Mathematical Modeling of Electrolyte Flow Dynamic Patterns and   Volumetric Flow Penetrations in the Flow Channel over Porous Electrode   Layered System in Vanadium Flow Battery with Serpentine Flow Field Design
  In this work, a two-dimensional mathematical model is developed to study the flow patterns and volumetric flow penetrations in the flow channel over the porous electrode layered system in vanadium flow battery with serpentine flow field design. The flow distributions at the interface between the flow channel and porous electrode are examined. It is found that the non-linear pressure distributions can distinguish the interface flow distributions under the ideal plug flow and ideal parabolic flow inlet boundary conditions. However, the volumetric flow penetration within the porous electrode beneath the flow channel through the integration of interface flow velocity reveals that this value is identical under both ideal plug flow and ideal parabolic flow inlet boundary conditions. The volumetric flow penetrations under the advection effects of flow channel and landing/rib are estimated. The maximum current density achieved in the flow battery can be predicted based on the 100% amount of electrolyte flow reactant consumption through the porous electrode beneath both flow channel and landing channel. The corresponding theoretical maximum current densities achieved in vanadium flow battery with one and three layers of SGL 10AA carbon paper electrode have reasonable agreement with experimental results under a proper permeability. 
Xinyou Ke, Joseph M. Prahl, J. Iwan D. Alexander and Robert F.   Savinell
cond-mat.soft physics.flu-dyn