Numerical Modelling of Membrane-Less Capillary-Driven Flow-Batteries
Authors: Sadeghi Pardis , Ibrahim Omar , Kjeang Erik 
Published: December 2020

Rapid diagnostic electronic kits (RDKs) are increasingly being used all around the world for preliminary and/or emergency screening [1]. In addition to their low price, such kits can provide lab-quality results within minutes rather than days. Currently, point-of-care (POC) kits are powered by lithium button cells. Although these batteries are very reliable, the chemicals which are used to extract lithium from raw minerals can pollute local aquifers and thereby potentially poison nearby communities. There are also environmental concerns when kits powered by such batteries are disposed of. Consequently, there is an urgent need for new battery technologies which can mitigate these environmental concerns. In recent years, flow-batteries have emerged as a viable option for single-use applications. Among different alternatives, membrane-less capillary-driven flow-batteries are a promising solution, given that they can be fabricated exclusively from biodegradable materials. A paper-based, biodegradable flow-battery using quinone redox couples has already been designed and prototyped by Esquivel et al. [2]. Figure 1 schematically shows the architecture of this novel flow-battery called PowerPAD. The reactants are seen to enter the porous electrodes of this flow battery in the vertical direction and exit the electrodes in the same direction. The waste is then collected by an absorbent pad which is also responsible for maintaining the required flow rate through capillary forces. The power output of this flow battery is well within the reach of many POC kits. However, for such batteries to be considered as a viable replacement to conventional lithium batteries, their operational performance and power-density should be further enhanced. The power-density of a given redox flow battery can be enhanced through optimizing its electrode materials, reactant electrolytes, or cell architecture. For capillary-flow batteries, the material used for the absorbent pad or the cellulose paper can also be tuned for this purpose. The objective of the present work is to investigate the possibility of enhancing the power output of capillary-flow batteries through modifying their flow architecture. A numerical model is used for this purpose based on the microfluidic fuel cell mathematical model developed by Krishnamurthy et al. [3], featuring electrochemical kinetics in flow-through porous electrodes. For ease of comparing different flow architectures, the laminar flow is assumed to be quasi-steady and pressure-driven. This approach enables numerical determination of pressure drop in the cell for a wide range of flow rates, which can be correlated to the design of absorbent pad. Figure 1 shows the three flow cell architectures considered for the analysis in this work. They can be classified as “vertical-flow” design, “horizontal-flow” design, and “mixed-flow” design. The first architecture has already been used in [2] while the other two designs are new. It is speculated that the new designs can improve cell’s performance by giving the reactants more time to reach the surface of carbon fibers for the reactions to take place. To simulate the energy conversion performance of these designs, we rely on COMSOL Multiphysics software. The software first solves the fluid-flow equations to provide us with pressure drop and velocity field. The velocity field is then used in the mass-transport equation which is coupled with the electrochemical equations through Butler-Volmer equation. An iteration method is then used to compute the concentration and local current density fields. The results are finally expressed in terms of polarization curves. Due to the qualitative nature of the present work, we have decided to use vanadium species dissolved in sulfuric acid in our study. To be able to verify our numerical scheme with published data, the same geometrical and electrochemical parameters, and also the same carbon-fiber electrode (Toray TGP-H 120) as used in [3] have been used in this study. Our numerical results show that the original “vertical-flow” design used in [2] is not optimized. It is predicted that horizontal-flow design enhances the power-density of this flow battery by roughly 30% while the mixed-flow design is predicted to have the opposite effect. The good energy-converting performance of the horizontal design together with its higher fuel utilization efficiency can be attributed to its higher “mass transport coefficient”. This is not surprising realizing the fact that the Reynolds number of the horizontal design is larger than the vertical and mixed designs. However, it should be noted that, the cell’s pressure drop is roughly doubled for the horizontal design suggesting that it needs a better pad material to compensate for the extra pressure drop. All in all, it is concluded that cell flow architecture can be used as a powerful tool to enhance the power output of membrane-less capillary-driven flow-batteries.

Figure 1