Battery cell configured for buoyancy-induced electrolyte circulation, and method of preventing thermal runaway of a battery cell

Abstract

A battery cell configured for buoyancy-induced electrolyte circulation includes battery cell components including a first electrode on a first current collector, a second electrode on a second current collector, the first electrode facing the second electrode, and a separator between the first electrode and the second electrode. The battery cell also includes an electrolyte. A hydraulic permeability of one or more of the components is sufficient for flow of the electrolyte through the respective component(s). Also or alternatively, one or more of the components includes in-plane channels, out-of-plane channels, and / or perforations configured to promote formation of electrolyte circulation loops within the battery cell during charging or discharging. A method of preventing thermal runaway of a battery cell is also described.

Description

BATTERY CELL CONFIGURED FOR BUOYANCY-INDUCED ELECTROLYTE CIRCULATION, AND METHOD OF PREVENTING THERMAL RUNAWAY OF A BATTERY CELL RELATED APPLICATION

[0001] The present patent document claims the benefit of priority under 35 U.S.C. 119(e) to U.S. Provisional Patent Application No. 63 / 676,995, which was filed on July 30, 2024, and is hereby incorporated by reference in its entirety. TECHNICAL FIELD

[0002] This disclosure is related generally to rechargeable and non-rechargeable batteries and more particularly to batteries that utilize liquid electrolytes. BACKGROUND

[0003] There is interest in reducing charging times for secondary or rechargeable batteries, such as lithium-ion batteries, which are widely used to power portable electronic devices, electric vehicles and grid storage. Thick electrodes may be used to produce batteries that last longer between charges and / or provide more power without increasing the overall size of the cell. Thick electrodes may pose problems during rapid operation, however, since lithium ions (Li+) must travel longer distances through the electrode material and the electrolyte. When the battery is charged or discharged rapidly, the demand for lithium ions at the electrode surface may increase sharply. This high demand can cause the local concentration of lithium salt in the electrolyte near the electrode to drop significantly, a phenomenon known as salt depletion, which may lead to increased resistance, reduced charge / discharge efficiency, and other problems, such as unwanted side reactions. In addition, high current operation associated with fast charging / discharging generates more heat within the battery, and a thicker electrodes may be associated with a higher thermal gradient between the surface of the electrode and the surrounding electrolyte. If the battery cannot dissipate this heat effectively, the temperature can rise, increasing the risk of thermal runaway, e.g., exothermic chemical reactions that may further raise the temperature in a self- accelerating cycle, ultimately resulting in fire, explosion, or catastrophic battery failure. Given that salt depletion and thermal runaway are critical concerns for batteries with thick electrodes operated under high-rate conditions, it would be advantageous to develop a strategy to mitigate these problems.BRIEF DESCRIPTION OF THE DRAWINGS

[0004] The embodiments may be better understood with reference to the following drawings and description. The components in the figures are not necessarily to scale.

[0005] FIGS. 1A and 1B show cross-sectional and top views of an exemplary battery cell that includes components (e.g., current collectors and electrodes) configured with perforations and out-of-plane channels to enhance electrolyte circulation.

[0006] FIGS. 2A and 2B show cross-sectional and top views of an exemplary battery cell that includes components (e.g., electrodes) with in-plane channels to enhance electrolyte circulation.

[0007] FIG. 3A shows porous electrode theory simulation of cell voltage versus time for 1C discharge of a LiCoO2 / graphite cell using electrodes of varied thickness ^.

[0008] FIG. 3B shows porous electrode theory simulation of salt concentration distribution at the end of discharge for the same cell cycled at 1C using electrodes of varied thickness ^.

[0009] FIG. 3C shows electrolyte density and density sensitivity versus LiPF6 concentration using propylene carbonate as solvent.

[0010] FIG. 3D shows deviation in concentration from uniformity as a function of the number of circulating passes.

[0011] FIG. 4A shows results of porous electrode theory simulation of cell voltage versustime for 1C discharge of a LiCoO2 / graphite cell using electrodes of varied ^^ with ^ ^500µm electrode thickness and ^ ^2 mm flow path length, where a certain velocity ^^^, governedby Darcy’s law including pressure and gravitational forces, is developed as a result of the accumulation and depletion of salt, which is governed by a salt conservation equation.

[0012] FIG. 4B shows cell voltage as a function time.

[0013] FIG. 4C shows velocity as a function of time, where values predicted from the steady-state theory described later are shown as dashed lines, along with the corresponding number of passes ^^in the legend.

[0014] FIGS. 4D-4F show salt concentration distribution halfway through discharge and at the end of discharge for electrodes having hydraulic permeability ^^equal to 2.5 µm2, 2.5x101µm2, and 2.5x102µm2, respectively.

[0015] FIGS. 5A and 5B show results of porous electrode theory simulation of current density, cell voltage, and velocity versus time for (FIG. 5A) pulsed-current cycling withtheoretical discharge in 1 hour and (FIG. 5B) constant-voltage cycling at 3.5 V for aLiCoO2 / graphite cell using electrodes with ^^=2.5x102 µm2, ^ ^500 µm electrode thickness,and ^ ^2 mm flow path length, where the resulting cell-voltage response and currentresponse for cases without flow are shown to benchmark the results obtained with flow for pulsed-current and constant-voltage cycling modes, respectively.

[0016] FIGS. 6A-6C are schematics of selected electrode geometries in which free convection is analyzed, including horizontal planar electrodes, vertical planar electrodes, and electrodes having a shape of a circular arc, respectively.

[0017] FIG. 7A shows a schematic of thru-plane (or out-of-plane) free convection in horizontally oriented electrodes.

[0018] FIG. 7B shows contours of the number of passes ^^in the space of separator permeability versus electrode thickness at 1C rate using a LiCoO2 / graphite cell, assuming electrodes with 10 µm2permeability.

[0019] FIG. 7C shows contours of hydraulic permeability ^^in the space of porosity versus solid-feature size, as predicted from the Kozeny-Carman (KC) relation with a Kozeny constant ^=5.0 assuming a cylindrical solid morphology.

[0020] FIG. 7D shows contours of hydraulic permeability, as predicted from the Kozeny- Carman relation with a Kozeny constant ^=5.0 assuming a spherical solid morphology.

[0021] FIG. 8A provides background for 2D numerical simulations of thru-plane flow.

[0022] FIGS. 8B and 8C show streamlines and concentration distribution for the 2D numerical simulations in a LiCoO2 / graphite Li-ion cell cycled at 3C rate (FIG. 6B) using 200-µm thick unpatterned electrodes with 20-µm thick separators each having 100 µm2permeability and (FIG. 8C) using 200-µm thick impermeable electrodes patterned having20% channel coverage ^ (where ^ ^ ^^^^^) with 20-µm thick unpatterned separators andcurrent collectors with 100 µm2permeability.

[0023] FIGS. 8D and 8E show the corresponding concentration polarization produced in such flows as a function of flow-mode wavelength respectively for unpatterned and patterned electrodes, where all simulations assume 2.5 mPa-s dynamic viscosity for 1 mol / L LiPF6 in mixed-carbonate solvent.

[0024] FIG. 9 shows concentration polarization ^^^as a function of unpatterned electrode permeability ^^for different values of flow-mode wavelength ^ when cycled at 1Crate, where electrode thickness is 500 µm with a 20-µm thick separator having 100 µm2permeability.

[0025] FIG. 10 shows concentration polarization ^^^ as a function inter-channel distance^ for different C-rates, assuming Bruggeman-type scaling of tortuosity and a 50% porosity.

[0026] FIGS. 11A-11E shows schematics of various electrode patterning schemes used in conjunction with permeable separators and collectors.

[0027] FIG. 12A shows concentration polarization as a function of in-plane electrode permeability for homogeneous, anisotropic electrodes using 160-µm wide through-thickness in-plane channels spaced at 20% channel coverage to produce a flow-mode wavelength of ^ = 1600 µm.

[0028] FIG. 12B shows hydraulic permeability ^ for microstructures using in-plane channels embedded as holes with diameter ^^, center-to-center distance ^^^, and channel coverage fraction ^. Flow is oriented “out of the page” for the inset schematic.

[0029] FIG. 12C shows center-to-center distance of the corresponding in-plane channels as a function of hole diameter.

[0030] FIGS. 13A-13D shows contours of the number of spontaneous recirculating passes ^^resulting from concentration-induced buoyancy in the space of electrode hydraulic permeability versus flow-path length, for both LiFePO4- and LiCoO2-based cells having either 100 µm or 200 µm thick electrodes for a horizontally oriented pouch cell cycled either at 1C rate or 0.5C rate.

[0031] FIG. 13E shows number of passes as a function of dimensionless path length^^^^^^^^^ for different cell chemistries cycled at 2C rate.

[0032] FIGS. 14A and 14B show side view of electrodes and separators with buoyancy- induced flow due to perforations / out-of-plane channels using foils coated with electrode film on a single side during (FIG. 14A) discharging and (FIG. 14B) charging steps of an electrochemical cycle.

[0033] FIGS. 14C and 14D show side view of buoyancy-induced flow using foils coated with electrode film on both sides during charging for electrodes and separators having (FIG. 14C) aligned and (FIG. 14D) mis-aligned perforations / out-of-plane channels.

[0034] FIGS. 15A-15E show patterning motifs used for buoyancy-driven flow.

[0035] FIGS. 16A and 16B show a contour mapcorresponding domains of arrangement based on the sign of^^^^^, respectively, wherecontours are only shown for the region of ^^^ ^ ^^^^^ where ^^^^ exceeds

[0036] FIGS. 16C-16G show free convection loop diagrams for jelly rolls that incorporate radially extending electrolyte passages; for each section bounded by electrolytepassages the magnitude of the orientation function^ ^^^^^ is shown, where non-zerovalues indicate that circulation is spontaneous. DETAILED DESCRIPTION

[0037] Described in this disclosure are a battery cell configured for buoyancy-induced electrolyte circulation and a method to produce convection within a battery cell – without the use of a pump – in order to simultaneously prevent both salt depletion and thermal runaway during fast charge or fast discharge. This technology is applicable to both rechargeable (secondary) and non-rechargeable (primary) batteries.

[0038] Components of a battery cell 100 are shown schematically in FIGS. 1A-2B to illustrate examples of perforation and channel features to promote buoyancy-induced circulation. The battery cell components 102 include a first electrode 104 on a first current collector 106, a second electrode 108 on a second current collector 110, where the first electrode 104 is facing the second electrode 108. A separator 112 lies between the first electrode 104 and the second electrode 108. In use, the battery cell 100 further includes an electrolyte. The battery cell is designed such that the hydraulic permeability of one or more of the components 102 is sufficient (i.e., sufficiently high) for flow of the electrolyte through the respective component(s) 102. Also or alternatively, one or more of the components 102 includes in-plane channels 116, out-of-plane channels 118a, and / or perforations 118b configured to promote formation of electrolyte circulation loops within the battery cell 100 during charging or discharging. As a result, the battery cell 100 does not require a pump for circulation of the electrolyte. The theoretical basis for controlling hydraulic permeability and / or incorporating flow channels / perforations 116,118a,118b into battery cell components to promote buoyancy-driven electrolyte flow is discussed in detail below.

[0039] To enable continuous flow under the action of a buoyancy force, the electrolyte is preferably a liquid, as opposed to a solid or gel. The electrolyte may comprise an organic solvent, which is typical in conventional Li-ion batteries, or an aqueous electrolyte, which istypical in lead-acid and nickel / metal-hydride batteries. Lower viscosity electrolytes are expected to experience greater circulation rates than those with a higher viscosity. It may thus be beneficial for the electrolyte to have a viscosity at room temperature (e.g., 18-22°C) no greater than 100 mPa·S, no greater than 10 mPa·S, no greater than 5 mPa·S, or no greater than 2 mPa·S. Also or alternatively, the viscosity at room temperature may be at least 0.2 mPa·S, at least 0.4 mPa·S, or at least 1 mPa·S. It is noted that typical electrolytes in Li-ion cells may have viscosities that are more than 2.5 times greater than the viscosity of an aqueous electrolyte.

[0040] Advantageously, the electrolyte utilizes a high molecular weight salt. As discussed below, electrolytes utilizing a high molecular weight salt are expected to exhibit the greatest circulation rates. Hence, battery cell chemistries that use electrolytes containing heavy ions (e.g., potassium in Ni / MH (39 g / mol), and zinc in zinc-ion (65 g / mol) batteries) may experience a greater buoyancy force than those containing lighter ions (e.g., lithium-ion systems (7 g / mol-Li)). In the above the molecular weight of the cation is the focus, but it is possible that the molecular weight of the counter-anion may be the predominant contributor to molecular weight, with the corresponding salts having the following sequence in molecular weight: LiBF6 (90 g / mol) < LiPF6 (150 g / mol) < LiTFSI (290 g / mol). Heavy cations may be used to increase salt molecular weight, but the anions may contribute substantially as well. This is likely true in Na-ion systems and in Zn-ion systems that use heavy cations such as sulphate (~100 g / mol), PF6- (~150 g / mol), or TFSI- (280 g / mol).

[0041] Hydraulic permeability refers to the intrinsic capacity of a battery cell component to permit flow of the electrolyte therethrough and is presented in units of square area. The hydraulic permeability of the separator, the first current collector, the second current collector, the first electrode and / or the second electrode may, in some examples, be sufficiently high for flow of the electrolyte through the respective component(s) without inclusion of the channels 118 or perforations 116 discussed in detail below. A sufficiently high hydraulic permeability may be due to the presence of porosity or other gaps amenable to electrolyte flow through the component and may be an inherent feature of a battery cell component, depending on its construction and constituent material(s). A component having a sufficient hydraulic permeability for electrolyte flow may have a hydraulic permeability of at least about 10 µm2, at least about 20 µm2, at least about 100 µm2, or at least about 200 µm2. The hydraulic permeability may in some examples be as high as about 500 µm2.

[0042] To obtain the desired hydraulic permeability, porosity (e.g., pore size) and / or solid feature size of the respective component may be appropriately selected or controlled. In addition to pore size, the morphology of the pores, such as whether they are interconnected within the otherwise solid battery cell component, may be important to promote flow. In the example of a particulate or fibrous battery cell component made up of fibers or particles, the solid feature size may refer to a nominal width or diameter of the fibers or particles. Microstructural feature size such as fiber diameter is linked to hydraulic permeability in an analysis below. The term hydraulic permeability may refer to an in-plane hydraulic permeability and / or to an out-of-plane hydraulic permeability of the component, where an in- plane direction is parallel to a surface of the electrode that serves as an interface with another battery cell component, and an out-of-plane direction is non-parallel with and may be perpendicular to the surface. If the in-plane hydraulic permeability and the out-of-plane hydraulic permeability are the same, then the respective component may have an isotropic structure. If the in-plane and out-of-plane hydraulic permeability are different, then the respective component may have an anisotropic structure.

[0043] As indicated above, the battery cell component(s) 102 may also or alternatively include in-plane channels 116, out-of-plane channels 118a, and / or perforations 118b configured to promote formation of electrolyte circulation loops. Such channels or perforations 116,118a,118b may be formed by additive manufacturing, such as 3D printing methods, or subtractive manufacturing, which may entail laser machining or other material removal methods. Also or alternatively, the channels 116, 118a and / or perforations 118b may be produced by forming methods, such as embossing and / or stamping. The channels and perforations 116,118a,118b described in detail below may promote buoyancy-induced electrolyte circulation even in battery cell components that have an insignicant hydraulic permeability.

[0044] Referring to FIG. 1A and 1B, the perforations 118b and / or the out-of-plane channels 118a are openings or holes 118 that extend partially or fully through the thickness of the respective component, where the thickness is understood to be (i) along the out-of-plane direction, perpendicular to the surface of the respective component and (ii) along the same direction as the depth of the perforations and / or channels. The perforations 118b and out-of- plane channels (or thru-plane channels) 118a may be understood to be openings 118 in the respective component configured to enhance out-of-plane or thru-plane flow. The term“perforation” 118b may in some places in this disclosure be used alternately with the term “out-of-plane channel” 118a to describe such openings 118. In some examples, however, a distinction may be made, such as when the opening 118 has a depth through the respective component that is roughly comparable to its width or diameter, or when the opening 118 has a depth that is significantly larger (e.g., two times or greater) than its width or diameter. In the former case, the term “perforation” 118b may be preferentially used, e.g., in reference to openings 118 configured for out-of-plane flow in thinner battery components, such as the separator 112 or the current collector 106, whereas the term “out-of-plane channels” 118a may be preferentially employed in the latter case, e.g., in reference to openings 118 configured to enhance out-of-plane flow in thicker battery components, such as the electrodes 104, 108. The depth of the perforations 118b and the out-of-plane channels 118a may be limited by the thickness of the respective component 102. For separators 112 or current collectors 106,110, for example, the perforations / channels 118b,118a may have a depth up to about 50 µm, whereas the perforations / channels 118b,118a in electrodes 104,108 may have a depth up to about 1 mm.

[0045] Referring to FIGS. 2A and 2B, the in-plane channels 116 may have a length limited by a lateral extent of the respective component 102 or by a spacing between the out- of-plane channels or perforations, when present. The in-plane channels 116 may be understood to be openings partially or fully embedded in the respective component 12 and configured to enhance in-plane flow. Some or all of the in-plane channels 116 may extend only partly through the thickness of the respective component 102, as illustrated in FIG. 2A. Some or all of the in-plane channels may be fully embedded within the respective component 102, also as shown in FIG. 2A. Alternatively, some or all of the in-plane channels 116 may extend fully through the thickness of the component, and / or to an interface with an adjacent component. These configurations are visible in FIG. 11A-11C, for example. Accordingly, depending on their configuration, the in-plane channels may function to enhance both thru- plane (out-of-plane) flow pathways and in-plane flow pathways.

[0046] The in-plane channels 116, the out-of-plane channels 118a and / or the perforations 118 may have any desired transverse cross-section, such as circular or rectangular as shown in the figures, or curved, polygonal, and / or irregular. In some examples, the in-plane channels 116, the out-of-plane channels 118a, and / or the perforations 118b may each have a width or diameter of at least about 20 microns, at least about 50 microns, or at least about 100microns, and / or as large as about 500 microns. Typically, a coverage fraction of the channels and / or the perforations 116,118a,118b over a cross-sectional area or a volume of the component 102 is at least 5%, at least 20%, at least 40%, and / or as large as about 50%. The channels and / or the perforations 116,118a,118b may be straight or tapered along a depth or length thereof. An arrangement of the channels and / or the perforations 116,118a,118b within the respective component 102 may be aligned, ordered, disordered, staggered, interdigitated, and / or intersecting, as illustrated for example in FIGS. 15A-15E.

[0047] The spacing (e.g., center-to-center spacing) between the out-of-plane channels 118a utilized for flow enhancement in electrodes 104,108 may be at least 10% of the thickness of the electrode (“electrode thickness”), at least 25% of the electrode thickness, at least 50% of the electrode thickness, at least 70% of the electrode thickness, at least 90% of the electrode thickness, or at least 120% of the electrode thickness, and / or up to 130% of the electrode thickness. Typically, the spacing (e.g., center-to-center spacing) between the in- plane channels 116 is less than about 5 mm, less than about 200 microns, less than about 100 microns, or less than about 50 microns. Generally, the spacing between the in-plane channels 116 is least about 10 microns. These dimensions are derived from analysis of hydraulic permeability’s effect on concentration polarization in 12A, of channel coverage’s effect on hydraulic permeability in 12B, and of channel coverage’s effect on spacing in 12C.

[0048] In some examples, one or both of the electrodes 104,108 may include the in-plane channels 116 and / or the out-of-plane channels 118a to promote the formation of electrolyte circulation loops. The separator 112 and / or the current collectors 106,110 may include the perforations 118b described above to enhance circulation. The out-of-plane channels or perforations 118a,118b in one component 102 may be aligned with the out-of-plane channels or perforations 118a,118b in an adjacent component 102. In-plane channels 116 in one component 102 may be angularly offset from, or perpendicular to, the in-plane channels 116 in an adjacent component 102, such that intersections may be formed at crossing points. In such examples, the in-plane channels 116 in the adjacent components 102 may extend along the interface between the components 102 and / or the in-plane channels 116 may be through- thickness channels, as illustrated in FIGS. 9A and 9B. The out-of-plane channels 118a or perforations 118b from one component 102 may intersect with in-plane channels 116 in an adjacent component 102. In such examples, as mentioned above, the in-plane channels 116 in the adjacent component 102 may extend along the interface between the two components 102and / or the in-plane channels 116 may be through-thickness channels. It is also contemplated that at least one of the battery cell components may be impermeable to flow of the electrolyte; that is, at least one of the components may have a low hydraulic permeability and may not contain channels or perforations to enhance flow.

[0049] The theoretical analysis of electrochemistry-coupled flow within a rechargeable battery discussed below reveals that steady recirculation of electrolyte between anode and cathode is spontaneously generated (i.e., without pumping of any sort) as a result of the buoyancy forces acting on the electrolyte which cations are intercalated from and deintercalated into. The body force acting on the battery cell to produce buoyancy may result from gravity, a centripetal acceleration, and / or another type of acceleration due either to rotation or translation of the battery. That is, buoyancy-induced flow may not require gravity, provided that a body force acts in the presence of a density gradient. Various implementations of the body force to produce buoyancy are discussed further below.

[0050] As noted above, battery cells 100 including thick electrodes 104,108 are particularly susceptible to salt depletion and thermal runaway. Thus, the buoyancy-induced circulation enabled by the technology described in this disclosure may be most beneficial for such battery cells. Thick electrodes may allow for an increased amount of active material in the battery cell and thus a higher energy density. In some examples, one or both of the first and second electrodes 104,108 may have a thickness of at least 50 µm, at least 100 µm, at least 200 µm, at least 200 µm, at least 500 µm, and / or up to 1 mm, or up to 1 cm. Typically, the separator 112, the first current collector 106 and the second current collector 110 are thinner and each may have a thickness in a range from about 5 µm to about 50 µm.

[0051] The battery cell components 102 may have a planar arrangement, as shown for example in FIGS. 1A-2B, and the battery cell 100 may thus have the form of a pouch or prismatic cell. Alternatively, the battery cell components may have a jelly roll or bobbin arrangement, and the battery cell may have the form of a cylindrical cell. In use, as illustrated in FIGS. 1A and 2A, the battery cell components 102 may have a long axis oriented horizontally, where the long axis is aligned with a plane or surface of the battery cell components 102. Also or alternatively, the long axis may be generally perpendicular to a main direction of current flow through the battery. The first electrode 104 may be positioned above the second electrode 108, and in use the first electrode 104 may be configured as ananode to carry out electrochemical oxidation, and the second electrode 108 may be configured as a cathode to carry out electrochemical reduction.

[0052] The technology described in this disclosure is applicable to various types of batteries that utilize a liquid electrolyte. The examples below are focused on batteries that use electrodes containing solid host compounds that intercalate lithium; however, buoyancy- induced electrolyte circulation is not limited to electrochemical reactions that intercalate lithium. Other kinds of electrochemical reactions are possible, and other types of ions can participate in the reactions. It is noted that that lead-acid, lithium-metal, and lithium / sulfur batteries may use at least one electrode that involves an electrochemical conversion reaction that does not involve an ion intercalation process per se. The technology is applicable for such electrodes where intercalation may not be used, in addition to being applicable for electrodes that utilize ion intercalation. Accordingly, the battery cell 100 may be a lithium- ion (Li-ion) battery cell or another rechargeable battery cell, such as a lead-acid battery cell, nickel / metal hydride battery cell, sodium-ion battery cell, potassium-ion battery cell, magnesium-ion battery cell, calcium-ion battery cell, zinc-ion battery cell, aluminum-ion battery cell, lithium-metal battery cell, or lithium / sulfur battery cell. As indicated above, the technology is also applicable to non-rechargeable (or primary) batteries, such as alkaline MnO2 / Zn batteries, non-aqueous lithium thionyl chloride batteries, lithium manganese dioxide batteries, and others, provided that the electrode reactions of interest result in substantial liquid-phase salt concentration change when electrode reactions occur. The battery cell may be a single battery cell as depicted in FIGS. 1A and 2A or part of a stack of battery cells including multiple cell pairs, as depicted in FIGS. 14A-14D. Additionally, the technology may be applicable to electrolytic capacitors, supercapacitors, or pseudo-capacitors or other charge storage devices that utilize an electrolyte. In such devices, charge is adsorbed into or desorbed from electric double-layers (EDLs) on the surface of porous electrodes that may also contain redox-active surface sites or groups, rather than undergoing intercalation into the bulk of a host material, as in a Li-ion battery.

[0053] In addition to the battery cell and component(s) configured to promote spontaneous circulation of the electrolyte as set forth above, also described in this disclosure is a method of preventing thermal runaway of a battery cell. A current-control strategy is envisioned in which temperature is measured on the surface of the battery or within the battery as a feedback signal that is used to induce heat convection. Accordingly, the methodmay include electrochemically cycling the battery cell described according to any embodiment or example in this disclosure, and during cycling, measuring a temperature of the battery cell. If the temperature reaches a critical temperature, a current signal is applied and buoyancy-induced circulation of the electrolyte occurs, effecting cooling of the battery cell. The current signal may be constant or time-varying (e.g., pulsed or sinusoidal). A variety of methods could be used to determine the temperature, including attachment of a temperature probe such as a thermocouple to the exterior of the battery; using the known dependence of open-circuit cell-voltage on temperature and state-of-charge for the cell chemistry of interest; and / or using one or a multiplicity of reduced-order models that link battery temperature and heat dissipation to measured electrochemical signals (e.g., current and voltage). It is envisioned that the method may also include measuring pressure or strain during cycling, and, if the pressure reaches a critical pressure or if the strain reaches a critical strain, applying the current signal.

[0054] As described above, the force acting on the battery cell may include gravity, a centrifugal force, a Coriolis force, and / or any other inertial force. The battery cell may be configured to undergo rotation to produce the centrifugal force. For example, the battery cell may be mounted at a suitable radius onto a rotating body, such as one of the wheels of a vehicle. In the context of a wheeled vehicle traveling at 65 mph (30 m / s), if the wheel has a 1-foot radius (0.33 m) the centripetal acceleration would be 302 / 0.33 = 2700 m / s2. Hence, by attaching batteries to a vehicle’s wheels while their out-of-plane direction is oriented along the wheel’s radial coordinate, the battery may effectively experience approximately 300 times the acceleration of gravity. Alternatively, the battery cell may be attached to a flywheel whose express purpose is to keep a battery cell or an array of battery cells rotating steadily, so as to sustain a steady centripetal acceleration, whether during charging or discharging of the battery. Centripetal acceleration could also be exploited in other contexts where power generation occurs as a result of shaft rotation: e.g., a wind turbine or a gas turbine engine. In any such context where a battery is attached to a frame that is rotating and / or translating, thegravitational acceleration vector #$ may be replaced by the mass-specific body force ^$% ^"&''$ ( )'&'$ ( *$+ " ^'&'$ ( ^'$ " ^,'$^^- " ^'&'$^^- ( *$ to account for its inertia. Here, ' &'$ is therotation-rate vector for the moving frame of reference in the fixed frame of reference, ,'$is the velocity vector for the moving frame of reference in the fixed frame of reference, *$ is the relative position vector extending from the center of rotation to a point of interest within theelectrolyte, and ^'$ is the electrolyte’s velocity in the moving frame of reference. In seeking touse centripetal acceleration to promote buoyancy-induced flow (such that ^$% ^"&''$ ( )'&'$ ( *$+), it is understood that the centrifugal force exerted on the electrolyte isdirected radially outward from the center of rotation. The use of centrifugal force may thus be applied to the design principles introduced in the context of gravity by understanding inward radial positions as the effective “top” positions of the battery while outward radial positions comprise the effective “bottom” positions of the battery. Thus, buoyancy-driven flow produced by centrifugal force will occur from an associated inward (top) anode into an associated outward (bottom) cathode.

[0055] Introduction to Theoretical Analysis

[0056] Based on theory described below, battery cells configured for inducing spontaneous electrolyte flows are described, including, for example, the use of flow channels and flow fields embedded in electrodes either (1) with judiciously placed perforations in separators and current collectors that facilitate inter-electrode flow or (2) that abut permeable porous separators or current collectors. The dimensions of the associated channels, solid features and porosity, and associated perforations that may be beneficial for facilitating substantial circulation rates are shown to be feasible by various manufacturing methods, including scalable subtractive and additive methods. In particular, the theory predicts that 15 recirculating passes can be generated during a single electrochemical charge or discharge step lasting between 1 to 5 hours (i.e., 0.2C to 1C rate), while limiting deviations of salt concentration to 25% at most (0.75 M minimum and 1.25 M maximum concentrations). Additionally, the transient response of free convection to applied current has potential to enable the addressability of internal cooling within the battery for the first time, motivating the feedback control of applied current using temperature-based feedback. Such circulation loops are shown to be especially effective when used within thick electrodes that possess the synergistic effect of reducing inactive material mass within the battery.

[0057] The analysis focuses on two different “modes” of free convection that induce spontaneous circulation between anode and cathode: (1) an in-plane mode and (2) a thru- plane mode. Among both modes, short flow path lengths and enhanced hydraulic permeability are shown to promote circulation rates, as achieved by permeability engineering and patterning of electrodes, separators, and current collectors. For the in-plane mode, perforations or out-of-plane channels may be connected in tandem to embedded in-planechannels using manifolds of various sorts, thus accommodating a variety of perforation and flow-path size scales and manufacturing methods. For the thru-plane mode, homogeneously permeable separators, current collectors, and electrodes with sufficiently high permeability are shown to produce a continuum of free convection modes with different wavelengths. Inspired by this result, results are presented for electrodes in which thru-thickness channels are incorporated, ultimately showing that impermeable electrode material can be employed to induce circulation rates high enough to sustain fast-charging conditions at 3C rate. In-plane channel patterning is also shown to be a viable path forward to realize low concentration polarization under aggressive cycling conditions.

[0058] The various approaches to promote free convection are also shown to be applicable to batteries having various form factors, including both single-sided and double- sided current collectors and both pouch- and cylindrical-cell formats. The use of single-sided current collectors may require perforation / permeability of either the separator or current collector to facilitate free convection during either charge or discharge (both charge and discharge can be achieved provided that both current collectors and separators are perforated / permeable), whereas the use of double-sided current collectors (e.g., foils) may require permeability of both components to achieve free convection during either charge or discharge. For cylindrical cells, the placement of perforations / out-of-plane channels that form the through-holes between electrodes is shown to be critical to realizing circulation throughout the entire jelly roll. When the associated circulation loop segments are made to have short angular extent, it is also shown that either or both the flow-path length of the segment or the apparent permeability of the segment can be made segment-specific, so as to result in the generation of a uniform number of passes among all segments in a jelly roll. Additionally, this technology is shown to apply to cell chemistries including Li-ion and beyond. For example, Na-ion and Zn-ion chemistries are promising due to the exceptionally low viscosities of their aqueous and non-aqueous electrolytes. In all cell formats considered, the circulation loops that are generated are further shown to mitigate the salt depletion and accumulation mechanism that can limit the charge / discharge capacity of thick-electrode batteries. Additionally, these effects are expected to enhance heat transfer within batteries by eliminating hot spots, so as to extinguish incipient thermal runaway.

[0059] Physics-based simulated results for cycling of conventional Li-ion batteries are provided as a benchmark. Simulations are then shown that incorporate flow induced by thebuoyancy of electrolyte in which both accumulation and depletion of salt occur locally. Subsequently, scaling analysis of buoyancy forces is presented to explain in simple terms how circulation loops develop as a result of salt depletion and accumulation. Results of steady-state theory for both flow modes are then presented, which are used to derive electrode patterning strategies to promote buoyancy-driven circulation of electrolyte. For the thru-plane free convection mode, a two-dimensional physics-based model is also used to study different strategies for the enhancement of circulation.

[0060] Conventional Li-Ion Batteries as a Benchmark

[0061] Simulations were performed for electrochemical cycling of conventional Li-ion batteries using stagnant, non-flowing electrolyte to serve as a benchmark for Li-ion batteries that use the present invention to induce flow. The model on which these simulations are based was implemented by the principal investigator and validated against results generated by the gold-standard porous-electrode-theory program Dualfoil 5.0, as described in previous work. This model includes the coupling between electron conduction, ion diffusion / migration in binary electrolytes, Li-ion intercalation within porous electrodes, and kinetics thereof. To this end, Figs. 1a and 1b show the simulated results of discharging a Li-ion battery containing a LiCoO2 cathode and a graphite anode, both having a specified thickness with 50% porosity, 50% active-material volume fraction, and ion-transport tortuosity set according to the Bruggeman relation. Each battery was simulated using a current corresponding to theoretical discharge of 60 minutes (i.e., a so-called “C-rate” of 1C).

[0062] As shown in FIG. 3A, the thin electrodes commonly used in commercialized batteries (e.g., 50 µm in thickness) produce near-theoretical capacity levels by cycling for ~60 minutes. FIG. 3B reveals that the associated salt concentration deviates from uniformity in such thin electrodes by less than 100 mM. However, when electrode thickness is increased to 200 µm, cell voltage is shown to decrease at all times by ~100 mV. While the resulting reduction in energy discharged is not significant, such cell “polarization” is evidence of the underlying maldistribution of salt within the electrolyte. In particular for this case, FIG. 3B shows that salt concentration in the electrolyte depletes to ~100 mM by the end of the discharge process for 200 µm thick electrodes. While 200 µm thick electrodes achieve similar capacity to their thin-electrodes counterpart despite salt depletion being significant, the same cannot be said of electrodes of even greater thickness. For electrodes having thickness .300 µm a drop in discharge capacity by more than 50% relative to theoreticalmay be observed, as evidenced by proportionally shorter cycle times (FIG. 3A). This effect is directly linked to the mode and extent of salt depletion that occurs inside of the battery.While extreme salt depletion occurs by the end of discharge for all batteries using thickness.300 µm, the spatial region over which it occurs becomes confined to the regions of thecathode and anode that are in direct proximity to each other (FIG. 3B). This effect occurs because Li-ion intercalation capacity of the electrodes is only utilized in regions that are in the immediate vicinity of the electrodes, thus resulting in local salt depletion there and thus limiting a given battery’s capacity to a miniscule fraction of its theoretical capacity (down to only ~10% for 1 mm thick electrodes). Aside from the very significant drop in capacity that results from these effects, operating thick electrodes under such extreme abuse conditions is likely to exacerbate side reactions, including anode-side Li-metal deposition and consequent capacity fade due to the loss of Li inventory by concomitant solid-electrolyte interphase (SEI) formation. Each of these effects is a direct result of the dynamic salt-depletion / -accumulation mechanism that the technology described in this disclosure is designed to mitigate.

[0063] Li-Ion Batteries with Buoyancy-Induced Circulation

[0064] To demonstrate the impact of buoyancy-induced circulation on battery capacity, such effects were incorporated into the same physics-based model used to obtain benchmark capacities without flow. The governing equations were modified as shown in FIG. 4A to include an advective flux of salt that arises from a buoyancy-induced velocity ^^^. By virtueof its coupling to salt concentration at the left ( / ^ 0) and right ( / ^ ^) ends of the electrodepair, ^^^is a quantity that evolves in time from an initially stationary state due to the lack of a pump to motivate circulation. Given that ^^^scales in direct proportion with the ratio of electrode thickness ^ to stream-wise length ^ (see FIG. 4A), cells were simulated using electrodes with 500 µm thickness and 2 mm streamwise length to promote circulation.

[0065] The resulting simulated discharge-voltage curves obtained at the same C-rate used in stationary-cell cases (1C) are shown in FIG. 4B for electrodes using a span of hydraulic permeability. Here, modest values of hydraulic permeability (^^=2.5 µm2) are shown to produce practically the same discharge characteristics as conventional Li-ion batteries that possess stationary electrolyte. However, more than two-fold increased capacity is obtained when increasing ^^to 2.5x101µm2, and capacity is further increased to near-theoretical values when using even larger permeability. These effects stem directly from the increased buoyancy-induced flow that is produced for higher permeabilities, as shown in FIG. 4C.Under such conditions where hydraulic permeability is large enough, the velocity increases within less than 5 minutes to a nearly constant value that is within 25% of the value predicted by the steady-state theory described later. For ^^=2.5x102µm2and 2.5x103µm2these steady- state velocities correspond respectively to the electrolyte circulating through electrode flow- loops 10 and 40 times during a given discharge sequence, as quantified by the “number of passes” ^^shown.

[0066] This buoyancy-induced circulation of electrolyte has a dramatic impact on the associated distribution of salt within a battery and is responsible for the increased capacityobtained when charging electrodes with high hydraulic permeability. FIG. 4D shows that for^^= 2.5 µm2, salt depletion and accumulation occur as though the electrolyte was stationary(cf., FIGS. 3A and 3B) because the associated velocity induced by it (0.66 mm / hr at termination) is too slow to complete even one circulation loop during discharge. In contrast, by increasing ^^ten-fold the maximum velocity induced increases nearly ten-fold to a level (5.2 mm / hr) that approaches one complete circulation loop over the theoretical dischargeperiod for the C-rate of interest (i.e., 60 min). As a result, velocity is large enough with^^=2.5x101 µm2 to limit the extent of salt depletion overall (FIG. 4E) by transferring salt-enriched electrolyte from the anode to the cathode where it experiences salt consumption because of Li intercalation there. However, within less than 1 mm from the inlet to the cathode, salt is shown to deplete to a level that is smaller than the initial concentration (1 mol / L). While circulation of salt-depleted electrolyte from the cathode back into the anode results in a degree of recovery in salt concentration, the velocity produced with ^^=2.5x101µm2is found to be too slow to prevent local depletion after discharge for 40 min. Further increased hydraulic permeability (FIG. 4F) is shown to prevent depletion throughout the entire 60-min theoretical discharge time-scale by increasing steady-state velocity in proportional to its square root: ^^^12^^. In addition, the maximal extent of salt depletion and accumulation is also shown to decrease with increasing hydraulic permeability.

[0067] In addition to the already described constant-current simulations, cycling with buoyancy-induced flow was simulated when pulsed current is applied. During a given pulse, the resulting velocity is shown to rise to 50% of its peak value only 1 min after the start of the associated pulse, as shown in FIG. 5A, which is considerably shorter than the time-scale for fast charging (approximately 15-30 min). The magnitude of the associated peak velocity (20 mm / hr) is large enough to produce a thermal Peclet number of order unity, indicating thepotential for dissipation of Joule heating by convection. The rapid response of velocity to current demonstrates the addressability and dispatchability of convective heat transfer via the temporal control of current. This finding is essential to the potential use of buoyancy-induced flow as a means to mitigate thermal runaway – a current-control strategy is envisioned in which temperature is measured on the surface of the battery or within the battery as a feedback signal that is used to induce heat convection, as discussed further below. As with results obtained under constant-current cycling, the results obtained under pulsed-current cycling with buoyancy-induced flow significantly outperform those obtained without flow, showing four-fold greater capacity. Additionally, simulations using constant-voltage cycling show as much as two-fold the current than without flow after the onset of flow occurs, as shown in FIG. 5B.

[0068] Scaling Analysis of Buoyancy Forces Indicates the Feasibility of Free Convection

[0069] To rationalize the effects described above, scaling analysis of the buoyancy forces that can be generated within Li-ion batteries is employed. The Rayleigh number 34 is a similarity parameter that captures the characteristic rate of buoyancy-induced advection to the diffusion rate of either heat or mass. Thus, the extent of flow due to free convection increases with increasing 34. For free convection in porous media, the Rayleigh number is expressedin terms of a characteristic pore-scale length 56 ^that depends on the electrode’s(Darcy-type) hydraulic permeability in addition to a macroscopic length-scale 5^with which the gravitational contribution to hydraulic head scales in direct proportion: 5^5 #^7 ^ 5 #^ 6 ^ ^734 ^ ^89 ^89

[0070] Here, ^% ^ #^7 is a volumetric body force acting on the fluid under the gravityfield #$ due to the characteristic density difference ^7, 8 is the electrolyte’s dynamic viscosity that resists the associated body force, and 9 is the diffusion coefficient for either mass or heat transfer.

[0071] Using this definition of Rayleigh number, it is found that a difference in theconcentration of LiPF6 salt produced by extreme salt depletion (2 mol / L) can produce34 :100 even with a low-permeability electrode (~0.1 µm2) for unpatterned intercalationelectrodes) and a small gravitational length-scale (e.g., 100 µm for the medial spacing between anode and cathode layers in a jelly roll). In contrast, it is found that a temperaturedifference in excess of that needed to incinerate a Li-ion battery (~1,000ºC) is needed togenerate the same Rayleigh number (34 :100) even when using high electrode permeability(25 µm2) obtained previously together with a large gravitational length-scale (50 mm). Surprisingly, the contrasting conditions needed to produce similar Rayleigh numbers do not result from differing abilities of temperature and concentration differences to produce a density change. Instead, this Rayleigh-number contrast results from three orders higherdiffusivity for heat (9 ^ ^^7^ ^ 5(10-7 m2 / -10 2; 6 s) than for mass (9<=>? ^ 3(10 m / s). Thisback-of-the-envelope analysis supports the following conclusions:

[0072] Spontaneous electrolyte flow due to free-convective mass transfer is feasible, provided that the product of hydraulic permeability with the gravitational length-scale 5^is sufficiently large. The buoyancy forces arising from temperature variations are orders-of- magnitude too weak to overcome the hydraulic resistance posed even by highly permeable porous media. Despite the negligible effect of temperature-induced buoyancy forces resulting from Joule heating, the electrolyte flow induced by the buoyancy forces generated via salt depletion and accumulation during charge and discharge are expected to enhance cooling of Li-ion batteries.

[0073] In what follows, the results of theoretical analysis of coupled mass transport are presented to show that the spontaneous free convective flows produced by salt depletion and accumulation occur in circulation loops between a battery’s anode and cathode in different ways that depend on the arrangement and orientation of the electrodes, among other factors. Furthermore, this analysis is used to show that these spontaneous circulation loops can result in 15 passes through the anode and cathode during a single electrochemical half-cycle, limiting the extent of salt depletion to only a 25% change from 1 M.

[0074] Theory of One-Dimensional Steady-State Free Convection

[0075] The theoretical analysis of electrochemistry-coupled flow within a rechargeable battery reveals that steady recirculation of electrolyte between anode and cathode is spontaneously generated (i.e., without pumping of any sort) as a result of the buoyancy forces acting on the electrolyte which cations are intercalated from and deintercalated into. Specifically, this analysis predicts that the number of recirculating “passes” ^^during a given half-cycle increases with increased electrode thickness, increased electrode permeability, and decreased flow-path length. Importantly, the maximum deviation in salt concentration ^@^^Afrom its initially uniform distribution is shown to decrease as the number of passes ^^increases:

[0076] To estimate ^@^^Avalues of specific capacity (BCD=170 mAh / g) and density (7CD=3.6 g / cc) for LiFePO4, the transference number of LiPF6in mixed-carbonate solvent(-^=0.34), a nominal electrode porosity of H=0.5, and a nominal solid volume fraction ofJ=0.5 in the electrode are used. Figure 1d shows that only 15 passes are required at aminimum to limit salt concentration deviations from uniformity to less than 0.25 mol / L, thus bounding salt concentration to within a range of 0.75 mol / L to 1.25 mol / L throughout the entire battery.

[0077] To achieve a certain number of passes requires engineering of flow through the associated electrodes either in the plane of the electrodes (i.e., in-plane flow) or flow through the electrodes perpendicular to their plane (i.e., out-of-plane or thru-plane flow). For in-plane flow, as facilitated by separator and current collector perforations and electrode patterning as needed, the coupling of the number of passes ^^to buoyancy forces generated by salt depletion / accumulation is captured through the following master formula:

[0079] The dependence of the number of passes ^^on system orientation and arrangement is captured in the above formula via the respective integrals over streamwiseposition ^ in the anode (^ c d0^ ^e) and cathode (^ c d^^ ^^e). FIGS. 6A-6C illustratesspecific electrode arrangements and orientations that are relevant to rechargeable batteries within which spontaneous flow is analyzed. In geometries like the planar horizontal case (Case 1), the fluid pressure difference between cathode and anode at either the left or right end of a given electrode pair depends on local electrolyte density there according toBernoulli’s equation:^ 7#^. Different densities at the respective ends ofthe pair therefore produce greater ^fb^Con one end than the other, resulting in opposing pressure gradients that create intra-electrode velocities with equal and opposite direction (FIG. 6A). While such principles can be applied to deduce how circulation may or may not occur for Case 1, other cases require a general, detailed analysis of density gradients in orderto derive the master formula above. Next, the results of that analysis are shown for Cases 1, 2, and 3.

[0080] Case 1 (FIG. 6A) uses horizontal planar electrodes as in a pouch-type Li-ion cell. Here, spontaneous circulation loops are produced when the anode (i.e., the electrode from which cations are de-intercalated by oxidation) is arranged above the cathode (i.e., theelectrode into which cations are intercalated by reduction). The associated number of passes^^ is found after evaluating its associated orientation integral asa^^ " `b a^^ ^ ^^, where^ is the height of the anode’s medial surface above the cathode’s:

[0081] While this equation predicts spontaneous flow for an anode arranged above a cathode (i.e., where ^ is positive), it also shows that spontaneous flow is not produced when the arrangement of electrodes is swapped (i.e., where a single cathode is above a single anode) because a negative value of anode height ^ produces a value of ^^that is purely imaginary (i.e., it is a complex number with no real component). Such a result indicates that spontaneous flow cannot occur due to the density of electrolyte in the upper electrode being lower than that of lower electrode, thus possessing a stable, stationary density field because less dense electrolyte rises. The direct scaling of ^^withi^ shows that the in-plane free convection mode occurring in horizontal orientation favors the use of thick electrodes.

[0082] Case 2 (FIG. 6B) uses the same planar electrodes as in Case 1, except that the electrodes are oriented vertically. This change in orientation is shown to nullify the effect ofgravity on the electrolyte (i.e., `C a^^ " `b a^^ ^ 0), resulting in stable, stationary electrolytethat lacks steady, spontaneous flow (i.e., ^^ ^ 0). However, dynamic conditions are possiblein which flow in the vertical orientation may be realized.

[0083] Case 3 (FIG. 6C) uses electrodes wrapped around a circular arc to model a section of a jelly roll used in Li-ion batteries having cylindrical format. In this case, the number of spontaneous flow passes ^^per half-cycle depends on both the angular position of the respective ends of the electrode pair (^^and ^^) and on whether the anode is internally or externally wrapped with respect to the cathode:

[0084] In addition, a limiting form is obtained for Case 3 when the angular extent of thesectionsmall:

[0085] Here, the effect of orientation is felt through a single parameter – the average angle ^lamong ^^and ^^.

[0086] Thru-plane free-convection mode is now discussed, where an intrinsically permeable separator, current collectors, and electrodes can be used to facilitate the effect, as depicted in FIG. 7A, rather than requiring accurately positioned perforations / channels as in the in-plane free-convection mode. Instead, the porosity and hydraulic permeability of the separator, current collector, and electrodes can be engineered to facilitate thru-plane free convection. Here, the effect of salt depletion and accumulation in horizontally oriented, planar electrodes is to induce density stratification, wherein the Rayleigh-Taylor instability arising among density-stratified immiscible liquids has been shown to cause buoyancy- induced viscous fingering at their interface within porous media. This new theory shows that in the context of a Li-ion battery such modes of flow can be sustained steadily when such a battery is charged or discharged at constant rate, provided that the associated separator (or current collector) and electrodes have sufficient hydraulic permeability. The associated number of passes ^^for this mode may depend not only on the thickness of the electrodes used ^^and their permeability ^^^but also on the thickness ^<and the permeability ^^<of the separator used:

[0087]

[0088] Of particular note is the apparent 2F^^^scaling of ^^with electrode thickness that results in the thru-plane mode of free convection favoring the use of thin electrodes, provided that separator hydraulic resistance is negligible. However, the micro-porous separators used in conventional Li-ion batteries have hydraulic permeability (~10-3µm2basedon a Gurley value of 10 s with 20 µm separator thickness) that is orders of magnitude smaller than the permeability of typical intercalation electrodes.

[0089] Design and Analysis for Thru-Plane Recirculation

[0090] This section provides details concerning the design approach used to achieve thru- plane recirculation with the aid of physics-based analysis. FIG. 7B shows the contours of the number of passes in the space of separator permeability versus electrode thickness for a LiCoO2 / graphite cell with 10 µm2electrode permeability using a 20 µm thick separator operated at 1C rate. This analysis indicates that a micro-porous separator with 10-3µm2permeability produces only one-tenth of a complete circulation during a single half-cycle (i.e., ^^10.1), whereas separators using a permeability of 10 µm2are capable of achieving ~10 complete circulating passes during a single half-cycle for electrodes that are 60 µm thick (i.e., ^^110). However, it is noted that this simplistic theory neglects the effects of diffusion and in-plane hydraulic resistance that are likely to play a significant role in determining the actual extent of circulation that is realized. Later, it is demonstrated using two-dimensional modeling how circulation loops, similar to Bénard rolls that occur within open-channel free convection, naturally develop as a result of the interplay between diffusion and in-plane hydraulic resistance.

[0091] Nonetheless, this simplistic thru-plane free-convection theory is used to quantify the material design constraints that would be needed to facilitate such a mode of free convection. Microstructural attributes are linked to hydraulic permeability by using theKozeny-Carman equation: ^^" H^^, where ^ is the Kozeny “constant” taken as5 and 4 is the volumetric surface area of the solid or aggregated phase. Assuming that theseparator is comprised of cylindrical fibers with diameter ^< (such that 4 ^ G^^<), FIG. 7Cshows that increasing the porosity of medium of interest for a given fiber diameter increases permeability – increasing porosity above that of conventional micro-porous separators (50%) to >80% can increase permeability by at least ten-fold. Further, increasing fiber diameter increases permeability for a certain porosity – 20 µm fibers produce 100 µm2permeability at 80% porosity. For a desired permeability and porosity, there exists a certain fiber-diameter threshold below which the desired permeability can be realized, the locus of all such microstructures being represented by the contours in FIG. 7C. Such conditions implied by FIG. 7C apply equally to the design and selection of permeable collector materials, provided that their solid morphology is cylindrical. While not a conventional approach, it is alsoconceivable to create electrode microstructures via additive manufacturing processes in which cylindrical domains of porous electrode material are arranged layer-by-layer with intervening macro-porous space, in which case FIG. 7C could be applied to their design by considering porosity as being associated with macro-porous domains. Later, more accurate permeability models for this particular case using aligned porosity are examined (see FIGS. 12A-12C).

[0092] The Kozeny-Carman equation can also be applied to the design of microstructures comprised of solid or aggregated-solid spheres by using the appropriate form for volumetricsurface: 4 ^ r^^<, where ^< is sphere diameter. The corresponding contours of permeabilityfor spheres are thus shown in FIG. 7D. The use of microstructures containing spheres is most relevant to electrodes, where spherical active-material particles or aggregates thereof are commonplace due to the high tap densities (:60%) that are achievable using packed spheres.

[0093] To assess the validity of this theory for thru-plane free convection, a steady, two- dimensional (2D) model for salt convection, accumulation, and depletion coupled to Darcy’s law incorporating a gravitational body force was implemented and tested, per FIG. 8A. Here, an LiCoO2 / graphite Li-ion cell was considered using a mixed-carbonate electrolyte using electrodes and separators with 100 µm2permeability. Since homogenously porous and permeable electrodes and separators possess no physical obstructions to break symmetry in the in-plane direction, there exists a spectrum of steady-state flow patterns that are admissible, each possessing a different wavelength ^ that is associated with a given flow pattern’s periodicity. Accordingly, representative flow patterns and salt-concentration distributions are shown in FIG. 8B for selected wavelengths. Each flow pattern is comprised of two counter-rotating Bénard rolls centered about the midpoint of the separator. For small enough wavelengths in-plane diffusion across each roll limits the magnitude of buoyancy forces that can be generated, thus resulting in weak circulation and consequently large thru- plane concentration gradients that can frustrate free-convective flow entirely. However, increased wavelength is shown to suppress in-plane diffusion, thus giving rise to increased circulation and consequently reduced thru-plane concentration gradients. The intensity of circulation is moderated with further increases of wavelength due to increased in-plane hydraulic resistance through porous electrode material. This competition between in-plane diffusion and in-plane hydraulic resistance produces a concentration polarization ^^^that varies non-monotonically with flow-mode wavelength ^, as shown in FIG. 8D. For the 1 Mmean salt concentration simulated here, only ^^^< 2 M is physically feasible, corresponding to an anti-symmetric salt distribution with a minimum salt concentration of zero, a maximum concentration of 2 M, and a mean value of 1 M. Thus, only flow modes existing over a finiteinterval of wavelength are feasible, while ^^^ is minimized at a certain optimum wavelengthFIG. 8D also shows that decreased C-rate reduces the magnitude of ^^^ atwhileincreasing electrode thickness is shown to have a relatively weak effect on it. However, increasing electrode thickness is shown to increase ^^^Z.

[0094] The sensitivity of thru-plane free convection within homogenously permeable electrodes and separators to electrode permeability ^^was also assessed by using 2D simulations. FIG. 9 shows the results of that analysis for different flow-mode wavelengthswhen using 500-µm thick electrodes cycled at 1C rate. Here, ^ ^ 1.2 mm is shown toproduce results that are close to achieving the minimum concentration polarization among all modes for all values of electrode permeability, for which reason we use it as a surrogate for the optimal mode of thru-plane free convection. It is observed that for sufficiently low electrode permeability, concentration polarization is invariant with permeability, as a result of the lack of free convection occurring below a threshold value of electrode permeability. Such a phenomenon is reminiscent of free convection heat transfer occurring between parallel, horizontal plates where a critical Rayleigh number must be exceeded for buoyancy forces to overcome viscous friction. Here, the onset of free convection occurs when permeabilityexceeds a threshold value of 2 µm2 for the ^ ^ 1.2 mm mode. However, only forpermeability substantially greater than 2 µm2is the associated concentration polarization decreased to a level that is feasible: ^^^is smaller than 2 M for ^^greater than 10 µm2. Thus, these results further motivate the development of electrodes with permeability in excess of 10 µm2, translating to solid or solid-aggregate diameters in excess of 60 µm for 50% porous electrodes after considering the analysis shown in FIG. 7D.

[0095] The 2D simulations of thru-plane free convection within homogeneously porous electrodes and separators also inspire the investigation of the use of porous, impermeable electrodes that are patterned with thru-thickness (out-of-plane) channels, the results of which are shown as a function of mode wavelength in FIG. 8C. To generate such 2D flow, both the separator and the current collector may be sufficiently porous. Because the associatedelectrode material is simulated as being impermeable (^^ s 0), the resulting streamlines areshown to be routed through the patterned channels and through separator and collectormaterial in counter-rotating rolls, rather than flowing directly through electrode material. Before proceeding it is noted that circulating flow can develop within such thru-thickness microchannels without requiring in-plane circulation, but such a three-dimensional flow will not be captured by this 2D model. In any case, it is believed that designing these channels for 2D flows is a conservative approach – if such 3D flows occur, they are expected to promote circulation and not suppress it. In this 2D context, the breaking of symmetry by patterned- electrode channels results in a single free-convection mode being associated with a certain pattern. The competition between in-plane diffusion and in-plane hydraulic resistance also results in a certain pattern producing minimal concentration polarization for a given electrode thickness and C-rate, as shown in FIG. 8E. It is noted, however, that the range of patterns that is feasible when using this strategy is smaller than when using highly permeable, unpatterned electrodes. In addition, it is observed that ^^^Zis larger for thick electrodes than for thin electrodes, potentially easing the patterning of channels within such electrodes due to their larger features. For example, ^^^Z=700 µm for 500-µm thick electrodes cycled at 1C, thus requiring 70-µm wide channels to produce 20% channel coverage. In practice, one might design the associated patterned channels to be larger than the optimum spacing would predict to further ease the manufacturability of such batteries. For that reason, the concentration polarization between parallel flow channels was analyzed as a function of inter- channel distance ^, as shown in FIG. 10. Note that the in-plane concentration polarization caused here by the presence of certain impermeable electrode material superimposes with the thru-plane concentration polarization occurring in flow channels. Hence, it is advisable to maintain in-plane concentration polarization below a threshold level, so as to maintain an acceptably low budget for total concentration polarization. To illustrate, 300 mM of in-plane concentration polarization is accepted, translating to maximum inter-channel distances of 200 µm, 350 µm, and 500 µm for operation at C-rates of 5C, 2C, and 1C, respectively. The present analysis was performed using the in-plane ion-transport tortuosity t based upon theBruggeman approximation: t ^ HPuvw, where H is porosity. This assumption is supported bythe relatively good agreement of the Bruggeman approximation for in-plane transport in LiCoO2, graphite, and NMC electrodes with detailed simulations, despite thru-plane transport possessing more than double that of the Bruggeman approximation.

[0096] Certain features of electrode patterning that might be used when implementing the thru-plane mode of free convection are now discussed. First, electrodes are patterned with in-plane channels extending through the thickness of the respective electrode, it is advisable to orient the in-plane channels on one electrode at an angle with respect to the in-plane channels on the other electrode. FIG. 11D illustrates that when this is done, projections of the associated channels onto the porous current collector(s) that both electrodes abut are caused to intersect, thus leading to continuity of permeable fluid passages from one electrode to the other. This effect is important in order to induce free convection not only during charging half-cycles but also during discharging half-cycles of complete charge / discharge cycles because the orientation of circulation loops changes as a result. Further, when double-sided current collectors are used in which cathodes or anodes are attached to both sides of current collectors, fluid transits through current collectors irrespective of whether charge or discharge occurs. In addition, FIGS. 11A-11C show that shallow in-plane channels can be patterned onto the top surface of each electrode films to spread electrolyte flow across the separator from deeper thru-thickness in-plane channels. In-plane channels may be oriented within the electrode in various ways or angles so as to connect with in-plane channels extending through-thickness or with out-of-plane channels. One feasible way to effect such in-plane channeling is by additive manufacturing, wherein electrode slurry is deposited and solidified filament-wise from a series of nozzles in a layer-by-layer fashion. In practice, the slurries commonly used in conventional Li-ion battery tape casting processes may be used, provided that the deposited electrode material may be immersed in a non-solvent bath (e.g., water). Because the associated in-plane channels need not be connected amongst themselves, a highly stable three-dimensional structure can be developed in which high apparent hydraulic permeability is achieved, as is shown next.

[0097] Inspired by the approach depicted in FIGS. 11A-11E to incorporate in-plane channels throughout the cross-section of electrodes, together with separate thru-thickness or out-of-plane channels that the ends of in-plane channels are adjoined to, using the 2D model free convection is simulated through homogeneously permeable electrodes having anisotropic permeability that is aligned with the in-plane direction. That is, the associated electrodes exhibit non-zero permeability along the in-plane direction, while being impermeable in the thru-plane direction. Further, we connected these anisotropic electrode domains to thru- thickness channels as investigated to obtain FIGS. 8C and 8E. The resulting concentration polarization under a fast-charging condition at 3C rate is shown in FIG. 12A to be feasible provided that the electrode’s in-plane hydraulic permeability exceeds 10 µm2. One type ofin-plane channel that could be used to effect such in-plane permeability is in-plane channels of circular transverse cross-section arrayed with a certain center-to-center spacing, as depicted as “holes” in the inset of FIG. 12B. FIGS. 12 and 12C show that aligned 100-µm diameter in-plane channels at a coverage fraction of only 5% and a center-to-center spacing of 300 µm can produce apparent permeability greater than 10 µm2. Importantly these length scales are of the same order as 3D-printing nozzles, adding confidence to the feasibility of this approach using other more scalable additive manufacturing strategies. In addition, this degree of center-to-center spacing is commensurate with a modest in-plane concentration polarization (~600 mM) predicted by FIG. 10.

[0098] Design and Analysis for In-Plane Recirculation

[0099] This section provides details concerning the design approach used to achieve in- plane recirculation with the aid of physics-based analysis. First, sensitivity to flow path length and electrode permeability is analyzed, followed by the enumeration of specific electrode patterning strategies used to achieve in-plane circulation.

[0100] Sensitivity to Flow Path Length and Permeability. Recognizing that the number of passes ^^has a similar formula except for certain case-specific orientation parameters, the formula for Case 1 that is representative of Li-ion pouch cells is used to quantify the length scales and hydraulic permeabilities needed to substantially enhance electrochemical cycling by mitigating the salt depletion / accumulation mechanism. These findings motivate the design, creation, and characterization of short-span circulation loops that are embedded in thick Li-ion intercalation electrodes with enhanced hydraulic permeability to mitigate salt depletion / accumulation. FIGS. 13A-13D, which show ^^versus ^^and ^, confirms the early conclusions derived from Rayleigh-number estimates, and it shows that a significant number of circulating passes is possible if either hydraulic permeability is sufficiently large or if flow-path length is sufficiently small. For a LiFePO4-based cell using 100 µm thick electrodes cycled at 1C rate, an electrode patterned to achieve 100 µm2permeability requires a flow-path shorter than 4 mm to achieve more than one pass during a single electrochemical half-cycle (FIG. 13A). In contrast, the same flow-path length realizes a value of ^^that is a small fraction of a pass (< 1 / 20th) when a permeability representative of unpatterned electrodes (0.1 µm2) is used. Further, increased active-material density (FIG. 13B), increased electrode thickness (FIG. 13C), and decreased C-rate (FIG. 13D) are all shown to increase the number of passes produced for a given permeability and flow-path length.

[0101] For a given cell chemistry (BCD,x7CD, -^, ^7^^^^^, and 8), porous electrodeproperties (H and J), operating condition (h), and buoyancy force (# y ^), the effects of flow-path length and permeability on the number of passes are captured succinctly by a dimensionless flow-path lengthas shown in FIG. 13E. Because capacity utilization at a given C-rate for a given battery chemistry with certain porous electrode properties and buoyancy force is solely a function of the number of passes ^^, capacityutilization is therefore principally a function of the dimensionless flow-path length^^^^^^^^^. Recognizing that ^^ :10 produced capacity utilization within 1% of the casewith ^^ s z, Table 1 shows the values of ^corresponding to ^ :10 for variousconditions. These can readily be used to determine the appropriate flow path length to employ with an electrode material having certain unpatterned hydraulic permeability. Table 1 shows that the corresponding flow-path lengths needed to produce ^^:10 are within feasible ranges for laser-based micromachining when ^^= 2.5 µm2and 12.5 µm2are considered. It is further shown that battery chemistries beyond Li-ion that use solvents with four-fold smaller viscosity than mixed-carbonate electrolytes (namely water in aqueous batteries or acetonitrile in non-aqueous Na-ion batteries) produce millimeter-scale flow-path lengths, providing even greater flexibility for design and manufacturing of electrodes to incorporate buoyancy-induced flow. Table 1: Dimensionless flow-path length corresponding to ten passes during one half-cycle. All cases use electrodes with 50% porosity, 50% active material volume fraction, and electrolyte comprised of LiPF6in mixed-carbonate solvent at 25 C, except for aqueous cells and non-aqueous Na-ion cell. Condition ^^^^ ^^^^^^^ @ ^ for:10 ^ 2^ for2^=2.5 µm ^^=12.5 µmLiFePO4 @ 1C, ^ ^ 100 µm 32.6 103 µm 230 µmLiCoO2 @ 1C, ^ ^ 100 µm 33.8 107 µm 239 µmLiCoO2 @ 1C, ^ ^ 200 µm 47.8 151 µm 338 µmLiCoO2 @ 0.5C, ^ ^ 200 µm 67.6 214 µm 479 µmLiCoO2 @ 1C, ^ ^ 500 µm 107 338 µm 756 µmLiCoO2 @ 1C, ^ ^ 1000 µm 151 477 µm 1.07 mmAqueous PBA / PBA-- 534 µm 1.20 mmNa-Ion Cell @ 1C, ^ ^ 500 µmNon-Aqueous PBA / Hard-Carbon-- 845 µm 1.89 mmNa-Ion Cell @ 1C, ^ ^ 500 µmAqueous Li / S or Zn / S Cell @ 1C, -- 534 µm 1.20 mm^ ^ 500 µm

[0102] After having determined the appropriate flow-path length to use in order to achieve sufficient recirculation, now the specific means of connecting the fluid within one electrode to that in other electrodes over the requisite flow path length ^ is considered. Given that the associated length-scales in Table 1 are much shorter than the macroscopic spans of typical batteries, novel motifs for separator / electrode perforations / channels and embedded flow fields are introduced. The motifs include a network of perforations / channels through the electrodes, foils, and separators in combination with in-plane channels embedded within the associated electrodes. Channels through the electrodes can be achieved either by manufacturing operations that occur prior to the casting of electrode films (e.g., weaving, forming, or die cutting) or by manufacturing operations after the casting of electrode films (e.g., die cutting, laser engraving, or subtractive machining). Perforations through separators can be achieved using similar manufacturing operations. The associated in-plane channels may be embedded within electrodes (1) during the roll pressing step commonly used to calender electrodes by introducing surface textures on the associated rolls (neither additive or subtractive manufacturing), (2) either before or after calendering using laser ablation (subtractive manufacturing), or (3) using other additive or subtractive methods.

[0103] Flow-field motifs can be divided into two different classes: flow-through and flow-by motifs. FIGS. 14A-14D show the side views of flow-through motifs where electrode channels and separator perforations 118a,118b are used without embedded (in-plane) flow channels to drive fluid through the flow-path length ^. Here, channels / perforations 118a,118b through the associated battery “sandwich” enable the development of a multiplicity of recirculation loops generated by salt depletion / accumulation in the presence of gravitational acceleration. Notably, when double-sided foils (current collectors 106,110) are used (FIG. 14C), the associated gravitational length scale becomes double the magnitude of a given electrode’s thickness, doubling the driving force for flow relative to batteries using single-sided foils (FIG. 14A). Also, while it is possible to produce flow by only perforating separators 112 if the anode 104 is above the cathode 108 (i.e., Li-ion battery discharging; FIG. 14A), in practice switching the direction of current causes the designations of cathode and anode to alternate (Li-ion battery charging; FIG. 14B). Therefore, electrodes 104,108 are preferably perforated, that is, constructed with out-of-plane channels 118a, in conjunction with perforation of separators 112 to facilitate buoyancy-driven flow during both steps of acomplete electrochemical cycle. Further, cells using double-sided foils (FIGS. 14C and 14D) may use electrode channels 118a in order to facilitate flow, irrespective of the orientation of gravity with respect to the anode 104 and cathode 108. Finally, FIG. 14D shows that when out-of-plane channels 118a within electrodes 104,108 are mis-aligned with the perforations 118b in separators 112 when using double-sided foils (current collectors 106,110), the actual flow path length that the fluid undergoes becomes increased relative to the distance between the channels / perforations 118a,118b in either the electrodes 104,108 or the separator 112. As a result, the most ideal embodiment as applied to double-sided foils includes the alignment of separator perforations 118b with electrode out-of-plane channels 118a. Alternatively, if the foil 106,110 itself is made as a mesh having an abundance of holes, the effect of mis- alignment or alignment with separator perforations 118b becomes insignificant. In contrast, the flows produced by the inclusion of out-of-plane channels 118a in electrodes 104,108 with single-sided foils 106,110, as shown in FIGS. 14A and 14B, may be insensitive to alignment with separator perforations 118b as long as in-plane channels are not appended to the electrode out-of-plane channels 118a. If in-plane channels are appended to electrode out-of- plane channels 118a, then misalignment of electrode and separator channels / perforations 118a,118b can lead to ineffective electrolyte transmission through said channels. Next, the different kinds of flow-field motifs that can be used are explored.

[0104] FIG. 15A-15E shows top views of different motifs that may be used to pattern battery electrodes and separators. Motifs #1 and #2 only use electrode and separator out-of- plane channels / perforations 118a,118b, whereas Motifs #3, #4, and #5 use them in conjunction with electrode-in-plane flow channels 116 and manifolds. The term manifold may be understood to refer to a multiplicity of parallel in-plane channels 116 that are connected to a pair of thru-plane (out-of-plane) channels 118a. Among all such motifs the flow-path length ^ can be tailored to a given battery chemistry, electrode formulation, and operation condition of interest, as shown by Table 1.

[0105] A certain fraction of active-material capacity is lost because of including such channels in the electrode material. In addition, the addition of channels to electrodes results in the constriction of electronic current through current-collecting foil that abuts electrode films, thus increasing Ohmic resistance. These tradeoffs motivate the design of interrupted, discontinuous channels, such that in-plane electronic continuity is sustained within the associated current-collecting foils. Motifs #1 and #2 make use of this approach using out-of-plane channels 118a having rectangular and circular cross-sections, respectively. In practice, manufacturability is likely to constrain the range of channel sizes and shapes that can be achieved, but laser ablation, for example, has been shown to produce tout-of-plane channels 118a as small as 20 µm. For such designs to function well electrochemically, it is beneficial that the flow that they produce is relatively uniform through the intervening porous electrode material. To this end, potential-flow theory was used to analyze Motif #2. This analysis shows that the spacing between perforations ^ should be smaller than one-third of the flow- path length ^ to produce uniform flow between inlet and outlet perforations. Further, perforations on isotropic lattices (e.g., a square lattice) used in the past without knowledge of the buoyancy-induced flow mechanism are likely to suffer from non-uniform flow distribution and consequently weaker extent of buoyancy-induced flow ceteris paribus.

[0106] Additionally, it is possible to append in-plane channels 116 to each thru-plane channel 118a (FIGS. 15C and 15D). Motif #3 achieves this by arranging the associated thru- plane channels 118a in such a way that in-plane channels 116 that append inlet channels 118a are interdigitated with respect to in-plane channels 116 that append outlet channels 118a. These interdigitated in-plane channels 116 may either be straight or tapered. For channels 116 that are tapered to provide uniform flow, the associated number of passesfor such a patterned electrode may depend on electrode coverage fraction ^ and the dimensionlesshydraulic resistance { ^ ^6^^ ^^^^^ ^^|u^^}^ within such channels, in addition to parametersassociated with the unpatterned electrode material:

[0107]

[0108] Thus, for a suitable electrode coverage fraction one may design such interdigitated in-plane channels 116 to have a sufficiently small { value in order to maximize ^^^^^^. In contrast, Motif #4 appends in-plane channels 116 to each thru-plane channel 118a in a different manner than Motif #3. Motif #4 introduces straight in-plane channels 116 that span directly from one inlet channel 118a to another outlet channel 118a. In doing so electrolyte is routed by electrode material rather than through electrode material. Consequently, such a design produces a degree of deleterious concentration polarization ^@^^Ain mol / L between stagnant electrolyte in the electrodes pores and electrolyte within the associated channels due to the finite salt diffusivityin the porous

[0110] In addition to its dependence on electrochemical parameters, electrode parameters, and operating condition, the degree of concentration polarization scales with the square of the distance between channels ^. One can therefore determine an appropriate spacing between channels in order to ensure that the extent of concentration polarization is small, e.g., 100 mV or less.

[0111] Motifs #3 and #4 can be combined with manifolds to deliver the transfer electrolyte between out-of-plane or thru-plane channels 118a and their associated in-plane channels 116. This type of design is depicted for parallel-flow channels 116 in FIG. 15E. By using a manifold to connect out-of-plane channels 118a to in-plane channels 116, a smaller number of out-of-plane channels 118a and perforations 118b can be inserted into the electrodes 104,108 and separator 112, respectively, thus affording additional design flexibility. While FIG. 15E depicts a manifold using a Y-type manifold with a straight header, in practice a variety of different manifolds can be employed (e.g., Z-type or U-type) to maximize flow uniformity and to minimize manifold pressure drop.

[0112] Implications for Cylindrical Cells

[0113] To engineer circulation loops in jelly rolls contained within cylindrical cells the orientation-dependence of the number of passes through a pair of electrodes wrapped into a circular arc (cf. FIGS. 6C and 16A-16G) is considered. In actuality, the use of patterns similar to that shown for a pouch cell in FIG. 16A is envisioned but where the chosen flowpath length ^^ for loop ^ determines the angular interval of the circular arc of interest^^^^^. Thus, the variations of the orientation functionthatappears in the expression for ^^ for Case 3 is first inspected. The contoursinFIG.16A exhibit two distinct domains of arrangement in which the function is either positive or negative with boundaries in between associated domains exhibiting a nullified buoyancyforce. FIG. 16B shows that domains with ^ ^ 0 produce circulation only when the anode isarranged outward of the cathode, whereas domains with ^ ^ 0 produce circulation only whenthe cathode is arranged outward of the anode.

[0114] Knowledge of the orientation function ^^^^^ ^^^^^ can therefore be used toevaluate different designs for spontaneous circulation in jelly rolls. FIGS. 16D-16G show a representative jelly roll containing continuous through-holes extending through the entirejelly roll along particular directions, the intent of which is to facilitate flow both between outward anodes and inward cathodes as well as inward anodes and outward cathodes. If only a horizontal through-hole is created (FIG. 16D), spontaneous circulation loops can begenerated above and below the through-hole because the magnitude of ^^^^^is shownto be non-zero for both angular intervals of the jelly roll. However, if only a single through- hole is created with vertical orientation (FIG. 16E), no spontaneous circulation loops areproduced because ^^^^ ^ ^^^^^ ^ 0 for both the left and right angular intervals of the jelly roll.One may alternatively perforate the jelly roll vertically and horizontally with through holes (FIG. 16F), the result of which is to generate counter-rotating circulation loops having equal strength in each quadrant. However, if the same perforated jelly roll is rotated by 45° (FIG. 16G), buoyancy becomes nullified in two of the associated quadrants, while the strength of circulation is mildly increased in the other two quadrants. One can therefore imagine perforating the associated jelly roll to varying degrees, either before or after wrapping the roll, to achieve circulating loops throughout the entire roll.

[0115] In addition to analyzing how the domains of orientation affect the formation of circulation loops, the limiting form of the number of passes for small angular segments can be used to inform the design of patterned electrodes. Namely, the effect of perforation placement appears in Case 3’s expression for ^^by way of reducing the effective gravitational acceleration acting on the associated segment when a segment’s meanorientation angle ^l ^ ^^^^^ n ^^^^^ deviates from vertical: #^ ^ # jk^ ^l. To compensate forthis effect, it is proposed to create electrodes that are patterned with a segment-specific flow- path length ^ that is made to scale in direct proportion to the square root of cosine of ^lfor thesegment of interest: ^ ^ ^u2^ jk^ ^l ^x where ^u is the flow-path length used for segmentswith ^l ^ 0. The use of such scaling ensures that the number of circulating passes producedamong all segments are equal, thus also resulting in equal departure of salt concentration from its initial value throughout the entire jelly roll. Qualitatively, the effect of such scaling will be to shorten circulation segments that possess average orientation that is near vertical, whereas circulation segments that possess average orientation that is near horizontal will be longer, relatively speaking. An alternative design strategy to achieve the same result could involve the use of a segment-specific pattern that produces a segment-specific apparentpermeability: ^^ ^ ^^^u^ ^^j ^l ^is the apparent permeability used for segmentswith ^l ^ 0 and ^^j ^l is secant of ^l. The effect of such scaling would therefore be to enhancethe permeability of segments that have orientation close to vertical, so as to achieve equal number of passes among all segments.

[0116] The present disclosure also includes the following aspects:

[0117] A first aspect includes a battery cell configured for buoyancy-induced electrolyte circulation, the battery cell comprising: components including: a first electrode on a first current collector; a second electrode on a second current collector, the first electrode facing the second electrode; and a separator between the first electrode and the second electrode; and an electrolyte, wherein a hydraulic permeability of one or more of the components is sufficient for flow of the electrolyte through the respective component, and / or wherein one or more of the components includes in-plane channels, out-of-plane channels, and / or perforations configured to promote formation of electrolyte circulation loops within the battery cell during charging or discharging.

[0118] A second aspect relates to the battery cell of the first aspect being a rechargeable battery cell, wherein the rechargeable battery cell is optionally selected from the group consisting of lithium-ion battery cell, lead-acid battery cell, nickel / metal hydride battery cell, sodium-ion battery cell, potassium-ion battery cell, magnesium-ion battery cell, calcium-ion battery cell, zinc-ion battery cell, aluminum-ion battery cell, lithium-metal battery cell, and lithium / sulfur battery cell.

[0119] A third aspect relates to the battery cell of the first or the second aspect being a non-rechargeable battery cell, wherein the non-rechargeable battery cell is optionally selected from the group consisting of alkaline MnO2 / Zn battery cell, non-aqueous lithium thionyl chloride battery cell, and lithium manganese dioxide battery cell.

[0120] A fourth aspect relates to the battery cell of any preceding aspect, wherein the electrolyte comprises a liquid electrolyte.

[0121] A fifth aspect relates to the battery cell of any preceding aspect, wherein the electrolyte comprises a viscosity at room temperature (e.g., 18-22°C) of at least 0.2 mPa·S, at least 0.4 mPa·S, or at least 1 mPa·S, and / or wherein the viscosity at room temperature is no greater than 100 mPa·S, no greater than 10 mPa·S, no greater than 5 mPa·S, or no greater than 2 mPa·S.

[0122] A sixth aspect relates to the battery cell of any preceding aspect comprising multiple cell pairs.

[0123] A seventh aspect relates to the battery cell of any preceding aspect, wherein each of the first and second electrodes has a thickness of at least 50 µm, at least 100 µm, at least 200 µm, at least 200 µm, at least 500 µm, and / or up to 1 mm, or up to 1 cm.

[0124] An eighth aspect relates to the battery cell of any preceding aspect, wherein each of the separator, the first current collector, and the second current collector has a thickness in a range from about 5 microns to about 50 microns.

[0125] A ninth aspect relates to the battery cell of any preceding aspect, wherein the hydraulic permeability is at least about 10 µm2, at least about 20 µm2, at least about 100 µm2, or at least about 200 µm2, and / or no greater than about 500 µm2.

[0126] A tenth aspect relates to the battery cell of any preceding aspect, wherein the hydraulic permeability is an in-plane hydraulic permeability and / or out-of-plane hydraulic permeability.

[0127] An eleventh aspect relates to the battery cell of any preceding aspect, wherein the in-plane hydraulic permeability and the out-of-plane hydraulic permeability are the same, the respective component having an isotropic structure.

[0128] A twelfth aspect relates to the battery cell of any preceding aspect, wherein the in- plane and out-of-plane hydraulic permeability are different, the respective component having an anisotropic structure.

[0129] A thirteenth aspect relates to the battery cell of any preceding aspect, wherein porosity and / or solid feature size of the respective component is controlled to obtain the hydraulic permeability sufficient for flow of the electrolyte.

[0130] A fourteenth aspect relates to the battery cell of any preceding aspect, wherein the respective component is made up of fibers or particles and the solid feature size is a nominal width or diameter of the fibers or particles.

[0131] A fifteenth aspect relates to the battery cell of any preceding aspect, wherein the perforations and / or the out-of-plane channels extend partially or fully through the thickness of the respective component.

[0132] A sixteenth aspect relates to the battery cell of any preceding aspect, wherein some or all of the in-plane channels extend through the thickness of the respective component.

[0133] A seventeenth aspect relates to the battery cell of any preceding aspect, wherein the in-plane channels, the out-of-plane channels, and / or the perforations each have a width ordiameter of at least about 20 microns, at least about 50 microns, or at least about 100 microns, and / or no greater than about 500 microns.

[0134] An eighteenth aspect relates to the battery cell of any preceding aspect, wherein the perforations have a depth of up to about 50 µm, the depth being limited by the thickness of the respective component.

[0135] A nineteenth aspect relates to the battery cell of any preceding aspect, wherein the out-of-plane channels have a depth of up to about 1 mm, the depth being limited by the thickness of the respective component.

[0136] A twentieth aspect relates to the battery cell of any preceding aspect, wherein the in-plane channels have a length limited by a lateral extent of the respective component or by a spacing between the out-of-plane channels.

[0137] A twenty-first aspect relates to the battery cell of any preceding aspect, wherein a spacing between the in-plane channels is less than about 5 mm, less than about 200 microns, less than about 100 microns, or less than about 50 microns, and / or at least about 10 microns.

[0138] A twenty-second aspect relates to the battery cell of any preceding aspect, wherein a spacing between the out-of-plane channels is at least 10% of an electrode thickness, at least 25% of the electrode thickness, at least 50% of the electrode thickness, at least 70% of the electrode thickness, at least 90% of the electrode thickness, or at least 120% of the electrode thickness, and / or up to 130% of the electrode thickness.

[0139] A twenty-third aspect relates to the battery cell of any preceding aspect, wherein the in-plane channels, the out-of-plane channels and / or the perforations have curved, circular, polygonal, and / or irregular cross-sections.

[0140] A twenty-fourth aspect relates to the battery cell of any preceding aspect, wherein the in-plane channels, the out-of-plane channels and / or the perforations are straight or tapered along a length thereof.

[0141] A twenty-fifth aspect relates to the battery cell of any preceding aspect, wherein an arrangement of the in-plane channels, the out-of-plane channels and / or the perforations within the respective component is aligned, ordered, disordered, staggered, interdigitated, and / or intersecting.

[0142] A twenty-sixth aspect relates to the battery cell of any preceding aspect, wherein the out-of-plane channels in the respective component are aligned with the out-of-plane channels in an adjacent component.

[0143] A twenty-seventh aspect relates to the battery cell of any preceding aspect, wherein the in-plane channels in the respective component are angularly offset from, or perpendicular to, the in-plane channels in an adjacent component, whereby intersections are formed at crossing points.

[0144] A twenty-eighth aspect relates to the battery cell of any preceding aspect, wherein a coverage fraction of the in-plane channels, the out-of-plane channels and / or the perforations is at least 5%, at least 20%, at least 40%, and / or no greater than about 50% of the respective component.

[0145] A twenty-ninth aspect relates to the battery cell of any preceding aspect, wherein the hydraulic permeability of the separator is sufficient for flow therethrough of the electrolyte, and / or wherein the hydraulic permeability of the first and second current collectors is sufficient for flow therethrough of the electrolyte.

[0146] A thirtieth aspect relates to the battery cell of any preceding aspect, wherein the separator and / or the first and second current collectors include the perforations.

[0147] A thirty-first aspect relates to the battery cell of any preceding aspect, wherein the hydraulic permeability of the first electrode is sufficient for flow therethrough of the electrolyte, and / or wherein the hydraulic permeability of the second electrode is sufficient for flow therethrough of the electrolyte.

[0148] A thirty-second aspect relates to the battery cell of any preceding aspect, wherein the first electrode includes the in-plane channels and / or the out-of-plane channels, and / or wherein the second electrode includes the in-plane channels and / or the out-of-plane channels.

[0149] A thirty-third aspect relates to the battery cell of any preceding aspect, wherein the first and second current collectors are single-sided, and wherein the hydraulic permeability of the separator or the hydraulic permeability of the first and second current collectors is sufficient for flow therethrough.

[0150] A thirty-fourth aspect relates to the battery cell of any preceding aspect, wherein the first and second current collectors are double-sided, and wherein the hydraulic permeability of the separator and the hydraulic permeability of the first and second current collectors are sufficient for flow therethrough.

[0151] A thirty-fifth aspect relates to the battery cell of any preceding aspect, wherein at least one of the components is impermeable to flow of the electrolyte.

[0152] A thirty-sixth aspect relates to the battery cell of any preceding aspect, wherein the separator and / or the first and second current collectors are impermeable to flow of the electrolyte.

[0153] A thirty-seventh aspect relates to the battery cell of any preceding aspect, wherein the components have a planar arrangement.

[0154] A thirty-eighth aspect relates to the battery cell of any preceding aspect comprising a pouch or prismatic cell.

[0155] A thirty-ninth aspect relates to the battery cell of any preceding aspect, wherein the components have a jelly roll arrangement.

[0156] A fortieth aspect relates to the battery cell of any preceding aspect, wherein, in use, the components have a long axis oriented horizontally, wherein the long axis is aligned with a plane of the respective component, and / or wherein the long axis is generally perpendicular to a main direction of current flow through the battery.

[0157] A forty-first aspect relates to the battery cell of any preceding aspect, wherein, in use, the first electrode is positioned above the second electrode, the first electrode is configured as an anode to carry out electrochemical oxidation, and the second electrode is configured as a cathode to carry out electrochemical reduction.

[0158] A forty-second aspect relates to the battery cell of any preceding aspect, wherein a force acting on the battery cell includes gravity, a centrifugal force, a Coriolis force, and / or any other inertial force.

[0159] A forty-third aspect relates to the battery cell of any preceding aspect, wherein the battery cell is configured to undergo rotation to produce the centrifugal force.

[0160] A forty-fourth aspect relates to the battery cell of any preceding aspect, wherein the electrolyte is not in fluid communication with a pump.

[0161] A forty-fifth aspect relates to the battery cell of any preceding aspect, wherein the one or more of the components including the in-plane channels, the out-of-plane channels, and / or the perforations are fabricated by additive manufacturing.

[0162] A forty-sixth aspect relates to the battery cell of any preceding aspect, wherein the one or more of the components including the in-plane channels, the out-of-plane channels, and / or the perforations are fabricated by subtractive manufacturing.

[0163] A forty-seventh aspect relates to a method of preventing thermal runaway of a battery cell, the method comprising: electrochemically cycling the battery cell of anypreceding claim; during cycling, measuring a temperature of the battery cell; and if the temperature reaches a critical temperature, applying a current signal, whereby buoyancy- induced circulation of the electrolyte occurs, effecting cooling of the battery cell.

[0164] A forty-eighth aspect relates to the method of the forty-seventh aspect, wherein the current signal is constant or time-varying (e.g., pulsed or sinusoidal).

[0165] A forty-ninth aspect relates to the method of the forty-seventh or forty-eighth aspect, wherein measuring the temperature comprises monitoring a thermocouple or other temperature probe attached to the battery cell.

[0166] A fifieth aspect relates to the method of any preceding aspect, wherein measuring the temperature comprises using a known dependence of open-circuit cell-voltage on the temperature and state-of-charge for applicable battery cell chemistry.

[0167] A fifty-first aspect relates to the method of any preceding aspect, wherein measuring the temperature comprises utilizing one or more reduced-order models linking the temperature and heat dissipation of the battery cell to measured voltage and / or current.

[0168] A fifty-second aspect relates to the method of any preceding aspect, further comprising: during cycling, measuring pressure or strain; and if the pressure reaches a critical pressure or if the strain reaches a critical strain, applying the current signal.

[0169] A fifty-third aspect relates to the method of any preceding aspect, wherein a force acting on the battery cell includes gravity, a centrifugal force, a Coriolis force, and / or any other inertial force.

[0170] A fifty-fourth aspect relates to the method of any preceding aspect, wherein the battery cell is configured to undergo rotation to produce the centrifugal force.

[0171] A fifty-fifth aspect relates to the method of any preceding aspect, wherein a pump is not used to circulate the electrolyte within the battery cell.

[0172] While various embodiments have been described, it will be apparent to those of ordinary skill in the art that many more embodiments and implementations are possible. Accordingly, the embodiments described herein are examples, not the only possible embodiments and implementations.

[0173] In addition to the features mentioned in each of the independent aspects enumerated above, some examples may show, alone or in combination, the optional features mentioned in the dependent aspects and / or as disclosed in the description above and shown in the figures.

Claims

CLAIMS 1. A battery cell configured for buoyancy-induced electrolyte circulation, the battery cell comprising: components including: a first electrode on a first current collector; a second electrode on a second current collector, the first electrode facing the second electrode; and a separator between the first electrode and the second electrode; and an electrolyte, wherein a hydraulic permeability of one or more of the components is sufficient for flow of the electrolyte through the respective component, and / or wherein one or more of the components includes in-plane channels, out-of-plane channels, and / or perforations configured to promote formation of electrolyte circulation loops within the battery cell during charging or discharging.

2. The battery cell of claim 1 being a rechargeable battery cell, wherein the rechargeable battery cell is optionally selected from the group consisting of lithium-ion battery cell, lead-acid battery cell, nickel / metal hydride battery cell, sodium-ion battery cell, potassium-ion battery cell, magnesium-ion battery cell, calcium-ion battery cell, zinc-ion battery cell, aluminum-ion battery cell, lithium-metal battery cell, and lithium / sulfur battery cell.

3. The battery cell of claim 1, being a non-rechargeable battery cell, wherein the non-rechargeable battery cell is optionally selected from the group consisting of alkaline MnO2 / Zn battery cell, non-aqueous lithium thionyl chloride battery cell, and lithium manganese dioxide battery cell.

4. The battery cell of claim 1, wherein the electrolyte comprises a liquid electrolyte.

5. The battery cell of claim 1, wherein the electrolyte comprises a viscosity at room temperature in a range from 0.2 mPa·S to 100 mPa·S.

6. The battery cell of claim 1 being one of multiple cell pairs.

7. The battery cell of claim 1, wherein each of the first and second electrodes has a thickness in a range from 50 µm to 1 cm.

8. The battery cell of claim 1, wherein each of the separator, the first current collector, and the second current collector has a thickness in a range from 5 microns to 50 microns.

9. The battery cell of claim 1, wherein the hydraulic permeability is in a range from 10 µm2to 500 µm2.

10. The battery cell of claim 9, wherein the hydraulic permeability is an in-plane hydraulic permeability and / or an out-of-plane hydraulic permeability.

11. The battery cell of claim 10, wherein the in-plane hydraulic permeability and the out-of-plane hydraulic permeability are the same, the respective component having an isotropic structure.

12. The battery cell of claim 10, wherein the in-plane and out-of-plane hydraulic permeability are different, the respective component having an anisotropic structure.

13. The battery cell of claim 1, wherein porosity and / or solid feature size of the respective component is controlled to obtain the hydraulic permeability sufficient for flow of the electrolyte.

14. The battery cell of claim 13, wherein the respective component is made up of fibers or particles and the solid feature size is a nominal width or diameter of the fibers or particles.

15. The battery cell of claim 1, wherein the perforations and / or the out-of-plane channels extend partially or fully through the thickness of the respective component.

16. The battery cell of claim 1, wherein some or all of the in-plane channels extend through the thickness of the respective component.

17. The battery cell of claim 1, wherein the in-plane channels, the out-of-plane channels, and / or the perforations each have a width or diameter in a range from 20 microns to 500 microns.

18. The battery cell of claim 1, wherein the perforations have a depth of up to about 50 µm, the depth being limited by the thickness of the respective component.

19. The battery cell of claim 1, wherein the out-of-plane channels have a depth of up to about 1 mm, the depth being limited by the thickness of the respective component.

20. The battery cell of claim 1, wherein the in-plane channels have a length limited by a lateral extent of the respective component or by a spacing between the out-of- plane channels.

21. The battery cell of claim 1, wherein a center-to-center spacing between the in- plane channels is in a range from 10 microns to 5 mm.

22. The battery cell of claim 1, wherein a center-to-center spacing between the out-of-plane channels is in a range from 10% to 130% of the electrode thickness.

23. The battery cell of claim 1, wherein the in-plane channels, the out-of-plane channels and / or the perforations have curved, circular, polygonal, and / or irregular transverse cross-sections.

24. The battery cell of claim 1, wherein the in-plane channels, the out-of-plane channels and / or the perforations are straight or tapered along a depth or length thereof.

25. The battery cell of claim 1, wherein an arrangement of the in-plane channels, the out-of-plane channels and / or the perforations within the respective component is aligned, ordered, disordered, staggered, interdigitated, and / or intersecting.

26. The battery cell of claim 1, wherein the out-of-plane channels in the respective component are aligned with the out-of-plane channels in an adjacent component.

27. The battery cell of claim 1, wherein the in-plane channels in the respective component are angularly offset from, or perpendicular to, the in-plane channels in an adjacent component, whereby intersections are formed at crossing points.

28. The battery cell of claim 1, wherein a coverage fraction of the in-plane channels, the out-of-plane channels and / or the perforations is in a range from 5% to 50% of the respective component.

29. The battery cell of claim 1, wherein the hydraulic permeability of the separator is sufficient for flow therethrough of the electrolyte, and / or wherein the hydraulic permeability of the first and second current collectors is sufficient for flow therethrough of the electrolyte.

30. The battery cell of claim 1, wherein the separator and / or the first and second current collectors include the perforations.

31. The battery cell of claim 1, wherein the hydraulic permeability of the first electrode is sufficient for flow therethrough of the electrolyte, and / or wherein the hydraulic permeability of the second electrode is sufficient for flow therethrough of the electrolyte.

32. The battery cell of claim 1, wherein the first electrode includes the in-plane channels and / or the out-of-plane channels, and / or wherein the second electrode includes the in-plane channels and / or the out-of-plane channels.

33. The battery cell of claim 1, wherein the first and second current collectors are single-sided, and wherein the hydraulic permeability of the separator or the hydraulic permeability of the first and second current collectors is sufficient for flow therethrough.

34. The battery cell of claim 1, wherein the first and second current collectors are double-sided, and wherein the hydraulic permeability of the separator and the hydraulic permeability of the first and second current collectors are sufficient for flow therethrough.

35. The battery cell of claim 1, wherein at least one of the components is impermeable to flow of the electrolyte.

36. The battery cell of claim 1, wherein the separator and / or the first and second current collectors are impermeable to flow of the electrolyte.

37. The battery cell of claim 1, wherein the components have a planar arrangement.

38. The battery cell of claim 1 comprising a pouch or prismatic cell.

39. The battery cell of claim 1, wherein the components have a jelly roll arrangement.

40. The battery cell of claim 1, wherein, in use, the components have a long axis oriented horizontally, wherein the long axis is aligned with a plane of the respective component, and / orwherein the long axis is generally perpendicular to a main direction of current flow through the battery.

41. The battery cell of claim 1, wherein, in use, the first electrode is positioned above the second electrode, wherein the first electrode is configured as an anode to carry out electrochemical oxidation, and wherein the second electrode is configured as a cathode to carry out electrochemical reduction.

42. The battery cell of claim 1, wherein a force acting on the battery cell includes gravity, a centrifugal force, a Coriolis force, and / or any other inertial force.

43. The battery cell of claim 42, wherein the battery cell is configured to undergo rotation to produce the centrifugal force.

44. The battery cell of claim 1, wherein the electrolyte is not in fluid communication with a pump.

45. The battery cell of claim 1, wherein the one or more of the components including the in-plane channels, the out-of-plane channels, and / or the perforations are fabricated by additive manufacturing.

46. The battery cell of claim 1, wherein the one or more of the components including the in-plane channels, the out-of-plane channels, and / or the perforations are fabricated by subtractive manufacturing.

47. A method of preventing thermal runaway of a battery cell, the method comprising: electrochemically cycling the battery cell of claim 1; during cycling, measuring a temperature of the battery cell; andif the temperature reaches a critical temperature, applying a current signal, whereby buoyancy-induced circulation of the electrolyte occurs, effecting cooling of the battery cell.

48. The method of claim 47, wherein the current signal is constant or time- varying.

49. The method of claim 47, wherein measuring the temperature comprises monitoring a thermocouple or other temperature probe attached to the battery cell.

50. The method of claim 47, wherein measuring the temperature comprises using a known dependence of open-circuit cell-voltage on the temperature and state-of-charge for applicable battery cell chemistry.

51. The method of claim 47, wherein measuring the temperature comprises utilizing one or more reduced-order models linking the temperature and heat dissipation of the battery cell to measured voltage and / or current.

52. The method of claim 47, further comprising: during cycling, measuring pressure or strain; and if the pressure reaches a critical pressure or if the strain reaches a critical strain, applying the current signal.

53. The method of claim 47, wherein a force acting on the battery cell includes gravity, a centrifugal force, a Coriolis force, and / or any other inertial force.

54. The method of claim 47, wherein the battery cell is configured to undergo rotation to produce the centrifugal force.

55. The method of claim 47, wherein a pump is not used to circulate the electrolyte within the battery cell.

Images