Rechargeable redox flow batteries with serpentine flow field designs have been demonstrated to deliver higher current density and power density in medium and large-scale stationary energy storage applications. Nevertheless, the fundamental mechanisms involved with improved current density in flow batteries with flow field designs have not been understood. Here we report a maximum current density concept associated with stoichiometric availability of electrolyte reactant flow penetration through the porous electrode that can be achieved in a flow battery system with a "zero-gap"serpentine flow field architecture. This concept can explain a higher current density achieved within allowing reactions of all species soluble in the electrolyte. Further validations with experimental data are confirmed by an example of a vanadium flow battery with a serpentine flow structure over carbon paper electrode.