Concentrated Solution Model of Transport in All Vanadium Redox Flow Battery Membrane Separator
In order to optimize and improve the VRFB performance; mathematical modeling can be utilized. A good review of these modeling studies has been reported by A. Z. Weber et al. . In general, the models developed are based on approaches adopted from polymer electrolyte fuel cell modeling and have common assumptions. In all of these models the dilute solution approximation has been utilized for species transport in the electrolyte. Therefore, the motivation for this work is to develop a performance model for VRFBs based on a comprehensive description of mass, charge energy and momentum transport and conservation with concentrated solution theory.
Concentrated solution theory has its basis in irreversible thermodynamics and Maxwell-Stefan diffusion . Solute-solute interactions are included and the theory accounts for transport by diffusion, migration and electrosmotic drag without the need for viscous- or pressure-driven terms. For ion-exchange membranes, since the distinction between solute and solvent is unclear, it is necessary to apply the concentrated solution theory for modeling studies . The equations for material balance, current flow, and electroneutrality remain valid for concentrated solutions, but the flux equation requires modification .
A comprehensive review of mathematical modeling of electrokinetics in a concentrated solution has been provided by Bazant et al. .
Also, detailed model validation is important to ensure veracity of the model assumptions and formulation. Besides charge/discharge cycle validation, we will discuss two additional techniques which provide through-plane and in-plane resolution for detailed model validation. In the first technique, an in-situ local potential measurement using micro potential probes were prepared with Pt materials and the local redox potential measurement was conducted by inserting these probes among multiple layers of carbon paper electrode. This technique was applied by Q. Liu et al. for the positive side of VRFBs . In the second technique, an in-situ methodology will be introduced where the in-plane current distribution using a printed circuit board has been obtained in an operating VRFB. Together these approaches provide much greater detail for model validation than just charge-discharge curves typically used.
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