Error of Darcy's law for serpentine flow fields: Dimensional analysis

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.