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Publication Date



UM campus only

Embargo Period


Degree Type


Degree Name

Doctor of Philosophy (PHD)


Mechanical Engineering (Engineering)

Date of Defense


First Committee Member

Hongtan Liu

Second Committee Member

Weiyong Gu

Third Committee Member

Xiangyang Zhou

Fourth Committee Member

Gang Wang


Fuel cell and flow battery are two most important promising energy devices in the future. Gas/Liquid Diffusion layer (GDL/LDL) as porous medium are widely used in fuel cells and flow batteries to transport reactants to the catalyst easily and uniformly, remove excess products, provide the electronic path, prevent the catalyst layer from degradation. Manufacture methods, surface treatment, compression ratio, degradation conditions of GDL/LDL affect the performance significantly. Permeability and inertial coefficient are two important parameters for GDL/LDL, since they directly relate the fluid velocity to the pressure difference in the porous medium. Permeability is usually measured and evaluated for different GDL/LDLs, but the inertial coefficient is rarely measured and studied. Darcy’s law is the most commonly used to describe the fluid transport inside the porous medium, but the inertial effect is neglected. This neglect of the inertial effect can cause large errors, especially under high flow rate. An additional Forchheimer term is added to Darcy’s law to take consideration of the inertial effect, so a modified Darcy’s law can be obtained. Normally, modeling results and experimental results are compared by either pressure drops or pumping power to check the accuracy of Darcy’s law and modified Darcy’s law, and then the under-land cross-flow rates between two adjacent channels are predicted. In this work, first, the effective permeability and inertial coefficient of GDL/LDL are measured under different flow fields. The experimental results show that the land width has a significant effect on the permeability, when the land width is no more than 2 mm, and the inertial coefficient decreases with increase of the land width. The experimental results also show that using Darcy’s law to determine the effective permeability can cause up to 48% error. Second, analytical models for under-land cross-flow rate are developed based on both Darcy’s law and modified Darcy’s law and the models are solved analytically to obtain closed-form solutions. It is the first time that the modeling results and experimental data of under-land cross-flow rates are compared. The modeling and experimental results show that Darcy’s law can causes significant errors in pressure drops and under-land cross-flow rates under some conditions. When the fluid flow in porous media for fuel cells with serpentine flow fields is modeled with modified Darcy’s law instead of Darcy’s law, the average error of pressure drop can be reduced from 24% to less than 11%, and the average error of under-land cross-flow rate can be reduced from 24% to less than 3%. Third, non-dimensional analyses have been performed using both the Pi-Theorem and the analytical models developed. By comparing the coefficients of each term of two models, two independent Pi terms for the under-land cross-flow rate error are obtained. Analyses of the variations of Darcy’s law error with the two Pi-terms result in simple criteria for applicability of Darcy’s law for serpentine flow fields under different accuracy requirements.


PEM Fell Cell; Darcy's Law; Gas Diffusion Layer; Under-land Cross-flow; Dimensional Analyses

Available for download on Thursday, April 30, 2020