Redox flow batteries with flow field designs have been demonstrated to boost their capacities to deliver high current density and power density in medium and large-scale energy storage applications. Nevertheless, the fundamental mechanisms involved with improved current density in flow batteries with serpentine flow field designs have been not fully understood. Here we report a three-dimensional model of a serpentine flow field over a porous carbon electrode to examine the distributions of pressure driven electrolyte flow penetrations into the porous carbon electrodes. We also estimate the maximum current densities associated with stoichiometric availability of electrolyte reactant flow penetrations through the porous carbon electrodes. The results predict reasonably well observed experimental data without using any adjustable parameters. This fundamental work on electrolyte flow distributions of limiting reactant availability will contribute to a better understanding of limits on electrochemical performance in flow batteries with serpentine flow field designs and should be helpful to optimizing flow batteries.