Although nanochannels in tortuous shape exhibit unusual transportational characteristics, the traditional theoretical analysis of nanofluidics in such kinds of systems remains challenging, partly due to their complicated boundary description. In this paper, by developing a curvilinear coordinate system for such tortuous nanochannels, we solve the electrostatic Poisson–Boltzmann equation analytically for a two-dimensional nanochannel, with its effectiveness confirmed through numerical calculation. The influences of the geometric profile on the distribution of electric potential, ionic concentration, and surface charge on channel walls are quantitatively evaluated in a facilitated way in terms of the curvilinear coordinates introduced. Such a technique can be widely applied to many nanofluidic systems in curved channels.

尽管曲折形状的纳米通道表现出不寻常的传输特性，但对此类系统中纳米流体的传统理论分析仍然具有挑战性，部分原因在于其复杂的边界描述。在本文中，通过为这种曲折的纳米通道开发曲线坐标系，我们对二维纳米通道的静电泊松-玻尔兹曼方程进行解析求解，并通过数值计算证实了其有效性。根据引入的曲线坐标，以方便的方式定量评估几何轮廓对通道壁上的电势、离子浓度和表面电荷分布的影响。这种技术可以广泛应用于弯曲通道中的许多纳米流体系统。