Two‐dimensional (2D) distribution of proton exchange membrane (PEM) fuel cell cathode overpotential η in the vicinity of parabolic anode tip is described by nonlinear Poisson–Boltzmann equation. The 2d shape of η is calculated numerically for the anode tip curvature varying by two orders of magnitude. It is shown that the reference electrode for measuring cathode overpotential can be located at a distance on the order of two characteristic lengths from the anode tip. For typical PEM fuel cell parameters, this distance is about 5.5 cm. A compact design for the reference electrode positioning is suggested.

中文翻译：

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PEM燃料电池中抛物线形阳极尖端的参考电极位置

抛物线形阳极尖端附近的质子交换膜（PEM）燃料电池阴极超电势η的二维（2D）分布由非线性Poisson-Boltzmann方程描述。对于以两个数量级变化的阳极尖端曲率，数值计算出η的2d形状。示出了用于测量阴极超电势的参考电极可以位于距阳极尖端大约两个特征长度的距离处。对于典型的PEM燃料电池参数，此距离约为5.5厘米。建议用于参考电极定位的紧凑设计。