Redox flow batteries: a review
- First Online:
- 24k Downloads
Redox flow batteries (RFBs) are enjoying a renaissance due to their ability to store large amounts of electrical energy relatively cheaply and efficiently. In this review, we examine the components of RFBs with a focus on understanding the underlying physical processes. The various transport and kinetic phenomena are discussed along with the most common redox couples.
KeywordsFlow battery Redox Regenerative fuel cell Flow cell Vanadium
List of symbols
Interfacial surface area between phases k and p per unit volume (cm−1)
Concentration of species (mol/cm3)
Fiber diameter (cm)
Fickian diffusion coefficient of species i in a mixture (cm2/s)
Standard cell potential (V)
Equilibrium cell potential (V)
Faraday’s constant, 96487 C/equiv
Superficial current density (A/cm2)
Exchange current density (A/cm2)
Transfer current density of reaction h per interfacial area between phases k and p (A/cm2)
Standard rate constant, varies
Valence state or number of electrons transferred in a reaction
Superficial flux density of species i (mol/cm2 s)
Rate of reaction l per unit of interfacial area between phases k and p (mol/cm2 s)
Ideal-gas constant, 8.3143 J/mol K
Rate of homogenous reaction g in phase k (mol/cm3 s)
Resistance of resistor i, j in Fig. 10 where ct stands for charge-transfer (Ω cm2)
Stoichiometric coefficient of species i in phase k participating in reaction l
Absolute temperature (K)
Mobility of species i (cm2 mol/J s)
Superficial velocity (cm/s)
Valence or charge number of species i
Transport coefficient of species i (mol2/J cm s)
Charge density (C/cm3)
Conductivity of the electronically conducting phase (S/cm)
Conductivity of the ionically conducting phase (S/cm)
Viscosity (Pa s)
(Electro)chemical potential of species i (J/mol)
Potential in phase k (V)
Permeation coefficient of species i (mol/s cm bar)
Electronically conducting phase
Ionically conducting phase
Renewable-energy sources, such as solar and wind, are being deployed in larger numbers than ever before, but these sources are intermittent and often unpredictable. These characteristics limit the degree to which utilities can rely upon them, and, as such, renewables currently comprise a small percentage of the primary power sources on the US electrical grid. Analysis suggests that an electric grid could become destabilized if non-dispatchable renewable energy exceeds 20% of the energy-generation capacity without energy storage . However, many utilities are mandating renewable portfolios approaching this level of deployment, thus there is a pressing need for storage technologies to complement and enable renewable standards. Other than capacitors, however, there is no way to store electrical energy as such. Instead, if electricity is to be stored, it must first be converted to some other form of energy. There are some technologies that enable practical storage of energy at their current levels of deployment, but only a very small fraction of North American power plants employ such technology . To ensure that renewable energy succeeds in delivering reliable power to US consumers, the nation needs cost effective and reliable storage at the grid scale.
As shown in Fig. 1, a key component of RFBs is the ability to separate power and energy. The power is controlled by the stack while the energy is stored within the separated reactants. Thus, one can optimize over a greater range of variables and storage can be increased with relatively ease and minimal cost compared to the stack, which is typically the most expensive system component. To examine the technologies that are under development to meet the cost requirements of the marketplace and enable wide-scale storage, we consider the existing portfolio of RFB storage technologies and the possibilities of each. To that end, we introduce the various technologies and discuss in more depth the general attributes and concerns facing RFBs. The overall purpose of this review is to examine systemic issues for the field of RFBs, and not just examine a specific chemistry or the various proposed RFBs. Excellent reviews of these latter issues and energy storage for the grid in general can be found in the literature [5, 6, 7, 8]. The structure of this paper is as follows.
After an introduction and short overview of the various major RFBs, the kinetic and transport issues are examined in turn. Next, some overall electrode/cell modeling and designs are reviewed. Finally, some comments about future research needs are made. It should be noted that this review is focused on cell-level issues and RFB chemistries, therefore issues of system integration and components are not examined in depth, although they can be critically important for system commercialization. Before discussing the various RFB chemistries, it is worthwhile to examine their current major applications.
1.1 Grid-storage needs
The present electric grid constitutes an enormous physical infrastructure, with a near-instantaneous transmission of value from primary power sources and generation assets to end users and with almost no storage capability. Because of this dearth of storage, the existing grid must conform to fluctuations in customer demand, resulting in the construction of power plants that may only operate for 100 h a year or less and can account for up to 30 MWh in capacity . These generators are dispatched to respond to small oscillations in demand over very short time scales of less than 1 h. They are also turned on and sped up to meet increasing load during the peak time of the day, and, at the other extreme of wastefulness, brought on by the lack of storage. For example, wind energy is wasted because of the inability to dispatch wind power at night when wind generation is at a maximum but customer demand is at a minimum; thus, there is a significant value added by the incorporation of storage . Similarly, photovoltaics and solar-energy implementation will also require arbitrage since although the solar irradiation received terrestrially in about 1 h is sufficient to meet worldwide energy requirements for a year, the sun does set daily. Storage is a vital tool that would uncouple customer demand from the generation side of the grid, thereby allowing vital flexibility in control and maintenance of the electric grid. To date, however, energy storage comprises only about 2% of the installed generation capacity in the U.S. Because of differences in government policy and more favorable economics, storage plays a larger role in Europe and Japan, at 10 and 15%, respectively .
The current worldwide electric generation capacity was estimated to be about 20 trillion kilowatt hours in 2007 . More than two-thirds of the current mix is from some form of fossil fuel, with most of the balance coming from nuclear and hydroelectric power generation; at present, only about 3% comes from renewable-energy technologies. Furthermore, developing economies and electrification of the transportation sector both point to strong year-over-year growth in terms of electrical demand. While coal is already the primary source of power in the US electricity sector, there are concerns that it will become a larger portion of electricity production as increased global demand competes for cleaner resources like natural gas. Coal is, of course, the most carbon-intensive resource used in this sector; however, while debate continues about how to address anthropogenic global warming gas emissions from a policy standpoint, coal plants are less capable of handling transient loads than the “peaker” plants that largely sit idle and which are deployed only to handle the peak loads. Growing demand implies not only an increase in the base load, which might be handled by coal if government and the energy sector choose not to prioritize carbon-emissions reductions, but also to larger peak loads, which will either require more intermittent generation assets or storage.
In addition to improvements in resiliency that can enable increased renewable-energy generation, integration of storage into the smart grid also promises to enable greater system efficiency, even with existing generation assets. The Electric Power Research Institute has completed a study that suggests that the widespread adoption of smart grid technologies could yield a 4% reduction in energy use by 2030 , roughly equivalent to eliminating the emissions of 50 million cars. Beyond the emissions impact, that savings translates to more than $20 billion annually for utility customers nationwide. With a more robust and efficient system, and more data about demand patterns, it will be easier for utilities to manage the integration of intermittent renewable-energy sources. Energy storage can also support requirements for reserve generation in place of fossil-fuel-based facilities, yielding zero emissions and lowered operating costs.
It seems apparent that being able to harvest energy from more diverse sources, and being able to deploy this energy to the end user when it is demanded, should lower operating costs and promote the robustness and quality of power on the grid. Why then, is the penetration of storage onto the grid so small? The answer is primarily cost. There are multiple costs associated with the installation and operation of a RFB system: one must consider the operation and maintenance costs, as well as up-front capital costs and life-cycle costs. Because of the decoupling of energy and power in RFB configurations, we can consider both cost per unit of power generation/storage capability ($/kW) and the cost per unit of energy-storage capacity ($/kWh). We note that the cost per unit energy storage is not the incremental cost of producing or storing that energy as would be expected in a utility bill, but the cost per unit of energy-storage capacity. In addition to costs, robust system lifetimes of ~10 years, high efficiency, and cyclic durability are necessary for grid-level storage.
Key performance targets for grid-storage applications, from Ref. 
Key performance targets
Area and frequency regulation (short duration)
Reconciles momentary differences between supply and demand within a given area
Service cost: $20/MW
Roundtrip efficiency: 85–90%
System lifetime: 10 years
Discharge duration: 15 min–2 h
Response time: milliseconds
Renewables grid integration (short duration)
Offsets fluctuations of short-duration variation of renewables generation output
Accommodates renewables generation at times of high grid congestion
Roundtrip efficiency: 90%
Cycle life: 10 years
Capacity: 1–20 MW
Response time: 1–2 s
Transmission and distribution upgrade deferral (long duration)
Delays or avoids the need to upgrade transmission and/or distribution infrastructure
Reduces loading on existing equipment to extend equipment life
Discharge duration: 2–4 h
Capacity: 1–100 MW
System life: 10 years
Load following (long duration)
Changes power output in response to the changing balance between energy supply and demand
Operates at partial load (i.e., increased output) without compromising performance or increasing emissions
Capital cost: $1,500/kW or $500/kWh
Operations and maintenance cost: $500/kWh
Discharge duration: 2–6 h
Electric energy time shift (long duration)
Stores inexpensive energy during low demand periods and discharges the energy during times of high demand (often referred to as arbitrage)
Capital cost: $1,500/kW or $500/kWh
Operations and maintenance cost: $250–$500/kWh
Discharge duration: 2–6 h
Response time: 5–30 min
2 Redox-flow-battery overview
One of the key attributes of RFBs that suggests significant promise for stationary applications is the fact that, for many configurations, there is no physical transfer of material across the electrode/electrolyte interface. While there are some configurations that can be categorized as flow batteries only in the sense that the active material flows from outside of the cell to the electrode surface, most flow-battery systems under development utilize reversible solution-phase electrochemical couples on two electrodes to store chemical energy. Instead of storing the electrochemical reactants within the electrode itself, as with metal/metal alloy or intercalation electrodes, the reactants are dissolved in electrolytic solutions and stored in external tanks. Both the oxidized and reduced form of each reactant are soluble in the electrolyte, so they can be carried to/from the electrode surface in the same phase. Only the relative concentrations of oxidized and reduced forms change in each stream over the course of charge and discharge.
The electrodes in most RFB configurations are not required to undergo physical changes such as phase change or insertion/deinsertion during operation because the changes are occurring in the dissolved reactants in the solution phase adjacent to the solid-electrode surfaces. Though there are exceptions to this formulation, as mentioned in the next section, this feature generally affords the opportunity to simplify the electrode design considerably. As a consequence of the charge-transfer characteristics, the cycle life of a RFB is not directly influenced by depth-of-discharge or number of cycles the way that conventional rechargeable batteries are. Side reactions can, of course, complicate design and operation, but if the reactions proceed as intended, degradation of the electrode surface need not proceed as a matter of course. The decoupling of storage and reaction in RFB systems is an advantage in terms of flexibility, but it complicates their designs relative to conventional batteries, and adds a mechanical balance-of-plant element for pumping the often highly corrosive liquid electrolyte; as a result, their specific mass and volumetric energy densities are much lower than conventional batteries. A RFB configuration can nevertheless exceed the performance of other grid-storage technologies and does not require specific geographical siting, as pumped hydroelectric and compressed-air energy storage (CAES) do.
Additionally, RFBs offer the important advantage that power and energy outputs are independent variables since the power is determined by the reactor size and the amount of energy stored depends on the reactants chosen, their concentration, and the size of the reactant tanks [16, 17, 18]. The amount of energy that can be stored in a conventional sealed battery is generally limited by the effective path lengths for diffusion and migration in the direction normal to the current collector; making an electrode thicker will add to the amount of active material, but one experiences diminishing returns in terms of energy extraction because of diffusional and ohmic losses in these systems.
As shown in Fig. 1, most RFB systems currently require two separate electrolyte tanks: one for the anolyte and another for the catholyte. This ensures that the potentials at each electrode are close to the reversible potential for each of the half-cell reactions, and side reactions or competition from the other half-cell reactions are minimized. This does, however, add to the size and cost of the system, and it also requires a uniform delivery of the dissolved species to the entire surface area as oftentimes most of the convective flow is parallel to the electrode surface rather than being flowed directly through it. Details of ion transport and flow configurations are discussed more thoroughly in a subsequent section.
The key costs of RFBs are the active material stored in the electrolyte and the electrochemical cell itself. The construction costs of the cell scale with the total power requirement of the application, but these costs are directly rated to the specific power of the device itself, i.e., how effectively the materials are utilized. While RFBs ought to be able to operate at relatively high current densities, as convection can be employed to deliver reactants to the electrode surface, RFBs have typically been operated at current densities consistent with conventional batteries without convection. It is anticipated that electrolyte management and cell design can deliver significant improvements in power density, thereby reducing considerably cell material costs.
2.1 Redox-flow-battery chemistries
The system can operate with an IEM/separator and low-cost carbon-felt electrodes. Both charge-transfer reactions require only a single-electron transfer, which is expected to simplify charge transfer and result in reasonable surface overpotentials without specific electrocatalysts. Indeed, the iron redox couple is highly reversible on carbon or graphite electrodes, but the chromium redox couple has significantly slower kinetics and does require electrocatalysts. This system has a relatively low open-circuit potential (between 0.90 and 1.20 V), and designers must endure crossover of iron to the chromium stream and vice versa. Some Japanese companies built similar batteries by licensing the NASA patents, but have not shown improvement in the low output voltage and efficiency .
The bromine/polysulphide RFB was patented by Remick  then extensively studied by Regenesys Technology  from 1993 until 2006 when it was acquired by VRB Power Systems . To date, three series of bromine/polysulphide RFB systems have been developed, including 5, 20, and 100 kW class systems. A commercial-size 15 MW system was successfully demonstrated. This plant used up to 120 modules, and 200 bipolar electrodes with an energy storage capacity up to 12 MWh and two 1800 m3 electrolyte storage tanks .
In this system, all of the electroactive species are anions, so a cation-exchange membrane is needed to prevent mixing of the anolyte and catholyte streams. Charge is carried via sodium ions through the membrane. When activated carbon/polyolefin composite electrodes were used in this system, the voltage increased from 1.7 to 2.1 V during the charging process due to adsorption of bromine in the activated carbon . This system is prone to crossover and mixing of the electrolytes, however, which can lead to precipitation of sulfur species and the formation of H2S and Br2.
While energy density is not necessarily a primary concern for stationary, grid applications, nonetheless, the VRB energy density is limited by the solubility of vanadium in the electrolyte stream and precipitation can occur; the solubility limits depend upon both acid concentration and temperature .
2.1.5 Hydrogen-based systems
2.1.6 Hybrid redox-flow batteries
There are other battery configurations that share a development heritage and some common issues with what we would classify as RFBs in that the active material can be introduced to, or removed from, the electrochemical cell without disassembling the cell structure, but which do not store all of the active material in a liquid or gaseous form per se. As such, we might consider them semi-flow cells with electrochemical reactions that are more complicated than simply shuttling between the oxidation states of a single species.
The metal negative electrode allows for a compact electrode, thus increasing the energy density. In addition, the zinc/bromine system has a high cell voltage, good reversibility, and expectations of low material costs. However, the demonstration of zinc/bromine has been limited due to material corrosion, dendrite formation and electrical shorting, high self-discharge rates, low energy efficiencies, and short cycle life. RedFlow Ltd. successfully demonstrated a zinc/bromine RFB unit up to MW size with an energy efficiency of nearly 74% in Australia . The cell architecture was designed to optimize plating and de-plating efficiency of zinc during charging and discharging operations. Derivatives of the zinc/bromine system include other halogens such as zinc/chlorine, which typically have similar performance and issues .
22.214.171.124 Soluble lead acid
126.96.36.199 All iron
2.1.7 Non-aqueous redox-flow batteries
The use of non-aqueous electrolytes in RFB configurations has been considered because of the higher cell potentials that are possible when one is not concerned by the breakdown of the aqueous electrolyte. In addition, many couples and reactants are much more soluble in non-aqueous solvents. However, the challenges of low electrolyte conductivities, stability, and cost limit the development of non-aqueous RFB systems.
Other examples of nonaqueous RFBs include that of Matsuda et al.  who demonstrated a redox system based on [Ru(bpy)3]2+/[Ru(bpy)3]3+ (bpy is bipyridine) as the anolyte and [Ru(bpy)3]+/[Ru(bpy)3]2+ as the catholyte in acetonitrile (CH3CN) with tetraethylammonium tetrafluoroborate (TEABF4) as the supporting electrolyte. This system yielded an open-circuit potential of 2.6 V, with an energy efficiency of 40%. Chakrabarti et al. evaluated a redox system based on a ruthernium acetylacetonate, obtaining a cell potential of 1.77 V . Yamamura et al.  studied a non-aqueous system which used various uranium beta-diketonates with the cell potentials of about 1 V.
Recently, Thompson and co-workers demonstrated a redox-flow system using M(acac)3 (M = V, Cr or Mn, and acac is acetylacetonate) with at least three different oxidation states [77, 78, 79]. The vanadium and chromium acetylacetonate systems showed higher open-circuit potentials, 2.2 and 3.4 V, respectively, compared to around 1.26 V for the aqueous VRB system. However, crossover and ohmic losses due to the large distances between positive and negative electrodes limited the coulombic efficiency. Although the Mn(acac)3 system shows a lower open-circuit potential (1.1 V) than that of V(acac)3, Cr(acac)3, and VRB, it exhibits better reversibility both for Mn(II)/Mn(III) and Mn(III)/Mn(IV) redox couples, with a columbic efficiency approaching 97% in a static H-type cell. Shinkle et al. studied the degradation mechanisms in the non-aqueous V(acac)3 redox systems , and showed that environmental oxygen and water are associated with side reactions that affect the long-term charge–discharge response of the battery.
2.1.8 Other configurations
There is recent interest in the development of the lithium-air battery, which operates with a static lithium negative electrode, as might be found in a lithium-ion or lithium-polymer battery. Lithium ions combine with oxygen from air to form lithium oxide at the positive electrode on discharge; oxygen is regenerated during charging. Kraytsberg and Ein-Eli provide an overview of the technology . There are many challenges with such a battery system, such as ensuring proper isolation of the negative electrode from oxygen and water crossover and ensuring an electrode structure that provides for facile oxygen transport and reversible oxide formation and stripping. However, the promise for high energy density and low material costs suggest tremendous research opportunities.
Another recent flow-cell concept was invented by Yet-Ming Chiang’s group at MIT and described by Duduta et al. [82, 83]. They proposed using typical intercalation electrode materials as active materials for a lithium rechargeable battery, but providing the active material in a slurry that can be mechanically pumped into and out of a reaction chamber. In the paper describing the concept, they note that they will be able to store much higher concentrations of active material in the solid component of the slurry than can be stored as ions dissolved in electrolyte (up to 24 M), thereby increasing the energy density well beyond what could be achieved in traditional RFBs.
3 Kinetics of redox reactions
Following the pioneering theoretical framework introduced by Gerischer , modern quantum chemical theory of redox kinetics at electrode surfaces has focused on the distance of the redox ion from the electrode surface . Modern theory typically distinguishes redox reactions as either “inner-sphere” or “outer-sphere”, the latter referring to reactions where the redox ion is “inside” the plane of the inner Helmholtz ionic layer and the former “outside” . Practically, this distinction is important in that inner-sphere reactions typically have a very large dependence of the reaction kinetics on the electrode material, in many cases by orders of magnitude; the hydrogen electrode is perhaps the most dramatic in this respect. For outer-sphere reactions, the kinetic effect of different electrode materials is much less, but not insignificant. However, this distinction in electrode-material dependence is not essential, and there are examples where inner-sphere reactions have a relatively small dependence on the electrode material, e.g. the Br2/Br− reaction. The detailed discussion of the effect of electrode materials on the kinetics is beyond the scope of this review.
Kinetic parameters for redox reactions used in flow batteries
2.2 × 10−5
1.2 × 10−5
2 × 10−4
3.0 × 10−7
1–3 × 10−6
4 × 10−3
1.6 × 10−3
1.7 × 10−2
5.8 × 10−4
The results in Table 2 show that of all the redox couples recently or currently in use in practical RFBs, only the VO2+/VO2+ couple has a clear kinetic limitation and, in fact, is clearly problematic. This is not surprising since this redox is not a simple one-electron transfer reaction, but is in modern terminology an oxygen transfer reaction as shown in Eq. 8. As discussed in detail recently by Gattrell et al. , this reaction is a multi-step reaction in which oxygen transfer (a chemical step) may precede or follow an electron-transfer step, denoted in modern terminology as a CE or EC mechanism. Such reactions usually have current–potential relations which differ significantly from the ideal Butler–Volmer form, and that is the case here. The kinetic data by Gattrell et al. were obtained using a graphite RDE, which should be directly applicable to practical cells which use carbon-felt electrodes. Although the quantitative data in Table 2 was obtained using a Hg electrode, the polarization curves shown for the V2+/V3+ electrode with a graphite RDE in Gattrell et al. indicate a rate constant ≫10−5 cm/s.
The dependence of the VO2+/VO2+ couple on electrode material has not been very well-studied. Skyllas-Kazacos and co-workers  reported somewhat larger exchange-current densities for less well-characterized “carbon” electrodes than Gattrell et al. and suggested it is possible to enhance kinetics by surface treatment of carbon-based electrodes. Zhong et al. fabricated conducting polyethylene (PE) composite electrodes with low resistivities by mixing PE with conducting fillers (carbon black, graphite power and fiber) . The chemical treatment of graphite fiber-based composite polymer electrodes with chromate-sulphuric acid was shown to enhance the surface and improve reactivity for the electrode reactions. Carbon-polypropylene (PP) composite electrodes modified with rubber show better mechanical properties, better impermeability and better overall conductivity compared to the PE composite electrodes . A voltage efficiency as high as 91% was obtained for the VRB with the carbon-PP composite electrodes. Graphene oxide nanoplatelets (GONPs) demonstrated a more favorable electrocatalytic activity for V(V)/V(IV) and V(III)/V(II) redox couples than pristine graphite for the VRBs. It is found that the V(III)/V(II) redox reaction strongly depends on the formation of surface active functional groups of C–OH and COOH . However, it is not clear that using an electrode material other than graphite/carbon would be cost effective.
In contemporary studies of heterogeneous electron transfer reactions, the Fe3+/Fe2+ reaction is still considered to be the prototypical outer-sphere reaction amenable to quantitative quantum chemical treatment using modern ab initio methods. The data shown in Table 2 are relatively recent measurements using sulfuric-acid solutions rigorously purified specifically of chloride ion (to ppb levels). Following the pioneering work by Nagy et al. , it is now widely recognized that with Pt and Au electrodes, the presence of even trace amounts of chloride ion enhances the experimental rate of electron transfer by at least two-orders of magnitude, probably by a mediated or bridging transfer of the electron via adsorbed chloride anions. While it has not been proven conclusively that the “chloride effect” is exclusive to Pt and Au, theoretical considerations are consistent with such an expectation, and qualitative data with carbon-felt electrodes suggest this is the case, and that the kinetic parameters given in Table 2 should be applicable to carbon electrodes in a practical battery.
The Ce4+/Ce3+ was studied in detail by Vetter  including rigorous correction for the partial current from oxygen evolution. The reaction has not been the subject of many studies since then. The corrosion of the electrode material and the parasitic effect of oxygen evolution are serious issues for a practical device. Use of stable electrode materials such as IrO2 evolve significant oxygen, thereby reducing efficiency and requiring active cell rebalancing and maintenance. Carbon electrodes will undergo significant corrosion and not have practical lifetimes at these operating potentials . Practical use of this redox couple in a RFB will require a scientific breakthrough in electrode material.
Before examining surface-area effects, a mention should be made about typical RFB electrode materials. As noted above, graphitic or vitreous carbon materials are widely used in RFBs [27, 28, 30, 100], such as graphite, carbon felt, carbon fiber, thermal and acid treated graphite, carbon-polymer composite materials, carbon nanotubes, Ir-modified carbon felt and graphene-oxide nanoplatelets. In general, RFB couples are chosen for the facile kinetics so highly active catalytic materials are not necessary. Nonetheless, it has been found that various surface treatments can lead to improved reaction kinetics on carbon electrodes. Chemical etching , thermal treatment , chemical doping , carbon nanotube addition , and addition of metallic catalyst sites to the carbon fibers  have all been attempted. Aside from catalytic activity, the main criteria for electrode materials are electrical conductivity, chemical stability and durability in the reaction environment. Carbon and graphite materials meet both these requirements, though metal foams and meshes are also candidates [105, 106]. The search for improved electroactive materials for RFBs will no doubt continue to be actively pursued.
3.1 Active surface area
Clearly, the fiber diameter dramatically impacts both aspects and unfortunately in opposing directions. Increasing the fiber diameter from 10 to 100 μm improves the permeability by a factor of 100, but reduces the surface area by a factor of 10. The same general trend would be true for other random electrodes such as particulate beds. Efforts to increase active surface area in a flowing electrolyte by using particles with microporosity have been reported , but, not surprisingly, this additional surface area does not contribute significantly to the electrochemically active area since such internal surfaces are highly diffusion limited. Attempts to increase the roughness of the electrode surface could be beneficial, but typically it is more profitable to modify the surface for increased kinetic or catalytic behavior rather than just surface area.
Another aspect of the active solid surface area that must be considered is the intimacy of the solid/electrolyte contact [18, 36]. Carbon and graphite materials have a neutral wettability to water  which prevents the spreading of electrolyte over the electrode surface. The trapped air pockets resulting from incomplete wetting reduce the electroactive surface area owing to the Cassie–Baxter effect. Such incomplete wetting would be exacerbated on roughened surfaces. Sun and Skyllas-Kazacos found that certain electrode pretreatments intended to improve catalytic activity also lead to somewhat improved wettability behavior . Litster et al.  report that briefly heating carbon fiber materials at 300 °C in an air environment rendered them fully hydrophilic, and Yan et al.  review various treatment procedures for altering carbon wettability. The presence of a gas phase at the solid/electrolyte interface could be due to residual air trapped during initial flooding of the electrode, or could appear due to evolution of gases such as the parasitic evolution of hydrogen and/or oxygen [13, 113].
4 Transport phenomena
Summary of different thermodynamic and transport parameters for various RFBs
Membrane charge carrier
Open-circuit potential (V)
Diffusivity, D (10−6 cm2/s)
VCl3 + H2SO4/Na2SO4, glassy carbon electrode
1.50 (pH = 4.0)
1.34 (pH = 2.0)
1.16 (pH = 1.0)
1.41 (pH = 0.0)
V2O5 + 1.8 M H2SO4/Na2SO4, glassy carbon electrode
V(IV) + 6.4 M HBr, 2 M HCl solution
Ce(III) ion in methanesulfonic acid
Non-aqueous vanadium acetylacetonate
4.1 Electrolyte flow
Flowing electrolyte through porous electrodes presents a number of challenges, both at the single-cell and full-stack level. At the pore scale within each electrode there will be significant differences in the interstitial flowrate in each pore owing to size differences, with flow largely confined to the largest pores in the medium. Such pore-scale-channeling behavior provides convective mass transport at a limited number of surfaces, while dead zones of relatively stagnant flow and localized limiting currents would exist elsewhere throughout the electrode. Fibrous materials are the favored porous-electrode substrate for several reasons because high porosity can be achieved while still maintaining electrical conductivity and percolation in the solid phase due the bridging between long fibers. As discussed above, high porosity is advantageous since (a) there is a strong positive correlation between porosity and permeability , thereby resulting in reduced pressure drop and associated pumping costs; and (b) the effective ionic conductivity of the electrolyte is directly proportional to porosity  and inversely proportional to tortuosity which tends to increase with decreasing porosity .
Due to the wide spread use of fibrous electrodes for various applications, a number of studies have looked at mass transfer in carbon-fiber electrodes [66, 121, 122, 123, 124]. Schmal et al.  compared mass transfer at single fibers to fiber assemblies (bundles and felts) and found that per unit length of fiber the mass transfer to a single fiber was significantly higher. This was attributed to channeling within the fiber assemblies causing dead-zones or stagnant regions, effectively reducing the active area for reaction. A porous material with very uniform pore-size distribution would help alleviate this problem, but such materials may be impractical. Saleh  studied the effectiveness factor in packed bed electrodes and found that ohmic resistance, which is a combination of fluid properties and bed geometry, also played a key role in determining the extent to which the porous electrode was utilized.
Another cell-scale issue arising from the convective flow in porous electrodes is large scale heterogeneities due to assembly tolerances or uneven thermal expansion, which could lead to bypassing of large sections of a cell. Moreover, flow through porous electrodes presents major manifolding issues at the stack-scale since each cell must have nearly identical permeability. This would be difficult to achieve since stacks may be compressed significantly when assembled. This situation is analogous to interdigitated flow fields proposed for low-temperature fuel cells, which showed very promising performance results in single-cell tests, but the inevitable differences in permeability from cell to cell in a stack created uneven flow distribution among cells .
4.1.1 Reactant concentration effects
The issue of reactant solubility in the flowing electrolyte solution can be important. The energy density of a RFB system is set by the concentration of dissolved species, but the maximum concentration in any stream is limited by the solubility of the least soluble species. Precipitation of reactants or products in the porous electrode is calamitous. Concentration limits on the electroactive species not only reduces the energy density of a system, but also negatively impacts the power density and cell efficiency as well. Lower concentrations mean reduced mass-transfer rates and current density, thus increasing concentration polarization and/or pumping power. Solubility is a function of temperature as well, which must be factored into cell design. For instance, it is observed that V2O5 precipitation occurs at elevated temperature, limiting the operating temperature to the range of 10 to 40 °C [37, 129]. Li et al. improved this situation with the development of a vanadium sulfate and chloride mixed electrolyte, enabling a vanadium concentration up to 2.5 M over a temperature range of −5 to 50 °C . However, temperature excursions in an operating cell could cause a precipitation event and lead to cell failure .
Other issues regarding concentrations include the fact that for many systems increasing the concentration of the reactants can lead to more complexing and lower diffusivities and perhaps even more viscous solutions. For example, recent data measured at LBNL show that Br2 diffusivity decreases by a factor of two as the concentration of HBr is increased from 1 to 7 M . Such tradeoffs require optimization for the specific system. Another ubiquitous issue present in flowing reactors of all types concerns the extent of reactant conversion, sometimes referred to as utilization or stoichiometry. The difficulty is determining the optimum reactant concentration at the outlet of the electrode. It is desirable or necessary that the electrode near the outlet is not starved of reactant to prevent parasitic reactions such as gas evolution or electrode corrosion. On the other hand, fully consuming or utilizing the reactants means recovery of the maximum amount of energy stored in the solution. For many systems, the stoichiometry is high for single-cell studies (typically over 10) , and it is not clear as to how this can be translated into actual systems where such performance would necessitate multiple passes through the electrodes. One such approach would be to have a cascade of reactors that are tailored to specific operating points and concentrations .
4.1.2 Shunt currents
One of the challenges of stack design that must be given particular attention in RFB configurations is protection against shunt currents. Generally speaking, a shunt current refers to a condition in which current deviates from the intended path, via a parallel path with a sufficiently low resistance to divert a portion of the current. In general, the path of least resistance in a cell or stack is designed to follow the direction of intended current flow. In a flow battery configuration in which cells are configured in series, it is intended for all of the current to flow in the electrolytic phase via ionic conduction from one negative electrode to the adjacent positive electrode, and in the current collector from one adjacent bipolar plate to another. In a well-designed stack, there should be no current flow except directly from one cell to another in the preferred series configuration.
In practice, however, there is no perfectly insulator, and current can flow from one cell to another in such a way that significant power is lost and stack output voltage is lowered. It is possible for stray electronic paths to allow redistribution of current from one cell of a multicell stack to another, and strict requirements on the resistance of stack externals such as manifolds and packaging help to minimize shunt currents via electrical conduction . The same general rules and restrictions that guide conventional battery and stack design and isolation can prevent shunt currents via electrically conducting pathways.
Of particular concern in flow batteries is the development of shunt currents via the liquid electrolyte. While shunt currents can develop in the liquid phase in conventional fuel-cell and battery designs [133, 134], the restriction of the primary electrolyte to the region between each pair of current collectors minimizes most obvious paths for current flow, at least in the electrolytic phase. While fuel cells do distribute fluids from one cell to another via the fuel manifolds, the effective conductivities of liquid-feed fuels and of most coolants are much lower than the conductivities of RFB electrolytes .
Because RFBs involve the circulation of electrolyte to each of the individual cells, there is an obvious ionic current path from one cell to another. The currents that flow in the circulating electrolyte from one cell to another via the electrolyte flow manifolds are best managed by increasing the effective resistance of the flow path, either by increasing the effective path length between cell flow inputs and outputs in the manifold, or by reducing the cross-sectional area of the ports. Unfortunately, increasing the resistance in such a way to minimize shunt currents also works to increase the resistance to flow. This has the result of increasing the requirements for parasitic power to circulate the electrolyte through the system; this complicates system design and increases both capital and operating costs. Several researchers have investigated the design implications for flow batteries for particular systems, though optimization will be required for specific electrolyte and cell configurations [135, 136, 137].
There are two main types of RFB separators. The first is a microporous separator that can allow for exchange of liquids between the anolyte and catholyte compartments. Such an approach is akin to the discussion above concerning a porous region. Because of this ability to mix, microporous separators often lead to higher rates of reactant and product crossover, and thus lower coulombic efficiencies. For this and other reasons, most RFBs use an ionically conducting membrane as a separator.
The IEM is one of the most critical components in RFBs. In terms of transport, the dual and opposing needs to enhance the desired charge transport while limiting undesired crossover of reactant, product, and other species is an unresolved engineering issue. There are a number of IEMs which have been used in RFBs, with the most common one being Nafion®, a perfluorosulfonic acid membrane that binds cations to its sulfonic acid sites . Nafion® is the membrane of choice in many RFBs due to its high proton and sodium conductivities and its proven stability in the chlor-alkali industry. It has a conduction mechanism that includes both hopping and vehicular modalities.
Summary and comparison of ion-exchange membranes used in all-vanadium RFB (VRB)
Ionic conductivity (mS/cm)
Liquid uptake (wt%)
Modified Nafion® 117
Two-step radiation-induced grafting
Skyllas-Kazacos et al. used the Amberlite CG 400 composite membrane in the VRBs. The membranes showed a good stability of more than 4000 h [43, 44]. Zhang et al. found that the current efficiency of 94 and 91% are achieved for Nafion® 115 and 112 membranes used in VRBs, respectively . However, the Nafion® membranes suffer from heavy active ion crossover and low ion selectivity. By incorporation of inorganic species (such as SiO2, TiO2, and ZrP) into Nafion®, the crossover of vanadium ions can be effectively reduced [143, 144, 152]. The ion selectivity can be enhanced using the organic/Nafion® hybrid membranes fabricated with interfacial polymerization and directly blending methods. Xi et al. prepared Nafion®/SiO2 hybrid membranes using in situ sol–gel method, and showed that the vanadium crossover was effectively reduced due to the polar clusters of the original Nafion® . The maximum energy efficiency of the VRB using this membrane was nearly 80% at 20 mA/cm2. Luo et al. modified Nafion® 117 membrane using interfacial polymerization method for VRB application . Sulfonated poly(tetramethydiphenyl ether ether ketone) (SPEEK) membrane showed one order of magnitude of vanadium ion permeability lower than that of Nafion® 115 . In the multiple-cycle tests, the SPEEK40 membrane shows high stability and high columbic efficiency above 98%. Generally, IEMs prepared with interfacial grafting, blend, radiation, non-fluorinated and hybrid membranes show lower ion permeability than that of Nafion® membrane. However, when Vn+ crossover is blocked, the protonic conductivity is also decreased which results in relatively low conductivity. So it is still a critical challenge for IEM development that ion selectivity is enhanced with high ionic conductivity. Vafiadis and Skyllas-Kazacos assessed a range of IEMs in vanadium/bromine RFBs considering ion-exchange capacity, conductivity, vanadium ion diffusion, water content, and chemical stability .
5 Cell modeling and design
In Fig. 10, the total current density, i, flows through the electrolyte phase (2) and the solid phase (1) at each respective end. In between, the current is apportioned based on the resistances in each phase and the charge-transfer resistances. The charge-transfer resistances can be nonlinear because they are based on kinetic expressions. Thus, the reaction will proceed depending on what is limiting. Since kinetics are typically facile in RFB systems, the main issues are reactant and ion movement to and away from the reaction site. For example, if the mass-transfer of a reactant is limiting, then the reaction will proceed near the inlet, whereas if ion conduction is limiting, then it will occur near the separator; a uniform reaction rate is rarely achieved without some kind of mass-transfer control (e.g., a microporous layer limiting flow of a reactant). An interesting issue is that one cannot diagnose what is limiting purely from a polarization curve, since even mass-transfer limitations can appear to be ohmic ones. For example, due to reactant mass-transfer limitations, a reaction may proceed at the electrode surface near the flow inlet yet the performance will look as if it is ohmically limited due to the distance the ions have to travel from the separator to the reaction site. Because of this and other reasons, mathematical modeling is often used to understand the limiting phenomena and processes in a RFB; yet, relative to the experimental and demonstration system development, analytical and computational modeling of RFBs has trailed, which may be due to the era in which they were heavily researched. Advanced modeling is needed to understand fully the various physiochemical phenomena involved to help minimize transport losses and facilitate optimized material design and architectures. The models help lead to optimized porous-electrode structures, which are crucial in increasing RFB performance and hence reducing cost. These issues are explored in more detail in this section.
5.1 Electrode structure
Whether a flow-through or a flow-by electrode can or must be used depends on a number of factors including the physical state of the flowing reactant (i.e. gas or liquid), the electrode reaction occurring (e.g. plating of solid or electron transfer in solution) and the conductivity of the electrolyte phase. For instance, in the prototypical or conventional RFB [57, 58] the reactants and products on both the anode and cathode are dissolved ions, and a porous 3D flow-through electrode, as shown in Fig. 11a, is typically used on both sides. In this configuration the liquid electrolyte flows through a porous matrix of electrochemically active solids, usually carbon fibers with appropriate catalytic surface properties. The ions produced by the reaction migrate through the electrolyte phase toward the opposing electrode and the electrons move through the network of carbon fibers to the current collector. The flow-through electrode is well suited to reactions of flowing liquid-phase species for a number of reasons. First, the diffusivity of liquid-phase species is quite low so forced convection through a porous electrode provides enhanced mass-transfer rates. Second, the concentration of reactive ions is generally low due to solubility limits so forced mass transfer helps maintain higher current densities. Finally, the flowing electrolyte will generally have a high ionic conductivity, which is necessary to avoid ohmic polarization losses over the long transport lengths created by the 3D configuration.
The planar electrode is most commonly used when a gaseous reactant is involved. A common example is the hydrogen/bromine cell  which uses a liquid mixture of bromine and aqueous hydrobromic acid on the cathode with a flow-through electrode (Fig. 11a) and gaseous hydrogen on the anode, with a flow-by electrode as shown in Fig. 11b. In this configuration a gaseous species flows in a channel parallel to the electrode and diffuses laterally to the essentially planar electrode surface. (In reality the electrode surface is a 3D porous zone of catalyst particles and immobilized electrolyte phase, but it behaves essentially as a planar surface on the scale of the electrode assembly.) The porous region of inert solid between the flow channel and the reactive surface acts to distribute gas uniformly to the catalyst and conduct electrons from the electrode to the current collector. The flow-by electrode is well suited to gaseous reactants for two reasons. First, the gaseous reactant stream does not conduct protons, so the reaction must happen at or near the electrolyte phase. Second, the diffusivity of gaseous species are 3 to 4 orders of magnitude higher than liquid-phase species so diffusive mass transfer is able to supply reactants to the electrode at a sufficient rate. Another variant of the flow-by electrode is shown in Fig. 11c, which is used when a solid is electrochemically plated out or dissolved as in the hybrid RFBs. Because the electrode grows during plating, it is not feasible to use a porous electrode as it would become plugged by the plating solid. The so-called single-flow cell reported by Pletcher, Wills and co-workers [2, 71] uses a solid electrode on both the anode and cathode where Pb and PbO are stored as plated solids. Ion conduction through the flowing electrolyte phase to the opposing electrode is at a maximum distance in this configuration so ohmic losses are high. Also, the surface area for reaction is at a minimum and equal to the geometric area of the cell. Consequently, this type of flow-by electrode is only used when absolutely necessary, as is the case of the aforementioned solid-plating electrodes.
The use of planar flow-by electrodes with liquid-phase reactants to demonstrate the viability of RFB technology is not uncommon in research papers on the subject [25, 63, 101], but flow-by electrodes, due to their limited surface area and long ion-transport distances, would almost never be preferred over 3D electrodes occupying the same volume. Even in the original RFB patent by Thaller , the possibility of using porous, 3D electrodes was included. Many of the tradeoffs of the various geometric placements and concerns can be found in the literature, including the pioneering work of Trainham and Newman [156, 157, 158] who examined optimum electrode placement and the tradeoffs between the two transport resistances in Fig. 10.
5.2 Cell modeling of certain chemistries
Fedkiw and Watts developed a mathematical isothermal model to describe the operation of a single anode-separator-cathode Fe/Cr cell based on electrode theory, redox kinetics, mass transfer, and ohmic effects. The parasitic hydrogen reaction was also considered . It is found that the separator ohmic resistance is the dominant cell resistance followed by the electrolyte ohmic resistance. The kinetic resistance was determined to be negligible at reasonable flow rates. It was predicted that countercurrent electrolyte flow improves global cell performance due to a more uniform current distribution. Decreasing the electrode area tended to decrease the cell current but resulted in high velocity and enhanced mass transfer within the penetration thickness and increased current. This model also provided a method of determined a charge–discharge protocol that obtained the maximum chromium conversion and minimum hydrogen evolution at the same time [159, 160]. Finally, Codina et al.  examined the issue of shunt currents when a cell is scaled up to larger sizes and stacks.
5.2.2 All vanadium (VRB)
Scamman et al. developed a numerical model that can be used for the design and optimization of large-scale bromine/polysulphide RFBs [170, 171]. They used the Butler–Volmer equation to estimate overpotential losses. The crossover of active species and self-discharge was also considered. This model is able to predict the concentration and current variation along the electrode and determine various efficiencies, energy density, and power density in the charge–discharge processes. It is found that the electrochemical rate constants of the bromide and sulphide are 4 × 10−5 and 3 × 10−6 cm/s, respectively.
6 Summary and future research needs
Charge transport and electrochemical reaction at and near the electrode surface.
The complex charge transport and nonidealities in the various RFB couples and electrolytes used.
Species charge transport and crossover in ionic-exchange membranes. For many systems, the membranes represent a key limiting component in system feasibility. Low-cost, low-permeability membranes with good ion selectivity, stability, high conductivity, and suitable mechanical properties are required.
The fluid mechanics and transport of electrolyte through the various electrode and cell architectures including coupled reaction rates and flow distribution to determine optimal electrode structures and properties.
To enable more complete studies in these areas, a new class of RFB diagnostics will also be needed. Another topic requiring future study as the systems with the greatest potential become defined is performance degradation. As in other, more studied, electrochemical-power-conversion systems, many modes of material degradation will likely be associated with transport processes that can be better optimized to promote longevity.
Finally, throughout this review not much mention has been made concerning other components within the RFB system. In particular, the typical solvents and chemistries are inherently highly corrosive due to their high ionic and perhaps protonic concentrations. Their nature makes sealing and material selection for pumps, flowfields, pipes, etc. very difficult and expensive; finding solutions to these issues is necessary for RFB systems to gain entrance to the market.
This work was partially funded by the Assistant Secretary for Energy Efficiency and Renewable Energy, Office of Fuel Cell Technologies, of the U.S. Department of Energy under contract number DE-AC02-05CH11231; work at UTK was carried out under NSF Early Career Development Award #0644811.
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
- 1.N. R. C. Committee for the National Academies Summit on America’s Energy Future (2008) The national academies summit on America’s energy future: summary of a meeting. National Academies Press, Washington, DCGoogle Scholar
- 2.EPRI (2004) Energy storage technology valuation primer: techniques for financial modeling. EPRI report 1008810, Palo Alto, CA, December 2004Google Scholar
- 3.Price A (2005) Proc Inst Civil Eng Civil Eng 158:52Google Scholar
- 4.EPRI (2002) Handbook of energy storage for transmission or distribution applications. EPRI report 1007189, Palo Alto, CAGoogle Scholar
- 5.Ponce De Leon C, Frias-Ferrer A, Gonzalez-Garcia J, Szanto D, Walsh FC (2006) J Power Sources 160:716Google Scholar
- 6.Li X, Zhang H, Mai Z, Vankelecom I (2011) Energy Environ Sci 4:1147Google Scholar
- 7.Skyllas-Kazacos M, Chakrabarti MH, Hajimolana SA, Mjalli FS, Saleem M (2011) J Electrochem Soc 158:R55Google Scholar
- 8.Yang ZG, Zhang JL, Kintner-Meyer MCW, Lu XC, Choi DW, Lemmon JP, Liu J (2011) Chem Rev 111:3577Google Scholar
- 9.Symons PC, Butler PC (2002) In: Linden D, Reddy TB (eds) Handbook of batteries, 3rd edn. McGraw-Hill, New YorkGoogle Scholar
- 10.Kaldellis JK, Zafirakis D (2007) Energy 32:2295Google Scholar
- 11.Makarov YV, Loutan C, Ma J, De Mello P (2009) IEEE Trans Power Syst 24:1039Google Scholar
- 12.Department of Energy Office of Electricity Delivery and Energy Reliability (2011, May) http://www.oe.energy.gov/
- 13.Department of Energy (2009, May) President Obama Announces $3.4 billion investment to spur transition to smart grid. http://www.energy.gov/news2009/8216.html
- 14.N. Group (2010) Advanced materials and devices for stationary electrical energy storage applications, Nexight Group. http://energy.tms.org/docs/pdfs/Advanced_Materials_for_SEES_2010.pdf
- 15.E. A. Committee (2008) Bottling electricity: storage as a strategic tool for managing variability and capacity concerns in the modern grid, Nexight Group. http://www.doe.gov/sites/prod/files/oeprod/DocumentsandMedia/DRAFT_EAC_Energy_Storage_Technologies_Report_11-21-08_CLEAN_COPY.pdf
- 16.Skyllas-Kazacos M, Grossmith F (1987) J Electrochem Soc 134:2950Google Scholar
- 17.Remick RJ, Ang PGP (1984) Electrically rechargeable anionically active reduction-oxidation electrical storage-supply system. USA Patent 4485154, November 27, 1984Google Scholar
- 18.Zhou HT, Zhang HM, Zhao P, Yi BL (2006) Electrochim Acta 51:6304Google Scholar
- 19.Thaller LH (1974) NASA TM-X-71540Google Scholar
- 20.Thaller LH (1979) NASA TM-79143, DOE/NASA/1002-79/3Google Scholar
- 21.Bartolozzi M (1989) J Power Sources 27:219Google Scholar
- 22.Walsh F (2001) Pure Appl Chem 73:1819Google Scholar
- 23.Price A, Bartley S, Male S, Cooley G (1999) Power Eng J 13:122Google Scholar
- 24.Lessner P, Mclarnon F, Winnick J, Cairns E (1992) J Appl Electrochem 22:927Google Scholar
- 25.Skyllas-Kazacos M, Rychcik M, Robins RG, Fane AG, Green MA (1986) J Electrochem Soc 133:1057Google Scholar
- 26.Skyllas Kazacos M, Rychick M, Robins RG (1988) All-vanadium redox battery. United States of America PatentGoogle Scholar
- 27.Sum E, Rychcik M, Skyllas-Kazacos M (1985) J Power Sources 16:85Google Scholar
- 28.Sum E, Skyllas-Kazacos M (1985) J Power Sources 15:179Google Scholar
- 29.Kazacos M, Cheng M, Skyllas-Kazacos M (1990) J Appl Electrochem 20:463Google Scholar
- 30.Skyllas-Kazacos M, Kasherman D, Hong D, Kazacos M (1991) J Power Sources 35:399Google Scholar
- 31.Rahman F, Skyllas-Kazacos M (1998) J Power Sources 72:105Google Scholar
- 32.Skyllas-Kazacos M, Peng C, Cheng M (1999) Electrochem Solid-State Lett 2:121Google Scholar
- 33.Kausar N, Howe R, Skyllas-Kazacos M (2001) J Appl Electrochem 31:1327Google Scholar
- 34.Hagg CM, Skyllas-Kazacos M (2002) J Appl Electrochem 32:1063Google Scholar
- 35.Sukkar T, Skyllas-Kazacos M (2003) J Membr Sci 222:235Google Scholar
- 36.Sukkar T, Skyllas-Kazacos M (2004) J Appl Electrochem 34:137Google Scholar
- 37.Rahman F, Skyllas-Kazacos M (2009) J Power Sources 189:1212Google Scholar
- 38.Skyllas Kazacos M, Kazacos G, Poon G, Verseema H (2010) Int J Energy Res 34:182Google Scholar
- 39.Vijayakumar M, Burton SD, Huang C, Li L, Yang Z, Graff GL, Liu J, Hu J, Skyllas-Kazacos M (2010) J Power Sources 195:7709Google Scholar
- 40.Chen J, Wang Q, Wang B (2006) Modern Chem Ind 9:26Google Scholar
- 41.Shibata A, Sato K (1999) Power Eng J 13:130Google Scholar
- 42.Shigematsu T, Kumamoto T, Deguchi H, Hara T (2002) Applications of a vanadium redox-flow battery to maintain power quality. Presented at the transmission and distribution conference and exhibition 2002: Asia Pacific. IEEE/PESGoogle Scholar
- 43.Mohammadi T, Chieng S, Skyllas Kazacos M (1997) J Membr Sci 133:151Google Scholar
- 44.Mohammadi T, Skyllas-Kazacos M (1997) J Appl Electrochem 27:153Google Scholar
- 45.Miyake S, Tokuda N (2002) Battery diaphragm. Google PatentsGoogle Scholar
- 46.Hennessy TDJ (2007) Telecommunication system incorporating a vanadium redox battery energy storage system. Google PatentsGoogle Scholar
- 47.Zhao P, Zhang H, Zhou H, Chen J, Gao S, Yi B (2006) J Power Sources 162:1416Google Scholar
- 48.Skyllas-Kazacos M (2003) J Power Sources 124:299Google Scholar
- 49.Skyllas-Kazacos M, Menictas C, Kazacos M (1996) J Electrochem Soc 143:L86Google Scholar
- 50.Skyllas-Kazacos M, Limantari Y (2004) J Appl Electrochem 34:681Google Scholar
- 51.Vafiadis H, Skyllas-Kazacos M (2006) J Membr Sci 279:394Google Scholar
- 52.Chang BJ, Garcia CP, Johnson DW, Bents DJ, Scullin VJ, Jakupca IJ (2007) J Fuel Cell Sci Technol 4:497Google Scholar
- 53.Grigoriev SA, Millet P, Porembsky VI, Fateev VN (2011) Int J Hydrogen Energy 36:4164Google Scholar
- 54.Li XJ, Xiao Y, Shao ZG, Yi BL (2010) J Power Sources 195:4811Google Scholar
- 55.Mitlitsky F, Myers B, Weisberg AH (1998) Energy Fuels 12:56Google Scholar
- 56.Neyerlin KC, Gu WB, Jorne J, Gasteiger HA (2006) J Electrochem Soc 153:A1955Google Scholar
- 57.Kim JT, Jorne J (1977) J Electrochem Soc 124:1473Google Scholar
- 58.Kosek JA, Laconti AB (1988) J Power Sources 22:293Google Scholar
- 59.Livshits V, Ulus A, Peled E (2006) Electrochem Commun 8:1358Google Scholar
- 60.Cathro KJ, Cedzynska K, Constable DC (1987) J Power Sources 19:337Google Scholar
- 61.Mader MJ, White R (1986) J Electrochem Soc 133:1297Google Scholar
- 62.Hromadova M, Ronald Fawcett W (2001) J Phys Chem A 105:104Google Scholar
- 63.Lim HS, Lackner AM, Knechtli RC (1977) J Electrochem Soc 124:1154Google Scholar
- 64.R. Ltd. (2011) URL: http://www.redflow.com.au/. Accessed May 2011
- 65.Jorne J, Kim JT, Kralik D (1979) J Appl Electrochem 9:573Google Scholar
- 66.Zito R (1973) US Patent 3719526Google Scholar
- 67.Hruska LW, Savinell RF (1981) J Electrochem Soc 128:18Google Scholar
- 68.Dougherty, B, Clarke RL, Harrion S, Millington PJ, Mohanta S (2009) Cerium batteries. U.S. PatentGoogle Scholar
- 69.P. Ltd. (2011) http://plurionsystems.com/tech_flow_advantages.html
- 70.Leung P, De León CP, Walsh F (2011) Electrochem Commun 13:770Google Scholar
- 71.Raju T, Basha CA (2008) Ind Eng Chem Res 47:8947Google Scholar
- 72.Crompton TR (ed) (2000) Elsevier science and technology books, vol 14, 3rd edn. Newnes, BostonGoogle Scholar
- 73.Fang B, Iwasa S, Wei Y, Arai T, Kumagai M (2002) Electrochim Acta 47:3971Google Scholar
- 74.Matsuda Y, Tanaka K, Okada M, Takasu Y, Morita M, Matsumura-Inoue T (1988) J Appl Electrochem 18:909Google Scholar
- 75.Chakrabarti M, Dryfe R, Roberts E (2007) Electrochim Acta 52:2189Google Scholar
- 76.Yamamura T, Shiokawa Y, Yamana H, Moriyama H (2002) Electrochim Acta 48:43Google Scholar
- 77.Liu Q, Sleightholme AES, Shinkle AA, Li Y, Thompson LT (2009) Electrochem Commun 11:2312Google Scholar
- 78.Liu Q, Shinkle AA, Li Y, Monroe CW, Thompson LT, Sleightholme AES (2010) Electrochem Commun 12:1634Google Scholar
- 79.Sleightholme AES, Shinkle AA, Liu Q, Li Y, Monroe CW, Thompson LT (2011) J Power Sources 196:5742Google Scholar
- 80.Shinkle AA, Sleightholme AES, Griffith LD, Thompson LT, Monroe CW (2011) J Power Sources (in press)Google Scholar
- 81.Kraytsberg A, Ein-Eli Y (2011) J Power Sources 196:886Google Scholar
- 82.Chiang Y, Carter WC, Ho B, Duduta M (2009) High energy density redox flow device. WO Patent WO/2009/151639Google Scholar
- 83.Duduta M, Ho B, Wood VC, Limthongkul P, Brunini VE, Craig Carter W, Chiang Y-M (2011) Adv Energy Mater 1Google Scholar
- 84.Vetter KJ (1967) Electrochemical kinetics: theoretical and experimental aspects. Academic Press, New YorkGoogle Scholar
- 85.Bard AJ, Faulkner LR (2000) Electrochemical methods: fundamentals and applications. Wiley, HobokenGoogle Scholar
- 86.Gerischer H (1960) Z Physik Chem. Neue Forschung 26:223Google Scholar
- 87.Newton MD, Smalley JF (2007) Phys Chem Chem Phys 9:325Google Scholar
- 88.Bard AJ (2010) J Am Chem Soc 132:7559Google Scholar
- 89.Nagy Z, Hung NC, Yonco RM (1991) J Electrochem Soc 138:2032Google Scholar
- 90.Randles JEB, Somerton KW (1952) Trans Faraday Soc 48:937Google Scholar
- 91.Gattrell M, Qian J, Stewart C, Graham P, Macdougall B (2005) Electrochim Acta 51:395Google Scholar
- 92.Zhong S, Kazacos M, Burford R, Skyllas-Kazacos M (1991) J Power Sources 36:29Google Scholar
- 93.Faita G, Fiori G, Mussini T (1978) Electrochim Acta 13:1765Google Scholar
- 94.Mastragostino M, Gramellini C (1985) Electrochim Acta 30:373Google Scholar
- 95.Haddadi-Asl V, Kazacos M, Skyllas-Kazacos M (1995) J Appl Electrochem 25:29Google Scholar
- 96.Han P, Wang H, Liu Z, Chen X, Ma W, Yao J, Zhu Y, Cui G (2011) Carbon 49:693Google Scholar
- 97.Hung NC, Nagy Z (1987) J Electrochem Soc 134:2215Google Scholar
- 98.Kinoshita K (1988) Carbon. Electrochemical and physiochemical properties. Wiley, New YorkGoogle Scholar
- 99.Rosseinsky DR (1965) Chem Rev 65:467Google Scholar
- 100.Inoue M, Tsuzuki Y, Iizuka Y, Shimada M (1987) J Electrochem Soc 134:756Google Scholar
- 101.De Leon CP, Reade GW, Whyte I, Male SE, Walsh FC (2007) Electrochim Acta 52:5815Google Scholar
- 102.Thaller LH (1976) Electrically rechargeable redox flow cell. US patent 3996064Google Scholar
- 103.EISA (2007) Energy independence and security act of 2007, in PL 110-140, United States of AmericaGoogle Scholar
- 104.Shao YY, Wang XQ, Engelhard M, Wang CM, Dai S, Liu J, Yang ZG, Lin YH (2010) J Power Sources 195:4375Google Scholar
- 105.Chiang YM, Bazzarella R (2010) Fuel system using redox flow battery. WO Patent WO/2010/118060Google Scholar
- 106.Van Brakel J, Heertjes PM (1974) Int J Heat Mass Transf 17:1093Google Scholar
- 107.Carta R, Palmas S, Polcaro AM, Tola G (1991) J Appl Electrochem 21:793Google Scholar
- 108.Dullien FaL (1992) Porous media: fluid transport and pore structure, 2nd edn. Academic Press, Inc., New YorkGoogle Scholar
- 109.Gostick JT, Fowler MW, Pritzker MD, Ioannidis MA, Behra LM (2006) J Power Sources 162:228Google Scholar
- 110.Newman J (1995) J Electrochem Soc 142:97Google Scholar
- 111.Roy A, Hickner MA, Einsla BR, Harrison WL, Mcgrath JE (2009) J Polym Sci A 47:384Google Scholar
- 112.Sankir M, Kim YS, Pivovar BS, Mcgrath JE (2007) J Membr Sci 299:8Google Scholar
- 113.Gostick JT, Ioannidis MA, Fowler MW, Pritzker MD (2010) In: Wang CY, Pasaogullari U (eds) Modern aspects of electrochemistry, vol 49. Springer, BerlinGoogle Scholar
- 114.Newman J, Thomas-Alyea KE (2004) Electrochemical systems, 3rd edn. Wiley, New YorkGoogle Scholar
- 115.Bird RB, Stewart WE, Lightfoot EN (2002) Transport phenomena, 2nd edn. Wiley, New YorkGoogle Scholar
- 116.Einstein A (1905) Ann Physik 17:549Google Scholar
- 117.Nernst W (1888) Zeitschrift fuer Physikalische Chemie 2:613Google Scholar
- 118.Weber AZ, Newman J (2004) Chem Rev 104:4679Google Scholar
- 119.Bear J (1988) Dynamics of fluids in porous media. Dover Publications Inc, New YorkGoogle Scholar
- 120.Chen YWD, Bard AJ (1984) Inorg Chem 23:2175Google Scholar
- 121.Sun B, Sykllaskazacos M (1992) Electrochim Acta 37:1253Google Scholar
- 122.Zhao P, Zhang HM, Zhou HT, Yi BL (2005) Electrochim Acta 51:1091Google Scholar
- 123.Sun B, Skyllaskazacos M (1992) Electrochim Acta 37:2459Google Scholar
- 124.Joerissen L, Garche J, Fabjan C, Tomazic G (2004) J Power Sources 127:98Google Scholar
- 125.Duarte MME, Pilla AS, Sieben JM, Mayer CE (2006) Electrochem Commun 8:159Google Scholar
- 126.Yan A, Xiao X, Kulaots I, Sheldon BW, Hurt RH (2006) Carbon 44:3116Google Scholar
- 127.Sioda R (1977) Electrochim Acta 22:439Google Scholar
- 128.Cano J, Böhm U (1977) Chem Eng Sci 32:213Google Scholar
- 129.Li L, Kim S, Wang W, Vijayakumar M, Nie Z, Chen B, Zhang J, Xia G, Hu J, Graff G (2011) Adv Energy Mater 1:394Google Scholar
- 130.Ridgway P, Cho K, Battaglia VS, Weber AZ, Srinivasan V (2011) Redox kinetics of the bromine-bromide reaction for flow batteries. Presented at the 220th meeting of the Electrochemical Society, Boston, MAGoogle Scholar
- 131.Horne C, Kinoshita K, Hickey DB (2010) Redox flow battery system for distributed energy storage. United States Patent 12/498103Google Scholar
- 132.Schroll CR (1984) Manifold dielectric barrier for a fuel cell electrical power generation system. United States of America PatentGoogle Scholar
- 133.Katz M (1978) J Electrochem Soc 125:515Google Scholar
- 134.Zhou G, Chen L, Seaba J (2006) Proceedings of the 4th international ASME conference on fuel cell science, engineering, and technology, Pts A and B, p 863Google Scholar
- 135.Codina G, Aldaz A (1992) J Appl Electrochem 22:668Google Scholar
- 136.Codina G, Perez JR, Lopezatalaya M, Vazquez JL, Aldaz A (1994) J Power Sources 48:293Google Scholar
- 137.Kanari K, Nozaki K, Kaneko H, Hashimoto T, Fujii T (1991) Denki Kagaku 59:237Google Scholar
- 138.Mauritz KA, Moore RB (2004) Chem Rev 104:4535Google Scholar
- 139.Weber AZ, Newman J (2004) J Electrochem Soc 151:A311Google Scholar
- 140.Pintauro PN, Bennion DN (1984) Ind Eng Chem Fundam 23:230Google Scholar
- 141.Weber AZ, Delacourt C (2008) Fuel Cells 8:459Google Scholar
- 142.Delacourt C, Newman J (2008) J Electrochem Soc 155:B1210Google Scholar
- 143.Xi J, Wu Z, Qiu X, Chen L (2007) J Power Sources 166:531Google Scholar
- 144.Teng X, Zhao Y, Xi J, Wu Z, Qiu X, Chen L (2009) J Power Sources 189:1240Google Scholar
- 145.Jia C, Liu J, Yan C (2010) J Power Sources 195:4380Google Scholar
- 146.Qiu J, Zhai M, Chen J, Wang Y, Peng J, Xu L, Li J, Wei G (2009) J Membr Sci 342:215Google Scholar
- 147.Qiu J, Zhao L, Zhai M, Ni J, Zhou H, Peng J, Li J, Wei G (2008) J Power Sources 177:617Google Scholar
- 148.Chen D, Wang S, Xiao M, Meng Y (2010) J Power Sources 195:2089Google Scholar
- 149.Chen D, Wang S, Xiao M, Meng Y (2010) Energy Convers Manag 51:2816Google Scholar
- 150.Chen D, Wang S, Xiao M, Meng Y (2009) Energy Environ Sci 3:622Google Scholar
- 151.Teng X, Zhao Y, Xi J, Wu Z, Qiu X, Chen L (2009) J Membr Sci 341:149Google Scholar
- 152.Sang S, Wu Q, Huang K (2007) J Membr Sci 305:118Google Scholar
- 153.Luo Q, Zhang H, Chen J, Qian P, Zhai Y (2008) J Membr Sci 311:98Google Scholar
- 154.Newman J, Tiedemann W (1975) AIChE J 21:25Google Scholar
- 155.Yue L, Li WS, Sun FQ, Zhao LZ, Xing LD (2010) Carbon 48:3079Google Scholar
- 156.Trainham JA, Newman J (1977) J Electrochem Soc 124:1528Google Scholar
- 157.Trainham JA, Newman J (1977) J Appl Electrochem 7:287Google Scholar
- 158.Trainham JA, Newman J (1978) J Electrochem Soc 125:58Google Scholar
- 159.Fedkiw PS, Watts RW (1984) J Electrochem Soc 131:701Google Scholar
- 160.Lopez-Atalaya M, Codina G, Perez J, Vazquez J, Aldaz A (1992) J Power Sources 39:147Google Scholar
- 161.Al-Fetlawi H, Shah AA, Walsh FC (2009) Electrochim Acta 55:78Google Scholar
- 162.Al-Fetlawi H, Shah AA, Walsh FC (2010) Electrochim Acta 55:3192Google Scholar
- 163.Knehr K, Kumbur E (2011) Electrochem Commun 13:342Google Scholar
- 164.Shah A, Al-Fetlawi H, Walsh F (2010) Electrochim Acta 55:1125Google Scholar
- 165.Shah A, Tangirala R, Singh R, Wills RGA, Walsh FC (2011) J Electrochem Soc 158:A671Google Scholar
- 166.Vynnycky M (2011) Energy 36:2242Google Scholar
- 167.You D, Zhang H, Chen J (2009) Electrochim Acta 54:6827Google Scholar
- 168.Shah A, Watt-Smith M, Walsh F (2008) Electrochim Acta 53:8087Google Scholar
- 169.Li M, Hikihara T (2008) IEICE Trans Fundam Electron Commun Comput Sci E91A:1741Google Scholar
- 170.Scamman DP, Reade GW, Roberts EPL (2009) J Power Sources 189:1220Google Scholar
- 171.Scamman DP, Reade GW, Roberts EPL (2009) J Power Sources 189:1231Google Scholar
- 172.Evans TI, White RE (1987) J Electrochem Soc 134:2725Google Scholar
- 173.Putt R (1979) Assessment of technical and economic feasibility of zinc/bromine batteries for utility load-levelling. EPRI report Em-1059, Project 635-1, Palo Alto, CA, Appendix MGoogle Scholar
- 174.Lee J, Selman J (1982) J Electrochem Soc 129:1670Google Scholar
- 175.Jorne J (1982) J Electrochem Soc 129:2251Google Scholar
- 176.Roayaie E, Jorne J (1985) J Electrochem Soc 132:1273Google Scholar
- 177.Trinidad P, De Leon CP, Walsh F (2008) J Environ Manag 88:1417Google Scholar