Flow field design and visualization for flow-through type aqueous organic redox flow batteries

Significance

The rapid electron-transfer rate of organic redox-active species requires enhanced electrolyte mass transport within porous carbon electrodes, ensuring adequate reactant supplies at the electrode surface. We design a flow field for flow-through type aqueous organic redox flow batteries (AORFBs) by placing multistep distributive flow channels at the inlet and point-contact blocks at the outlet, to achieve a uniform and adequate electrolyte supply at the electrode. We propose a method to visualize the electrolyte flow within cell stacks and verify the simulation results. The uniform distribution of electrolyte flow within the porous electrode effectively decreases local concentration overpotentials and significantly improves the power density, capacity utilization, and energy efficiency of the aqueous organic redox flow battery, particularly under fast battery charging conditions.

Abstract

Aqueous organic redox flow batteries (AORFBs), which exploit the reversible redox reactions of water-soluble organic electrolytes to store electricity, have emerged as a promising electrochemical energy storage technology. Organic electrolytes possess fast electron-transfer rates that are two or three orders of magnitude faster than those of their inorganic or organometallic counterparts; therefore, their performance at the electrode is limited by mass transport. Direct adoption of conventional cell stacks with flow fields designed for inorganic electrolytes may compromise AORFB performance owing to severe cell polarization. Here, we report the design of a flow field for flow-through type AORFBs based on three-dimensional multiphysics simulation, to realize the uniform distribution of electrolyte flow and flow enhancements within a porous electrode. The electrolyte flow is visualized by operando imaging. Our results show that multistep distributive flow channels at the inlet and point-contact blocks at the outlet are crucial geometrical merits of the flow field, significantly reducing local concentration overpotentials. The prototype pH-neutral TEMPTMA/MV cell at 1.5 M assembled with the optimized flow field exhibits a peak power density of 267.3 mW cm⁻². The flow field design enables charging of the cell at current densities up to 300 mA cm⁻², which is unachievable with the conventional serpentine flow field, where immediate voltage cutoff of the cell occurs. Our results highlight the importance of AORFB cell stack engineering and provide a method to visualize electrolyte flow, which will be appealing to the field of aqueous flow batteries.

Aqueous flow batteries are considered a promising long-duration energy storage technology for grid-scale integration of renewable electricity because of their high safety, decoupled energy and power, and potentially low cost (1–5). Particularly promising is the aqueous organic redox flow battery (AORFB), which exploits the reversible redox reactions of water-soluble organic electrolytes (6–10). Extensive research efforts have been devoted to understanding the electrochemical behavior of redox-active organic molecules and their degradation (or degradation mitigation) during prolonged cell cycling, while the cell assembly of AORFBs (Fig. 1A) adopts the most traditional serpentine flow field (11–13). The serpentine flow field is designed for fuel cells or flow batteries based on inorganic redox couples. Nevertheless, the properties of organic electrolytes are considerably different from those of gas-phase media (H₂, O₂, vapor, or air for fuel cells) or inorganic electrolytes. For instance, organic redox-active species possess fast electron-transfer rate constants that are two or three orders of magnitude greater than those of inorganic and organometallic species (Fig. 1B and SI Appendix, Table S1) (11, 14–24). Therefore, the simple adoption of these flow fields, including the serpentine, parallel, and interdigitated flow fields, may not be appropriate for AORFBs.

Fig. 1.

(A) Illustration of the AORFB cell stack components. (B) The diffusion coefficient D and electron-transfer rate constant $k^0$ of various redox-active species, including organic, inorganic, and organometallic electrolytes. The diffusivity of organic redox-active species is similar to that of inorganic and organometallic species, whereas their electron-transfer rate constants are two or three orders of magnitude greater. (C) Schematic showing the diffusive layer in the vicinity of the porous carbon electrode. $c_e$ is the bulk electrolyte concentration, and $c_s$ is the electrolyte concentration at the electrode surface. The concentration overpotential $\eta$, due to concentration polarization, is positively correlated with $k^0$.

The simple adoption of conventional flow field will cause obvious concentration polarization in AORFB cells, and mass transport intensification of organic electrolytes to match the rapid electrochemical reactions on electrode surfaces is highly needed. As the AORFB cell is charged and discharged, the organic reactant in the bulk electrolyte is transferred to the electrode surface, giving or receiving electrons at the electrode, and the oxidized or reduced reactant diffuses back to the bulk electrolyte (25). During this process, both mass transport and electron transfer contribute to the total overpotential (26, 27). Note that the diffusion coefficient of organic redox-active species is ~10⁻⁵ cm²/s, whereas the electron-transfer rate constants are 3 orders of magnitude greater. The sharp difference in diffusion coefficients and electron-transfer rate constants will result in rapid consumption of organic reactants at the electrode and induce a significant concentration gradient between the bulk electrolyte and the electrode surface. As a consequence, the concentration overpotential increases, which can be estimated by the Nernst equation (28, 29). Taken together with the concentration terms from Fick’s law and the Butler–Volmer equation, the Nernst equation indicates that the concentration overpotential is positively correlated with the electron-transfer rate constant (Fig. 1C and SI Appendix, Note 1). Therefore, considering the large electron-transfer rate constants of organic redox-active species for AORFBs, rational flow field design is highly demanded to eliminate the mass transport limitations on battery performance.

Few recent research efforts have been devoted to three-dimensional numerical models for simulating the concentration overpotential (30–33) and rational flow field designs for improving the battery performance of AORFBs. The major optimizations are focused on the layer number of carbon paper (30), the electrode configuration (rectangle, trapezoid, or sector) (34), the flow field structure (spindle or cuboid) (35), and the shape of flow channel sections (36), while these optimizations were conducted on a serpentine flow field, a flow-by type flow field with short flow paths requiring a high electrolyte flow rate at the expense of extra energy consumption (14, 37, 38).

Inspired by the flow of natural river water (39–41), we designed a flow-through type flow field for AORFBs and demonstrated the effectiveness of this design with a pH-neutral AORFB adopting N,N,N-2,2,6,6-heptamethylpiperidinyl oxy-4-ammonium chloride (TEMPTMA) and N,N'-dimethyl-4,4-bipyridinium dichloride (MV) as the redox couple (21), as shown in Fig. 2. We establish multiphysical computational models to investigate the space-varying characteristics of the flow velocity, reactant concentration, and concentration overpotential in the presented flow field. We used operando imaging to visualize the flow of electrolytes and characterize battery performance to verify the flow field design. A uniform distribution of electrolytes within the porous electrode is achieved by arranging multistep distributive flow channels at the inlet and point-contact blocks at the outlet of the flow field. The 1.5 M TEMPTMA/MV cell with the optimized flow field exhibited a peak power density of 267.3 mW cm⁻². The cell can be cycled at current densities up to 300 mA cm⁻², which is not achievable for identical cells assembled with conventional flow fields where immediate voltage cutoff of the cell occurs. This work proposes an approach for designing AORFB cell stacks and may be broadly applicable to other types of flow battery with mass transport limitations.

Fig. 2.

Molecular structures of TEMPTMA (N,N,N-2,2,6,6-heptamethylpiperidinyl oxy-4-ammonium chloride, the catholyte) and MV (N,N'-dimethyl-4,4-bipyridinium dichloride, the anolyte) for the pH-neutral AORFB and their redox reactions at the electrode. The dashed line indicates an ion-selective membrane, and Cl^- is the charge-carrying ion.

Results

We designed a flow-through type flow field targeting application in AORFBs. With a flow-through type flow field, the electrolyte flows through the main entrance, the distribution channels at the inlet, the porous carbon felt electrode, and finally to the collection channels at the outlet and the main export, as shown in Fig. 3 A–C. The flow field channel is shaped by the flow frame for easy fabrication and adjustments rather than being carved on bipolar plates. To improve the uniform distribution of organic redox-active species in the porous electrode, we designed three separate flow frames (SI Appendix, Fig. S1), labeled 2&S, 3&S, and 3&F, which shape three different flow field patterns. Our design has two important features, i.e., multistep distributive flow channels at the inlet and blocks at the outlet. The shape and configuration are shown in Fig. 3 D–G. In our design, the electrolyte flows through two-step distributive channels at the inlet of 2&S and three-step distributive channels at the inlet of 3&S and 3&F. Sharp blocks are placed at the outlets of 2&S and 3&S, while they are flat for 3&F.

Fig. 3.

Schematic illustrations of the flow frames, including (A) 2&S, (B) 3&S, and (C) 3&F. (D–G) Schematic illustrations showing the probable electrolyte flow direction at the inlet and outlet. The flow frame structures at the 2&S outlet and the 3&F inlet are the same as those of 3&S.

We established multiphysical computational models to predict the impact of flow field configurations on battery performance due to the difficulty in simultaneously monitoring the flow and electrochemical reactions of the electrolyte within a cell stack (42, 43). The representative redox couple TEMPTMA/MV was utilized for calculations. The geometry model of the flow field at the inlet is shown in SI Appendix, Fig. S2. A set of governing equations (given in the multiphysical simulation section in Materials and Methods) were employed for continuity, conservation, and reaction kinetics for the TEMPTMA/MV cell (14, 26, 28, 30–32) and solved by the commercial package COMSOL Multiphysics^®. Relevant parameters of the electrolyte and electrodes, collected from either experimental measurements or research data available in the literature (14, 21, 28), are given in SI Appendix, Tables S2 and S3.

We first investigated the steady-state spatial velocity distributions of the electrolyte flow within the flow fields with no porous electrode, as shown in Fig. 4. Our simulation results show that the electrolyte flow at the 3&S and 3&F inlets is more uniform than that at the 2&S inlet because of an extra step in the electrolyte distribution. The sharp blocks at the outlets of 2&S and 3&S minimize the contact area, thereby reducing the obstruction of the electrolyte outflow and leading to fewer dead zones of electrolyte flow than in 3&F. Overall, 3&S shows the most uniform electrolyte flow distribution according to our simulation. These conclusions were held for other sections of the flow frames (SI Appendix, Fig. S3) and in the presence of porous carbon felts (SI Appendix, Fig. S4).

Fig. 4.

The steady-state spatial velocity distributions inside flow frames of (A) 3&S, (B) 2&S, and (C) 3&F at identical volume inflow rates of 140 mL/min. (D–F) Spatial concentration overpotential distributions at ~85% state of charge (SOC) and (G) average concentration overpotentials at various SOCs, within the electrode for different flow frames. All the results are derived from a three-dimensional multiphysical simulation.

The electrolyte flow distribution affects the concentration polarization and overpotentials of the cell. We thus quantitatively analyzed the concentration overpotentials within different flow fields. The cell voltage $U_{\mathit{cell}}$ can be expressed as (28)

$$U_{\mathit{cell}}=U_{\mathit{OCV}}+U_{\mathit{ohmic}}+{\eta }_{\mathit{total}},$$ [1]

where $U_{\mathit{OCV}}$ and $U_{\mathit{ohmic}}$ are the open-circuit voltage and overall ohmic term, respectively, and ${\eta }_{\mathit{total}}$ is the total overpotential, including the activation and concentration overpotentials. $U_{\mathit{OCV}}$ is determined by the reversible positive and negative half-cell potentials, which depend on the states of charge (SOCs) and can be determined by the Nernst relation. At each SOC, the $U_{\mathit{OCV}}$ of the assembled cells remained nearly the same (SI Appendix, Fig. S5). The overall ohmic term and activation overpotential are also independent of the flow field configuration. The remaining term, the concentration overpotential $\eta$, is described as (25) (SI Appendix, Note 2):

$$\eta =\frac{\mathit{RT}}{\mathit{nF}}\text{ln}\left(1-\frac{i}{nF{a}_m{\nu }^{b_m}{c}_e}\right),$$ [2]

where $i$ is the current density; $a_m$ and $b_m$ denote experimentally determined fitting parameters; and $\nu$ and $c_e$ are the electrolyte velocity and concentration, respectively. For galvanostatic cell cycling, the spatial distribution of $\eta$ within the cell can be derived from the spatial velocity distribution (SI Appendix, Fig. S4) and concentration distribution (SI Appendix, Fig. S6). For example, at ~85% SOC, the spatial characteristics of the concentration overpotentials inside the electrode are portrayed in Fig. 4 D–F for flow fields 2&S, 3&S, and 3&F, and much higher overpotentials are observed at the outlet of 3&F. At 60 mA cm⁻², we calculated the $\eta$ values according to Eq. 2 at other SOCs by COMSOL Multiphysics^® (SI Appendix, Table S4) and put these values in Eq. 1 to obtain the cell voltages during the charging process. Our calculations are in agreement with the experimental results and imply that the numerical model is reliable (SI Appendix, Fig. S7). Notably, $\eta$ increases with increasing SOC, probably due to inadequate reactant supplies at high SOCs. At the same SOC, the uniform distribution of electrolytes within the 3&S flow field contributes to relatively low average concentration overpotentials (Fig. 4G).

We also built an operando imaging system to visualize the electrolyte flow (Fig. 5A and SI Appendix, Fig. S8), in which hot water (65 °C) was pumped into the flow field that was filled with cold water (20 °C). The heat exchange was reflected in real-time by the thermosensitive liquid crystal (SI Appendix, Fig. S9), simulating the spatial velocity distributions. The time-dependent reflections of electrolyte flow within different flow fields were recorded in Movies S1–S3. The operando images at different time intervals (Fig. 5 B–D) verify that the 3&S flow field guarantees the most uniform velocity distribution, whereas more dead zones are observed in the 2&S and 3&F flow fields.

Fig. 5.

(A) Schematic illustration demonstrating the operando imaging system. Live images reflecting the electrolyte flow inside flow frames of (B) 3&S, (C) 2&S, and (D) 3&F, respectively, recorded by the operando imaging system.

We finally investigated the influence of the flow field on the battery performance of the TEMPTMA/MV cells at an electrolyte concentration of 0.5 M. The volume inflow rate was optimized and fixed at 140 mL/min (SI Appendix, Figs. S10 and S11). The potentiostatic charge and discharge curves of the 0.5 M TEMPTMA/MV cell were recorded for different flow fields (SI Appendix, Fig. S12). During both charge and discharge, the cell assembled with the 3&S flow field consumes the least time to achieve complete charge and discharge, owing to the enhanced mass transport. Polarization curves show that the cell assembled with 3&S has the highest peak power density of 138.4 mW cm⁻² (Fig. 6A). When cycled under identical conditions (60 mA/cm²), the cell assembled with the 3&S flow field approaches the most battery capacity (Fig. 6B), which can be attributed to the low ohmic and concentration overpotential (SI Appendix, Figs. S13 and S14) (44). As the current density increases, the redox reactions on the electrode surface become faster, imposing more serious mass transport limitations and leading to more severe performance deterioration (Fig. 6 C and D, derived from the repeated charge-discharge cycles in SI Appendix, Fig. S15). Notably, the TEMPTMA/MV cell assembled with the 3&S flow field always exhibited the best performance.

Fig. 6.

(A) Polarization curves of the TEMPTMA/MV cells assembled with different flow frames at ~100% SOC. (B) Voltage-normalized capacity profiles for the TEMPTMA/MV cells assembled with different flow frames at 60 mA cm⁻². The charge and discharge cutoff voltages are 1.6 V and 0.5 V, respectively. (C) Capacity utilization and (D) energy efficiency of the TEMPTMA/MV cells assembled with different flow fields at various current densities. All the TEMPTMA/MV cells were assembled with the Selemion^® AMVN anion-exchange membrane at an electrolyte concentration of 0.5 M for both the positive and the negative sides.

We conducted a comparison study between the cells assembled with the 3&S flow field and those assembled with the conventional serpentine flow field to evaluate the practicality of our design using two cell stacks of the same size (Fig. 7). We increased the electrolyte concentration to 1.5 M and assembled the cells with a recently reported anion-exchange membrane (MTCP-50, specifically designed for pH-neutral AORFBs) (45–48). Electrochemical impedance spectroscopy (EIS) can reveal battery kinetics (49–51). Both the ohmic resistance (derived from the x-intercept) and electron transfer resistance (related to the redox kinetics of the redox-active species) are independent of the flow field. The diffusion impedance (also known as Warburg’s impedance, W_d) is associated with the electrolyte diffusion process in the flow field. The lower the slope of the low-frequency branch (dotted lines in Fig. 8A) is, the smaller W_d is. Compared with the serpentine flow field, the 3&S flow field achieves a smaller W_d as well as overall impedance, thereby intensifying the mass transport to meet the rapid electron-transfer rates of organic redox-active species. The cell with the 3&S flow field exhibited a peak power density of 267.3 mW cm⁻², which was higher than that with the serpentine flow field (Fig. 8B). When galvanostatically cycled, the cell with the 3&S flow field displays superior charge–discharge profiles, approaching more battery capacity (Fig. 8C). Notably, the 1.5 M TEMPTMA/MV cell with a 3&S flow field can operate at current densities up to 300 mA cm⁻², realizing a capacity utilization improvement of 33.5% and an energy efficiency gain of 30.1% over those of the conventional serpentine flow field, where immediate voltage cutoff of the cell occurs (Fig. 8D and SI Appendix, Fig. S16). The cell assembled with the 3&S flow field also demonstrated high battery performance at lower current densities (60 to 160 mA cm⁻²) (SI Appendix, Figs. S17 and S18) and could be easily stacked (SI Appendix, Fig. S19) (52, 53), further illustrating the practicality of the 3&S flow field design.

Fig. 7.

Photos showing (A) the 3&S flow field and (B) the serpentine flow field. The unit for dimensions is mm.

Fig. 8.

(A) EIS spectra of the TEMPTMA/MV cells assembled with the 3&S and serpentine flow fields. The inset shows the equivalent circuit. (B) Polarization curves of the TEMPTMA/MV cells assembled with the 3&S and serpentine flow fields at ~100% SOC. (C) Charge and discharge curves collected at various current densities (solid lines for the 3&S flow field and dotted lines for the serpentine flow field). The charge and discharge cutoff voltages are 1.6 V and 0.5 V, respectively. (D) The capacity utilization (solid lines) and energy efficiency (dotted lines) of the TEMPTMA/MV cells with the 3&S and serpentine flow fields at various current densities. All the TEMPTMA/MV cells were assembled with the MTCP-50 anion-exchange membrane at an electrolyte concentration of 1.5 M for both the positive and the negative sides.

Discussion

We design the flow field for flow-through type AORFBs by arranging multistep distributive flow channels at the inlet and point-contact blocks at the outlet. We reveal the space-varying characteristics of the flow velocity for each flow field via three-dimensional multiphysics simulation. With an optimized flow field design, a uniform distribution of electrolytes within the cell stack is achieved and visualized by operando imaging. Both simulation and experimental results support that the resulting mass transport enhancement reduces the concentration overpotentials of AORFB cell stacks at each SOC, as exemplified with a pH-neutral TEMPTMA/MV cell. The cell with the optimized flow field exhibited a peak power density of 267.3 mW cm⁻². When galvanostatically cycled at 300 mA cm⁻², the 1.5 M TEMPTMA/MV cell with the optimized flow field can realize a capacity utilization improvement of 33.5% and an energy efficiency gain of 30.1% over those assembled with the conventional serpentine flow field.

Materials and Methods

Materials.

N,N,N-2,2,6,6-heptamethylpiperidinyl oxy-4-ammonium chloride (TEMPTMA), N,N'-dimethyl-4,4-bipyridinium dichloride (MV), carbon felts, and bipolar plates were purchased from Suqian Time Energy Storage Technology Co., Ltd. (Suqian, China). Sodium chloride (NaCl) was purchased from Energy Chemical Co., Ltd. (Shanghai, China). All materials were used as received without further purification. Deionized (DI) water was utilized throughout the experiment. The active area and depth of the flow frames were 7 × 7 cm² and 3 mm, respectively. The flow channels were set to 2 mm. The specific parameters are shown in SI Appendix, Fig. S20. For the serpentine flow field, flow channels with a depth of 2 mm (SI Appendix, Fig. S21) were sculpted on a bipolar plate.

Multiphysical Simulation.

A set of governing equations was employed for continuity, conservation, and reaction kinetics in the TEMPTMA/MV cell and solved by the commercial package COMSOL Multiphysics®.

For the electrolyte flow in porous carbon felts and free distribution/collection channels, the Brinkman equation was employed as follows:

$$\frac{\mu }{K}\overrightarrow{v}=-\nabla P+{\mu }^{\ast }\left[\nabla \overrightarrow{v}+{\left(\nabla \overrightarrow{v}\right)}^T\right],$$ [3]

$$\nabla ·\overrightarrow{v}=0,$$ [4]

where $\overrightarrow{v}$ and $P$ are the velocity vector and the pressure, respectively, and $\mu$ and ${\mu }^{\ast }$ denote the intrinsic and effective viscosity of the electrolyte, respectively. Compared with the Darcy term and the pressure term in porous electrode regions, the viscosity term in the Brinkman equation can be neglected. $K$ represents the permeability of the porous electrode, which is calculated by the Carman–Kozeny equation:

$$K=\frac{d_f^2{\epsilon }^3}{16k_{\mathit{CK}}{\left(1-\epsilon \right)}^2},$$ [5]

where $\epsilon$ is the carbon felt porosity, $d_f$ is the fiber diameter, and $k_{\mathit{CK}}$ is the dimensionless Carman–Kozeny constant.

In AORFBs, the transport process of organic redox-active species is mainly based on the diffusion flux caused by the concentration gradient and the convection flux caused by electrolyte flow, without considering the migration flux caused by an electric field. We employed the Nernst–Planck equation as follows:

$$\overrightarrow{v}\nabla c_e^i-D^{i,eff}{\nabla }^2{c}_e^i=S_i,$$ [6]

where $c_e^i$ is the concentration of the reduced/oxidized TEMPTMA or MV. $D^{i,eff}$ is the effective diffusion coefficient of the reduced/oxidized TEMPTMA or MV and can be described by a Bruggeman correlation in the porous electrode domains:

$$D^{i,eff}={\epsilon }^{\frac{3}{2}}{D}^i,$$ [7]

where $D^i$ is the diffusion coefficient of the reduced/oxidized TEMPTMA or MV applied in the free distribution/collection channels.

$S_i$ is the source term for the reduced/oxidized TEMPTMA or MV. The source terms for the species and charge conservation equations are shown in SI Appendix, Table S5.

The reversible redox reactions of organic redox-active species on the surface of the porous electrode are described by the Butler–Volmer law.

In the positive electrode domain:

$$\begin{array}{c}{i}^P=F{k}^{0,P}{\left(c_e^{P,red}\right)}^{{\alpha }_{P_c}}{\left(c_e^{P,oxi}\right)}^{{\alpha }_{P_a}}\hfill \\ \left[\frac{c_s^{P,oxi}}{c_e^{P,oxi}}\text{exp}\left(-\frac{{\alpha }_{P_c}F{\eta }^P}{\mathit{RT}}\right)-\frac{c_s^{P,red}}{c_e^{P,red}}\text{exp}\left(-\frac{{\alpha }_{P_a}F{\eta }^P}{\mathit{RT}}\right)\right].\hfill \end{array}$$ [8]

In the negative electrode domain:

$$\begin{array}{c}{i}^N=F{k}^{0,N}{\left(c_e^{N,red}\right)}^{{\alpha }_{N_c}}{\left(c_e^{N,oxi}\right)}^{{\alpha }_{N_a}}\hfill \\ \left[\frac{c_s^{N,oxi}}{c_e^{N,oxi}}\text{exp}\left(-\frac{{\alpha }_{N_c}F{\eta }^N}{\mathit{RT}}\right)-\frac{c_s^{N,red}}{c_e^{N,red}}\text{exp}\left(-\frac{{\alpha }_{N_a}F{\eta }^N}{\mathit{RT}}\right)\right],\hfill \end{array}$$ [9]

where $k^{0,P}$ and $k^{0,N}$ are the electron-transfer rate constants of TEMPTMA and MV, respectively. $c_e^{P,red}$ and $c_e^{P,oxi}$ are the concentrations of TEMPTMA and oxidized TEMPTMA, respectively, in the bulk electrolyte, $c_s^{P,red}$ and $c_s^{P,oxi}$ are the concentrations of TEMPTMA and oxidized TEMPTMA, respectively, on the electrode surface, and ${\alpha }_{P_c}$ and ${\alpha }_{P_a}$ are the cathodic and anodic transfer coefficients, respectively, in the positive domain. $c_e^{N,red}$ and $c_e^{N,oxi}$ are the concentrations of reduced MV and MV, respectively, in the bulk electrolyte, $c_s^{N,red}$ and $c_s^{N,oxi}$ are the concentrations of reduced MV and MV, respectively, on the electrode surface, and ${\alpha }_{N_c}$ and ${\alpha }_{N_a}$ are the cathodic and anodic transfer coefficients, respectively, in the negative domain.

The total overpotentials ${\eta }^P$ and ${\eta }^N$ in the positive and negative domains are defined as

$${\eta }^P={\varphi }_s-{\varphi }_l-\mathrm{\Delta }{\varphi }_{\mathit{eq}}^P-\frac{\mathit{RT}}{\mathit{nF}}ln\frac{c_e^{P,oxi}}{c_e^{P,red}},$$ [10]

$${\eta }^N={\varphi }_s-{\varphi }_l-\mathrm{\Delta }{\varphi }_{\mathit{eq}}^N-\frac{\mathit{RT}}{\mathit{nF}}ln\frac{c_e^{N,oxi}}{c_e^{N,red}},$$ [11]

where $\mathrm{\Delta }{\varphi }_{\mathit{eq}}^P$ and $\mathrm{\Delta }{\varphi }_{\mathit{eq}}^N$ represent the formal half-cell potentials for TEMPTMA and MV at T = 298.15 K, respectively.

A detailed description of the boundary and initial conditions is given in SI Appendix, Note 3.

Operando Imaging.

A flow frame was well sealed between a transparent sealing plate and a thermosensitive liquid crystal plate. A camera directly above the transparent sealing plate recorded the color changes of the thermosensitive liquid crystal. Initially, the flow frame was filled with cold water (20 °C). Then, hot water (65 °C) was pumped into the flow frame at a flow rate of 140 mL/min. The heat exchange was reflected in real time by the thermosensitive liquid crystal, thereby simulating the spatial velocity distribution.

Full Cell Tests.

Flow frames were used on both sides. The space between the membrane and flow frames was well sealed with Viton gaskets. The electrode on each side was carbon felt with a geometric area of 7 × 7 cm² and a thickness of 3 mm. The membranes were pretreated by immersion in 1 M NaCl aqueous solution for at least 72 h. The electrolytes were pumped through the cell stack at various flow rates using a Masterfles L/S peristaltic pump (Cole-Parmer, Vernon Hills, IL). All tubing and electrolyte reservoirs were made from chemically resistant fluorinated ethylene propylene (FEP). Full-cell tests were performed in a glovebox with an oxygen concentration <2 ppm on a Bio-Logic BCS-815 electrochemical workstation. For the 0.5 M TEMPTMA/MV cells, the negolyte comprised 70 mL of 0.5 M MV and 1.0 M NaCl, while the posolyte comprised 50 mL of 0.5 M TEMPTMA and 1.0 M NaCl. For the 1.5 M TEMPTMA/MV cells, the negolyte comprised 70 mL of 1.5 M MV, while the posolyte comprised 50 mL of 1.5 M TEMPTMA. The cutoff voltages during galvanostatic charge and discharge were set at 1.6 V and 0.5 V, respectively.

Supplementary Material

Appendix 01 (PDF)

Movie S1.

The time-dependent reflections of electrolyte flow within the 2&S flow field.

Movie S2.

The time-dependent reflections of electrolyte flow within the 3&S flow field.

Movie S3.

The time-dependent reflections of electrolyte flow within the 3&F flow field.

Data, Materials, and Software Availability

All study data are included in the article and/or supporting information.