The influence of channel geometry on the ion selectivity and ionic current rectification (ICR) of soft nanochannels was numerically investigated. The nanochannels coated with polyelectrolyte layers (PELs) are termed as soft nanochannels. Two categories of channels, asymmetric (trumpet, conical, bullet, and cigar-like) and symmetric (cylindrical), were considered in this study. When PEL is dense, the ionic partitioning effect can not be ignored. To this end, through adopting a numerical approach using the finite element method (FEM), Poisson-Nernst-Planck and Navier-Stokes equations were solved at steady-state conditions by considering different values of permittivity, diffusivity, and dynamic viscosity for the PEL and the electrolyte. The model findings were verified by comparing them with the existing simulation data. For the cylindrical type nanochannels, the results indicate that the rectification factor is approximately equal to unity, and the ion selectivity at positive voltages is approximately equal to that at negative voltages. For other geometries, the ion selectivity factor of the channel was ${\mathrm{S}}_{\text{Trumpet}}>{\mathrm{S}}_{\text{Conical}}>{\mathrm{S}}_{\text{Bullet}}>{\mathrm{S}}_{\text{Cigar}}$. On the other hand, at low bulk concentrations, the rectification factor was ${\mathrm{R}}_{{\mathrm{f}}_{\text{Cigar}}}>{\mathrm{R}}_{{\mathrm{f}}_{\text{Bullet}}}>{\mathrm{R}}_{{\mathrm{f}}_{\text{Conical}}}>{\mathrm{R}}_{{\mathrm{f}}_{\text{Trumpet}}}$, while at high bulk concentrations, it was ${\mathrm{R}}_{{\mathrm{f}}_{\text{Bullet}}}>{\mathrm{R}}_{{\mathrm{f}}_{\text{Cigar}}}>{\mathrm{R}}_{{\mathrm{f}}_{\text{Conical}}}>{\mathrm{R}}_{{\mathrm{f}}_{\text{Trumpet}}}$. Considering a charge density of $80\text{mol}/{\mathrm{m}}^3$ and a bulk concentration of $20\text{mM}$, we demonstrate that the rectification factors for the bullet and trumpet types nanochannels, from $3.35\text{and}0.56$ by ignoring the ion partitioning effect, can reach the values of $5.78$ and $0.83$ by considering the ion partitioning effect, respectively.

数值研究了通道几何形状对软纳米通道的离子选择性和离子电流整流（ICR）的影响。涂有聚电解质层 (PEL) 的纳米通道称为软纳米通道。本研究考虑了两类通道，不对称（喇叭形、圆锥形、子弹形和雪茄形）和对称（圆柱形）。当 PEL 密集时，离子分配效应不可忽视。为此，通过采用有限元法 (FEM) 的数值方法，通过考虑 PEL 的不同介电常数、扩散系数和动态粘度值，在稳态条件下求解 Poisson-Nernst-Planck 和 Navier-Stokes 方程和电解质。通过将模型结果与现有模拟数据进行比较来验证模型结果。对于圆柱型纳米通道，结果表明整流因子近似等于1，正电压下的离子选择性近似等于负电压下的离子选择性。对于其他几何形状，通道的离子选择性因子为${\mathrm{秒}}_{\text{喇叭}}>{\mathrm{秒}}_{\text{锥}}>{\mathrm{秒}}_{\text{子弹}}>{\mathrm{秒}}_{\text{雪茄}}$. 另一方面，在低体积浓度下，整流因子为${\mathrm{电阻}}_{{\mathrm{F}}_{\text{雪茄}}}>{\mathrm{电阻}}_{{\mathrm{F}}_{\text{子弹}}}>{\mathrm{电阻}}_{{\mathrm{F}}_{\text{锥}}}>{\mathrm{电阻}}_{{\mathrm{F}}_{\text{喇叭}}}$，而在高体积浓度下，它是 ${\mathrm{电阻}}_{{\mathrm{F}}_{\text{子弹}}}>{\mathrm{电阻}}_{{\mathrm{F}}_{\text{雪茄}}}>{\mathrm{电阻}}_{{\mathrm{F}}_{\text{锥}}}>{\mathrm{电阻}}_{{\mathrm{F}}_{\text{喇叭}}}$. 考虑电荷密度$80\text{摩尔}/{\mathrm{米}}^3$ 和大量浓度 $20\text{毫米}$，我们证明了子弹型和喇叭型纳米通道的整流因子，从 $3.35\text{和}0.56$ 通过忽略离子分配效应，可以达到 $5.78$ 和 $0.83$ 分别考虑离子分配效应。