slip at the pore surface modifies the nanopores electrokinetic characteristics by modifying the convective transport of fluid and ions. We have elucidated the impact of pore hydrophobicity and ion steric interactions on the EOF, ionic current, ion concentration polarization (ICP) and ion selectivity when the pore length is considered to be in the order of the pore radius. The effect of pore length on the electrokinetics in the hydrophobic nanopore is also analyzed. Our numerical solution for large pore length merged with the analytic expression for the EOF in the hydrophobic nanopore of length much higher than the radius. Hydrophobicity creates significant enhancement in EOF and the rate of EOF augmentation is higher for the thinner Debye length. The perm-selectivity performance of the nanopore is enhanced when the wall is considered to be hydrophobic. The steric interactions of ions create an enhancement in EOF, ion selectivity, and ICP. The pore hydrophobicity diminishes the impact of these steric interactions.

数值研究了疏水圆锥形纳米孔连接储层内的电渗流（EOF）和离子迁移。修改离子传输方程，以考虑有限离子尺寸的离子空间效应。采用修正的Poisson-Nernst-Planck方程和Navier-Stokes方程编译的基于连续体的模型来分析流体动力学和电场。完整形式的控制方程是通过非均匀交错网格布置上的控制体积方法以耦合方式求解的。通过将体积排阻效应纳入离子物种的电化学势中，可以获得具有较大膜厚度的疏水纳米孔中EOF的解析溶液。通过考虑基于Bikerman模型或Carnahan-Starling（CS）模型的空间相互作用来获得解析解。然而，基于CS模型的空间相互作用提出了数值解。这些解析溶液和现有的相关性基于实验数据验证了具有大孔径的疏水性纳米孔的数值结果。孔表面的流体滑移通过改变流体和离子的对流传输来改变纳米孔的电动特性。我们已经阐明了当孔长按孔半径的顺序排列时，孔疏水性和离子空间相互作用对EOF，离子电流，离子浓度极化（ICP）和离子选择性的影响。还分析了孔长对疏水纳米孔中电动动力学的影响。我们的大孔径数值解与EOF在长度远大于半径的疏水纳米孔中的解析表达式相结合。疏水性使EOF显着增强，并且Debye长度越薄，EOF的增加速率就越高。当壁被认为是疏水的时，纳米孔的渗透选择性性能得到增强。离子的空间相互作用可增强EOF，离子选择性和ICP。孔疏水性减小了这些空间相互作用的影响。疏水性使EOF显着增强，并且Debye长度越薄，EOF的增加速率就越高。当壁被认为是疏水的时，纳米孔的渗透选择性性能得到增强。离子的空间相互作用可增强EOF，离子选择性和ICP。孔疏水性减小了这些空间相互作用的影响。疏水性使EOF显着增强，并且Debye长度越薄，EOF的增加速率就越高。当壁被认为是疏水的时，纳米孔的渗透选择性性能得到增强。离子的空间相互作用可增强EOF，离子选择性和ICP。孔疏水性减小了这些空间相互作用的影响。