This modeling and experimental study quantifies and explains mass transfer rates in RFBs as a function of active species concentration, flow rate, and flow field design in a systematic fashion. Based on porous electrode theory,1we develop a steady-state, one-dimensional model to describe electrode polarization, considering losses due to the electrolyte resistivity, charge transfer, and convective mass transfer. Combining the Butler-Volmer kinetic equation, linear mass transfer relationships, Ohm’s Law and several assumptions for a model redox cell, a second-order, dimensionless, and ordinary differential equation emerges for the potential as a function of position and two dimensionless parameters. Solved numerically, the model produces a series of dimensionless plots that illustrate how the RFB electrode behaves across a range of exchange and limiting current values. For each steady-state cell polarization (I-V characteristic), the model reveals an explanatory spatial variation in overpotential and current distribution across the electrode. The dimensionless nature and reduction to two parameters enable facile curve fitting of the model to experimental polarization curves, such as shown in Figure 1.
In conjunction with the model, we implement a single electrolyte diagnostic flow cell technique,2 with an iron chloride electrolyte, to probe the polarization performance as a function of the aforementioned experimental parameters. Quantitative mass transfer coefficients (km) are extracted by fitting the two model parameters to experimental polarization curves, and the only additional experimental data required is the electrolyte conductivity. In this work, power-law proportionalities between mass transfer coefficient and electrolyte velocity are revealed for 4 flow field types: flow through (FTFF), interdigitated (IDFF), parallel (PFF), and serpentine (SFF).
Quantifying mass transfer rates for 4 common RFB flow fields offers mechanistic insight into transport phenomena and provides tangible parameters for future engineering optimization. In terms of mechanistic understanding, the FTFF measurements indicate that traditional mass transfer coefficient correlations for packed powder beds are shifted relative to porous carbon paper electrodes used here. The small km values associated with the PFF and weak flow rate dependence confirms the findings of prior studies that the PFF does not promote forced convection in the porous electrode and is thus unsuitable for implementation in RFBs.2Additionally, the surprisingly high mass transfer rates associated with the SFF and the intermediate velocity dependence of the IDFF raise interesting questions as to the role of mixed transport in flow field designs.
The mass transfer coefficient data and correlations in this work can serve as a basis for more advanced computational studies, for optimizing electrolyte flow rate to balance electrochemical performance and pump work, and for more detailed system-level descriptions of technical performance and cost. Moreover, this combined modeling and experimental approach offers transparency and applicability to a range of porous electrode materials, electrolyte compositions, and flow field geometries for other flow batteries, or other flowable electrochemical systems, with porous electrodes.
J. D. M. and K. M. T. contributed equally to this work. This project was supported by the Joint Center for Energy Storage Research (JCESR), an Energy and Innovation Hub funded by the United States Department of Energy. J. D. M. acknowledges additional funding from the National Science Foundation Graduate Research Fellowship, and K. M. T. recognizes support from the MIT summer research program.
1. J. Newman and K. E. Thomas-Alyea, Electrochemical Systems, 3rd ed., Chapter 22, John Wiley & Sons, Inc., Hoboken (2004).
2. R. M. Darling and M. L. Perry, J. Electrochem. Soc., 161, A1381–A1387 (2014).