A serpentine flow field is commonly used in both fuel cells and redox flow batteries. Accurate prediction of mass transfer in the porous gas/liquid diffusion layer (GDL/LDL) is essential for both flow field design optimization and pressure drop predictions. Darcy's law has been widely used to predict fluid flow through GDL/LDL in fuel cells and flow batteries. However, since the inertial effect is neglected in the Darcy's law, significant errors can arise when it is applied to serpentine flow fields. In this work, dimensional analyses are performed using both the Buckingham Pi-theorem and the analytical models developed earlier based on Darcy's law and modified Darcy's law. From the Pi-theorem, four and five non-dimensional parameters are obtained from the Darcy's law and the modified Darcy's law, respectively. The variations of Darcy's law errors in predicting under-land cross-flow rate with each of the non-dimensional parameters are studied. By comparing the coefficient of each term of the two models, two independent Pi-terms for under-land cross-flow rate are obtained. The criterion for applicability of Darcy's law is developed based on the two Pi-terms. The model predicted errors of Darcy's law compared very well with experimental data, thus further confirms the applicability of developed criterion.

蛇形流场通常用于燃料电池和氧化还原液流电池中。准确预测多孔气体/液体扩散层（GDL / LDL）中的传质对于流场设计优化和压降预测都至关重要。达西定律已被广泛用于预测燃料电池和液流电池中通过GDL / LDL的流体流量。但是，由于达西定律忽略了惯性效应，因此将其应用于蜿蜒的流场时可能会产生明显的误差。在这项工作中，使用白金汉Pi定理和较早基于达西定律和修改后的达西定律开发的分析模型进行了尺寸分析。根据Pi定理，分别从达西定律和修正的达西定律中获得四个和五个无量纲参数。研究了用每个无量纲参数预测地下横流速率时达西定律误差的变化。通过比较两个模型各项的系数，得出了两个独立的Pi项，用于地下交叉流率。达西定律的适用标准是根据两个Pi项制定的。该模型预测的达西定律误差与实验数据相比具有很好的一致性，从而进一步证实了开发标准的适用性。的定律是根据两个Pi项制定的。该模型预测的达西定律误差与实验数据相比具有很好的一致性，从而进一步证实了开发标准的适用性。的定律是根据两个Pi项制定的。该模型预测的达西定律误差与实验数据相比具有很好的一致性，从而进一步证实了开发标准的适用性。