This invention relates to flow batteries that maximize energetic efficiency utilizing non-Newtonian fluids.
The integration of renewable energy sources (e.g., wind and solar) and the efficient management of electricity on the existing grid stands to benefit from scalable, low-cost energy storage technology.1-4 Several recent electrochemical energy storage approaches attempt to hybridize aspects of static and flowing batteries and thereby gain improvements in energy density and cost.5-7 Amongst these is the semi-solid flow cell (SSFC) of Duduta et al.,5 which integrates solid-state ion-insertion compounds in a mixed-conducting, flowable suspension. Instead of flowing an electronically insulating fluid through a porous current collector as in conventional flow batteries, the conductive suspension of the SSFC provides intrinsic electronic conductivity and can be flowed through unobstructed channels in the flow battery stack. By leveraging the high charge capacity of solid-state active materials and the high operating voltage of non-aqueous electrode couples, energy density can be increased dramatically over conventional aqueous flow batteries.5 Although suspensions typically have higher viscosity than solutions, for shear-thinning rheology it has been shown that flow-related losses can be <5% of stored electrochemical energy when the cell is operated in an intermittent flow mode, wherein fluid is replenished in discrete steps and electrochemically cycled when at rest.5,8,9 Subsequent studies adopting the semi-solid approach have integrated various electroactive solids in aqueous9 and non-aqueous10,11 electrolytes. The SSFC concept has also been extended to electrolytic flow capacitors.12-14
Even for redox couples that remain purely in solution form, a conductive suspension approach may offer advantages over the conventional flow architecture. The energy density of redox solutions increases in proportion to solubility (concentration), and large molecules tend to have higher solubility than small. Thus, increases in energy density are accompanied by higher viscosities that tend to inhibit flow through the conventional cells' porous current collectors.15,16 A suspension of percolating conductive particles (e.g., carbon black) in a redox solution can produce an electronically conductive redox electrode that can be used without a porous current collector.17,18 This intrinsic current collector network can also support precipitates formed upon cycling of low-solubility redox molecules (e.g., metal-coordinated couples19-21) and Li-polysulphides,7,22 and use of high surface area conductors such as carbon-blacks (˜1000 m2/g-carbon) may enhance charge transfer kinetics.
However, a viscous, conductive suspension may incur at least two efficiency loss mechanisms not encountered in conventional flow batteries. In addition to viscous dissipation, the electroactive region may extend outside the cell stack, leading to dissipation of electrochemical energy and thermal losses.23 As we will demonstrate, the electrochemical performance is also coupled to the uniformity of the flow field; in general, non-uniformity leads to reduced coulombic and energetic efficiency.
The flow battery according to the invention includes high energy density fluid electrodes having a selected non-Newtonian rheology and structure for providing intermittent flow pulses of controlled volume and duration of the fluid electrodes, the structure adapted to promote interfacial slip to improve flow uniformity.
In a preferred embodiment, the fluid electrodes are suspensions. The suspensions may contain active materials or conductive networks in redox solutions. It is preferred that the controlled volume be a critical aliquot for intermittent flow mode operation. Surface roughness, textures, or patterns may be selected to promote slip.
a, b, c and d are schematic illustrations of the four part strategy to maximize efficiency constituted by flow volume control, suspension rheology, active-material thermodynamics, and interfacial slip promotion.
a is a perspective view of a simulated half-cell. Gray and black particles (not drawn to scale) respectively represent active materials and conductive additive that comprise a suspension.
b is a cross-sectional view of a two-dimensional domain employed in the present invention.
a is a graph of voltage against charge time for different active materials.
b and c illustrate state-of-charge as a function of time for a two-aliquot plug-flow cycle with an aliquot factor of m=1.0.
a is a graph of voltage against charge time for three active materials.
b illustrates state-of-charge as a function of time for a two-aliquot cycle with Newtonian flow in the absence of slip and an aliquot factor of m=1.0.
a are graphs of voltage against charge time for three active materials.
b illustrates state-of-charge as a function of time for a two-aliquot cycle with Newtonian flow in the absence of slip and an aliquot factor of m=0.5.
a are graphs of voltage against charge time for three active materials.
b illustrates state-of-charge as a function of time for a four aliquot cycle with Newtonian flow in the absence of slip and an aliquot factor of m=0.5.
a, b, c, d and e illustrate performance as a function of aliquot factor for a Newtonian flow without slip.
a, b, c, d and e illustrate performance as a function of slip number S1 with infinite mean velocity and with critical aliquots.
a, b, c, d and e illustrate performance as a function of Bingham number Bn without wall slip and with critical aliquots.
In this patent application, these loss mechanisms are simulated, and provide four strategies by which the energetic efficiency of suspension-based flow batteries can be maximized (
A schematic of the simulated flowing half-cell appears in
Three active materials (Table 1) were simulated.
Two of these active materials are solid-state Li-ion intercalation compounds LiFePO4 and LiCoO2, and the other is a redox solution (VO2+/VO2+). Each equilibrium potential versus state-of-charge (SOC) curve is illustrated in
LiFePO4→LixFePO4+(1−x)Li++(1−x)e−.
A consequence of this two-phase equilibrium is that spatial SOC gradients can exist at thermodynamic equilibrium because LiFePO4 particulates can have a particular phase fraction with any average SOC between 9% and 97% and maintain at the same equilibrium potential However, for LiCoO2,25,26
LiCoO2→Li1-yCoO2+yLi++ye−
the two phase plateau is much smaller. As a consequence, such equilibrium SOC gradients can exist over a smaller SOC window (15-50%). Thus, over most of a full SOC swing, LiCoO2 exhibits single-phase behavior for which equilibrium gradients cannot exist. We model these solid-state active materials with non-aqueous electrolytes, e.g., 1 mol/L LiPF6 in mixed carbonate solvent.27
We also analyze the cathodic couple of the vanadium-redox aqueous solution (VO2+/VO2+). The following simplified reaction is modeled in which VO2+ is oxidized to VO2+ during charging:25
VO2++H2O→VO2+2H++e−.
This system is hereafter referred to as “V-redox.” The solubility and mobility of redox ions in the electrolyte enables mixing of SOC throughout the cell. We modeled a suspension in which this redox solution contains a percolating network of electronically conductive particles. The resulting suspension has finite electronic conductivity as well as ionic conductivity, and charge transfer reactions are assumed to occur at the conductor-solution interface. Representative aqueous electrolytes for this system include H2SO4 (Ref. 28) and chloride solutions (Ref. 29).
Previous work5,8 has demonstrated that operating SSFCs in an intermittent flow mode reduces pumping losses relative to the continuous flow mode in which conventional flow cells are typically operated. Accordingly, we emphasize the intermittent flow mode, although continuous flow behavior can be inferred directly by extrapolating to the limit of many short duration intermittent pulses.
An alphanumeric rubric is used to distinguish the cycle steps for all of the subsequent results, as shown in
The cycle above represents the simplest in a class of intermittent cycles for which we now describe the possible operational parameters. We define the pumped volume relative to that of a unit aliquot (i.e., the cell's internal volume) and refer to this quantity as the aliquot factor m, (e.g., m=1 and m=0.25 correspond to pumping one full aliquot and one-quarter aliquot per pump stroke, respectively.) The system's total suspension volume is given as a multiple of unit aliquots. The flow rate at which pumping occurs dictates the flow profile shape for a particular suspension rheology, suspension/wall interface, and cell channel design. As we show below, the influence of flow rate, material parameters (both rheological and slip), and channel dimensions can be captured in terms of two dimensionless parameters describing the complete space of velocity profiles for a typical non-Newtonian flow electrode exhibiting both wall slip and steady shear in the suspension's bulk.
The electrochemical operation of the cell is specified by the upper and lower voltage cutoff limits applicable to the electrochemical couple (Table 1) and the time dependence of the applied current, Iapplied. One of the attributes of flow batteries is that the relative capacities of the stack and tanks can be varied arbitrarily. Here we stimulated current rates for the cell of C/3 (full charge and discharge of the stack in 3 hours), corresponding to long-duration storage for a complete system that is some multiple of 3 hours.
The computational model includes simultaneous electrochemical processes (electronic conduction, reaction kinetics, and redox-species diffusion) and fluid flow. The symmetry of the simulated cell allows it to be modeled as two-dimensional [
In the absence of flow, electronic conduction occurs via the conductive-particle percolating-network suspended in the electrolyte, and the solid-phase potential φx is governed by charge conservation:
∇·(−σs∇φs)+ain=0, (1)
where φs is the effective electronic conductivity of the suspension. The second term in Eq. (1) is a source term that couples electronic conduction to the electrochemical surface reaction characterized by the local reaction current density in and surface area per unit suspension volume a. Because the entire suspension is electronically conductive, electrochemical reactions can occur outside the immediate electroactive region of the cell 23 (this is implicit in Eq. 1). It has been shown that the electronic conductivity varies widely with carbon black content.5,9,31 Here, we assume a value of 1 mS/cm for σs corresponding to experimental results for −1 vol. % Ketjen black in non-aqueous31 and aqueous9 suspensions. Recent work has also shown that the electronic conductivity of semi-solid suspensions depends on shear rate,32 but such variations will have negligible impact on the intermittent flow mode used here (i.e., charging takes place when the semi-solid electrode is static). In addition, conductivity variations due to microstructural relaxation after a flow pulse are expected to be minimal, since oil-based suspensions of carbon black have exhibited gelation times33 that are at least five orders of magnitude smaller than the present charge/discharge time-scales.
For suspensions using typical Li-ion intercalation compounds (e.g., LiFePO4 and LiCoO2) of fine particle size, intercalated lithium concentration at the particle surface differs by less than 1% of the bulk value at C/3 rate (based on room-temperature diffusivities inferred from Refs. 34,35). Consequently, the intercalated lithium fraction xLi at a given time t is assumed uniform and is governed by the following conservation equation:
where cs,max is the volumetric concentration of intercalated lithium at saturation, vs is the volume fraction of active material, and F is Faraday's constant. The values of cs,max for LiFePO4 and LiCoO2 are 22.8 mol/L (Ref. 36) and 51.6 mol/L (Ref. 37), respectively. (It is these high molarities, compared to the 1-2 mol/L concentrations typical of aqueous redox flow batteries,15,16 that allow semi-solid electrodes to have high energy densities.) SOC is defined by the intercalated lithium fraction relative to those at the charge and discharge cutoff voltages listed in Table 1.
In the case of the V-redox system, the diffusion time-scale for redox molecules through the electrode thickness is much shorter (˜10 s) than the cycling time-scale. The flux of redox species is dominated by diffusion (i.e., not migration), because the high ionic conductivity of concentrated, acidic electrolytes (e.g., H2SO4 (Ref. 28) or chloride solutions29) minimizes the electric field that drives migration. Therefore, mass conservation of VO2+ and VO2+ in the absence of migration sufficiently describes the electrochemical processes that occur in the V-redox system:
where cj and Deffj are the concentration and effective diffusivity of redox species j in the electrolyte. The SOC of the electrode is equivalent to the concentration of VO2+. Source terms in Eqs. 3 and 4 couple redox-species diffusion to the electrochemical reaction that occurs at conductor-electrolyte interfaces. The exclusion of electrolyte volume from the suspension by the conductive carbon (1 vol. % loading) is negligible, and the suspension's porosity ε is approximately 100%. The diffusivities for both V-redox species are assigned bulk values of 3.9×10−01 m2/s from literature.38
The surface overpotential η drives electrochemical reactions at solid-electrolyte interfaces and is given as η=φs−φe−φeq, where φe and φeq are the ionic potential of the electrolyte and the equilibrium potential of the active material, respectively. The equilibrium potential models of the three active materials (as a function of xLi and redox species concentrations) were taken from the literature39-41 and are shown in
where i0 is the exchange current density and RT has its usual meaning. In general, the exchange current density i0 depends on the concentration of active species. This dependence reflects the competition between forward and reverse reactions at the conductor-electrolyte interface, and, therefore, the functional form of i0 depends on the type of reaction. Table 2 summarizes the kinetic parameters and volumetric surface area, a (m2/m3), for each suspension. For the solid-state active materials, a is the active-particle/electrolyte interface area (per unit suspension volume), and the exchange current density can be expressed as:42
i
0
=Fkc
s,max(ce)0.5(1−xLi)0.5(xLi)0.5, (6)
where ce is the ion-conducting species concentration in the electrolyte (taken as 1 mol/L here), k is the reaction rate-constant, and xLi is the intercalated lithium fraction (determined by solving Eq. 2). The values of a used here assume 100 nm diameter LiFePO443 and 4 μm diameter LiCoO237 particles.
The exchange current density i0 for the cathodic V-redox reaction depends on the concentration of redox species j at the reaction surface, cjs:28
i
0
=Fk(cVO
Pore-scale mass-transfer resistance causes surface concentrations, cjs, to differ from the bulk electrolyte concentrations, cj, of a given species j:28
where dp is the pore diameter of the material on which the surface reaction takes place. We utilize the procedure described in Ref. 28 to determine the surface concentrations, for the V-redox suspension 1 vol. % loading of Ketjen black is assumed with a specific surface area of 1453 m2/g (Ref. 44) and a pore diameter of 100 nm (in between the size of the carbon black aggregates and the individual particles comprising them45).
When intermittent flow pulses occur much faster than electrochemical processes, pure advection governs both intercalated lithium fraction:
and species concentration fields:
where {right arrow over (v)} is the suspension velocity field. Fully developed, axial flows are considered here, the velocity fields of which are non-zero only in the x-direction and depend only on the y-coordinate [see
{right arrow over (v)}=u(y)î, (12)
where î is the unit vector along the channel's axis (taken as the x-coordinate). Results for a variety of velocity profiles are presented below.
To simulate galvanostatic charge/discharge conditions a time-invariant total current Iapplied is imposed at current-collector/suspension boundaries (denoted, Γcc):
where d{right arrow over (Γ)} is the inward-pointing differential area vector. The present simulations use an applied current concomitant with the complete charging of the electroactive region in 3 hours (i.e., C/3 stack-level rate). Potential drops due to bulk resistance of the metallic current collector are neglected. Contact resistance at the suspension/current-collector interface is also neglected, as its value is highly material-dependent. We note that contact resistance would increase the effective impedance of the cell and is not expected to change the qualitative trends observed here. Though flow-induced contact resistance in electrochemical flow capacitors has been suggested,14 their effect in the intermittent flow mode will be minimal because all charge transfer takes place when the electrode is static. All remaining surfaces in contact with the suspension are modeled as electronically insulating.
For the V-redox system, a proton-conducting membrane impenetrable to redox species is assumed in place of the separator in
The governing equations for electrochemistry without flow were discretized with the finite volume method46 with implicit discretization in time and central difference discretization in space. The fully coupled set of electrochemical equations was solved with the aggregation-based algebraic multigrid program.47-50 Iterative convergence of all overpotentials was achieved within 10−9 V. Because the transfer of charge and species is purely advective during intermittent pumping, a semi-Lagrangian method was implemented to obtain solutions to Eqs. 10 and 11. Specifically, intercalated-lithium fraction and species concentration were determined using backward-time, nearest-neighbor interpolation along streamlines. The resulting numerical scheme conserves species, because the streamlines (along which nearest-neighbor interpolation is performed) are horizontal and parallel to the flow field's streamwise x-coordinate. The scheme lacks the artificial numerical diffusion that plagues upwind differencing schemes.46 The lack of numerical diffusion of the present scheme enables accurate solutions even for coarse meshes in the streamwise direction along the cell's axis (i.e., the x-direction). Therefore, the computational domain was discretized with an anisotropic, rectilinear mesh having cells of length 0.500 mm and 0.010 mm in the x (streamwise) and y (transverse) directions, respectively. A time step of 8.6 s was used to march the solution forward in time, adapted as necessary to ensure convergence of the iterative solver.
First, the temporal variation of voltage and SOC during the cycling of two aliquots of suspension is shown for three flow scenarios to elucidate efficiency-loss mechanisms: (1) plug flow of a unit aliquot (m=1), (2) Newtonian flow of a unit aliquot (m=1) in the absence of slip, and (3) Newtonian flow of a half-aliquot (m=0.5) in the absence of slip. Effects of increasing total flow-volume are also simulated. Subsequently, optimization with respect to aliquot factor is addressed for fixed flow profiles. Finally, performance for flows having various degrees of slip and bulk shear is assessed for optimized aliquot factors.
The following five metrics are used to quantify electrochemical performance:
When an aliquot of charged suspension is pumped out of the electroactive region of the flow cell, ideal plug flow, defined as uniform translation of charged material, is not typically observed. Instead, the shear-thinning rheology of semi-solids5,31 results in bulk shear, which in turn distorts SOC and concentration fields upon advection.
To illustrate this effect, we compare ideal plug flow to ideal Newtonian flow without wall slip. Plug flow is a reasonable lower bound to the extent of flow non-uniformity because it can be induced in attracting colloidal suspensions by the formation of lubricating liquid layers at walls upon shear.51 And, shear-thinning fluids adopt some degree of plug flow even without wall slip. However, the other extreme is pure Newtonian flow without slip, which results in greater non-uniformity (quantified as the ratio of the centerline velocity to the mean velocity) than is seen for shear-thinning fluids (e.g., Bingham plastics, power-law fluids,52 and Cassonian fluids53). Therefore, Newtonian flow without slip is a reasonable upper bound representing maximum non-uniformity of flow.
Consider first the plug flow of two sequential aliquots each having unity aliquot factor (m=1). Shown in
The SOC field [
Newtonian flow without slip was simulated for the same cycle. The impact of the greater flow non-uniformity on the cell voltage [
a) and Table 3 show that under Newtonian flow without slip coulombic efficiency is sensitive to the voltage-capacity relationship for the active material. LiFePO4 with its wider two-phase coexistence (flat voltage-capacity curve) is much more efficient (96%) than the two other suspensions (80%) which have small (LiCoO2) or no (V-redox) equilibrium voltage plateaus. This inefficiency results from the transfer of charge outside of the electroactive region after flow. SOC snapshots at the start and end of the second charge (charge, S2 and E2) show this effect most clearly. At the start of the second charging step, SOC gradients induced by non-uniform flow are apparent, but with sufficient time, charge transfer outside of the electroactive region induces equilibration with discharged suspension transverse to the flow direction (charge, E2). The effect is most visible for LiCoO2 and V-redox suspensions, again because their reactions occur primarily as single-phase transformations. In concert, these processes lengthen suspension aliquots and reduce the SOC inside the aliquot. This process wherein chemical diffusion is apparently enhanced by shear is referred to as dispersion.54 On the final discharge step [discharge, E2, in
The previous result demonstrates that non-uniform flow leads to inefficient electrochemical cycling. Though plug flow is ideal, in practice it is not realizable for all suspensions. Thus, in many situations this non-ideal behavior may need to be managed so as to minimize inefficiencies. One strategy is to pump suspension aliquots of lesser volume (i.e., m<1), in a pseudo-continuous mode. The effect of such m<1 aliquot cycles is illustrated in
The three cases considered so far have cycled one-half of the total system volume (2 aliquots out of 4 total). As more cycles are added, we find an interesting result where the capacity is further reduced due to a different mechanism than already described, but the round-trip coulumbic efficiency improves. This is seen in the last two rows of Table 3, which compare m=0.5 Newtonian flow results for pumping 2 aliquots versus 4. Suspension near the centerline that was charged on the first step protrudes into the electroactive region during later charge steps [
The preceding results illustrate that flow velocity profiles, displaced aliquot size, and active-material phase equilibria all influence charge capacity and coulombic efficiency. Extending the comparison of m=0.5 and m=1.0, we now test the conjecture that an optimum aliquot factor must exist, at which the total discharge energy and energetic efficiency are maximized. The electrochemical performance for aliquot factors from m=0.125 to m=1 are shown in
A critical aliquot factor {tilde over (m)} can be defined that corresponds to the geometric condition where the upstream edge of the displaced aliquot is tangent to the downstream edge (i.e., outlet) of the electroactive region. When this condition is met, the critical aliquot factor can be calculated via streamline integration for laminar flows. For steady (i.e., time-invariant) flow that is one-dimensional, fully developed, and incompressible, the critical aliquot factor is:
{tilde over (m)}=ū/umax, (14)
where ū and umax are the mean and maximum axial velocities of the flow. For the no-slip Newtonian case, {tilde over (m)}=2/3. For Newtonian flow without slip,
b) shows that the cell polarization decreases monotonically with increasing aliquot factor. This scaling is primarily due to the constriction of current when the electroactive region is not completely replenished. Residue left behind from prior cycle steps results in a heterogeneous distribution of SOC within the electroactive region. Consequently, current becomes localized on region of the current collector nearest fresh suspension. Due to this localization of current, heightened ohmic drop occurs across the section of fresh suspension, manifesting as polarization at the cell level. This interpretation is supported by the good agreement between the calculated polarization and that predicted by a simplified model of current localization [red-dotted line,
For the continuous-flow limit (extrapolated to m→0), because the mean cell voltages on charge and discharge approach their respective cut-off voltages, the average polarization scales roughly with the magnitude of the voltage cut-off window [
The reasons why the discharge energy [
These results also show that the intermittent flow mode can reach higher energetic efficiency and discharge energy than the (conventional) continuous flow mode. The trends in
To this point, we have neglected the departure of velocity profiles from the respective limits of plug flow and Newtonian flow without wall slip. Because semi-solid suspensions exhibit a finite yield stress above which shear-thinning behavior is observed,29 their viscoplastic (i.e., rate-dependent, inelastic) rheology is manifested as a variety of velocity profiles under pressure-driven flow conditions. In addition, concentrated suspensions are know to slip at the walls along which they flow,55 and this process increases flow uniformity even when the suspension undergoes bulk shear. We introduce a model for viscoplastic flow with wall slip to simulate the influence of (1) wall slip and (2) bulk shear on electrochemical performance. For each of several velocity profiles the critical aliquot factor was determined. Two dimensionless parameters are introduced that embody the coupling of flow profile to material properties (describing both rheology and slip behavior), mean flow velocity, and channel width. Comparing these velocity profiles, each operated at the critical aliquot factor, the highest efficiency is found to occur for plug flow. This is realizable in either the limit of (1) highly slippery interfaces or (2) suspension with large elastic stress relative to viscoplastic contributions.
The effects of slip and viscoplastic flow do not occur independently—they are fluid-mechanically coupled through rheological constitutive and momentum balance equations. Consideration of this coupling is necessary to quantify the efficiency trade-offs between the rheological and transport properties of semi-solid suspensions. Slip can be modeled by a linear velocity/shear-stress relationship uw=βτw attributed to Navier,56 where uw and τw are velocity and shear stress, respectively, at the channel wall and β is the Navier slip coefficient. Various means can be employed to control the degree of wall slip, including surface roughness51,57 and the volume fraction of suspended particles.55 We model a simple viscoplastic case, a Bingham fluid, for which viscosity μ varies with shear rate {dot over (γ)} as μ=μp+τ0/∥{dot over (γ)}∥, and the flow is rigid (i.e., ∥{dot over (γ)}∥=0) for shear stresses less than the yield stress τ0. This rheology exhibits shear-thinning behavior (i.e., viscosity μ decreases monotonically with increasing shear-rate magnitude ∥{dot over (γ)}∥), with viscosity converging to the material-dependent plastic viscosity μp at high shear rates (i.e., μ(∥{dot over (γ)}∥→∞)=μp). The pressure-driven (i.e., Poiseuille) velocity profiles of these fluids are governed by momentum balance, and their shape is uniform where rigid, and quadratic in space where flowing (see analysis in Refs. 52,55,58). The critical aliquot factor for a given velocity profile depends on two dimensionless numbers: the Bingham number [Bn=τ0w/(2μpū)], and the slip number (Sl=2μpβ/w). Bn is a characteristic scale of elastic shear stresses (given by yield stress τ0) relative to the characteristic contribution from viscoplastic stress (given by 2μpū/w). Sl is a measure of the flow's slipperiness and is the ratio of the slip extrapolation length (see Ref. 59) to the channel's half-width in the high-velocity limit (Bn→0).
The slip ratio s and yield radius Ry depend on the Bingham number Bn and slip number Sl. In other words, for each point defined by (Ry,s) on the displacement profile map (
The set of possible velocity profiles for Bingham-plastic flow with slip comprise a two-dimensional space (
In like manner,
Maximizing efficiency is essential to the practical utilization of energy-dense flow batteries for large-scale energy storage. A model of electrochemical kinetics and flow was developed to identify operating conditions and rheological behavior that maximize electrochemical performance. The results suggest that electrochemical efficiency can be maximized through (1) flow volume control, (2) tailoring of suspension rheology, (3) promotion of interfacial slip, and (4) selection of active-material thermodynamics. Precisely tuned flow volumes, large yield stresses, large Navier slip coefficients, and two-phase-like active-materials produce the greatest electrochemical efficiencies. These considerations provide a critical aliquot size for intermittent flow mode operation. Three active-material systems were modeled (LiFePO4, LiCoO2, and V-redox). In the worst case (unit aliquots of Newtonian flow in the absence of slip), coulombic and energetic efficiencies can be as low as 80%. However, by flowing critically-sized aliquots in a plug-like manner, discharge energy as a percentage of the theoretical value, and energetic efficiency, can both exceed 95%.
Understanding the present results in the wider context of design and operational constraints of suspension-based flow batteries is essential to their useful integration in scaled devices:
The present invention may be used with other electrochemical devices that use slurry electrodes such as zinc/air batteries, copper etching and recovery, coal oxidation, electro-catalysis, photochemical cells and capacitive deionization.
The contents of all of the references listed herein are incorporated herein by reference in their entirety.
It is recognized that modifications and variations of the present invention will occur to those of ordinary skill in the art and it is intended that all such modifications and variations be included within the scope of the appended claims.
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This application claims priority to provisional application Ser. No. 61/892,588 filed on Oct. 18, 2013, the contents of which are incorporated herein by reference.
The United States Government has rights in this invention pursuant to DOE-FOA-0000559, Energy Innovation Hub—Batteries and Energy Storage, and ANL Subcontract No. 3F-31144, issued under DOE Prime Contract No. DE-AC02-06CH11357 between the United States Government and UChicago Argonne, LLC representing Argonne National Laboratory.
Number | Date | Country | |
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61892588 | Oct 2013 | US |