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Selection, testing and validation of electrolyte candidates for Li-ion cells are discussed, based on a 10-minute target for extreme fast charge (XFC). A combination of modeling and laboratory measurements create a timely and synergistic approach to identifying candidate electrolyte formulations. Multi-solvent systems provide a balanced set of properties, wherein lower molecular-weight solvents offer reduced viscosity, increased species diffusivity, and mitigation of concentration polarization at high charge rates. Carefully selected formulations can exhibit peak conductivity and usable conductivity range of two to three times that of the baseline EC-EMC (3:7, wt.) + LiPF6. Candidates are also chosen based on stability and longevity within the cell environment. Lab testing coincides with property predictions from the Advanced Electrolyte Model (AEM) and a macro-scale cell model. Cell testing utilized coin and pouch cells having NMC532 or NMC811 cathodes with graphite electrodes. Results indicate combinations of low-molecular weight solvents are key for fast-charge electrolytes as they extend the useful conductivity range to both low and higher salt concentrations, and possess higher self-diffusivities compared to conventional solvents. This reduces impacts from concentration polarization. The choice of electrolyte also influences the tendency for lithium metal deposition at the anode, as showcased by experimental and modeling results herein.

Enabling extreme fast charging (XFC, ≤10–15 min charging) requires a comprehensive understanding of its implications. While lithium plating is a key bottleneck for the anode, the full extent of limitations for the cathode are not well-understood, particularly in extended-cycle settings with well-defined battery designs and conditions. This article presents cycle-life implications of XFC on cathodes at multiple length scales, combining electrochemical analyses, degradation modeling, and post-test characterizations. The comprehensive test matrix includes 41 well-defined gr/NMC pouch cells under varied fast-charge rates (1–9C) and state-of-charges cycled up to 1000 times. Cathode issues remain minimal in early cycling, but begin to accelerate in later life, when distinct cracking is found and identified as a fatigue mechanism. The bulk structure of cathodes remains intact, but distinct particle surface reconstruction is observed; however, this shows less pronounced effect on cathode aging than does cracking.

Li4Ti5O12/LiMn2O4 (LTO/LMO) chemistry was evaluated as a potential candidate for behind-the-meter storage (BTMS) applications. Its long-term cycle performance at 45 °C was tested using ethylene carbonate (EC) and propylene carbonate (PC) solvent electrolytes. Over 1000 cycles, LTO/LMO cells exhibited ~80% capacity retention and Coulombic efficiency higher than 99.96%. Electrochemical test results showed the major degradation mode of LTO/LMO cells arises from continuous electrolyte decomposition at the LTO anode and loss of Li inventory. EC and PC electrolytes created distinct surface layers, where the EC reduction products were more effective in passivating the LTO electrode surface. Dissolution and migration of Mn from the cathode was probed as Mn2+ species distributed throughout the surface layer at the anode. By utilizing a prelithiated LTO electrode, the LTO/LMO cell performance was significantly enhanced with EC electrolyte. On the other hand, PC electrolyte resulted in accelerated electrolyte decomposition at the lithiated LTO surface due to the lack of surface passivation. Thus, mitigating parasitic reactions at the LTO electrode is the key to developing successful LTO/LMO cells.

Extreme fast charging (XFC) of commercial lithium-ion batteries (LIBs) in ≤10-15 minutes will significantly advance the deployment of electric vehicles globally. However, XFC leads to considerable capacity fade, mainly due to graphite anode degradation. Non-destructive three-dimensional (3D) investigation of XFC-cycled anodes is crucial to connect degradation with capacity loss. Here, we demonstrate the viability of simultaneous neutron and X-ray tomography (NeXT) for ex-situ 3D visualization of graphite anode degradation. NeXT is advantageous because of the sensitivity of neutrons to Li and H and X-rays to Cu. We combine the neutron and X-ray tomography with micron resolution for material identification and segmentation on one pristine and one XFC-cycled graphite anode, thereby underscoring the benefits of the simultaneous nature of NeXT. Our ex-situ results pave the way for the design of NeXT-friendly LIB geometries that will allow operando and/or in-situ 3D visualization of graphite anode degradation during XFC.

The potential for operating automotive battery packs at high upper cutoff voltages (UCV) has been explored using preliminary data on eight cathode materials. The pack level energy density, specific energy, and battery cost are calculated using the spreadsheet tool BatPaC. The tool used experimental data for some cathode materials such as the lithiated oxides of nickel manganese cobalt (NMC), nickel cobalt aluminum (NCA), layered lithium- and manganese-rich nickel manganese cobalt (LMRNMC). The half-cell data were obtained at UCVs between 4.2 and 4.7 V vs. Li/Li+. The experimental data showed LMRNMC with the highest lithiation capacity gain, increasing from 176 mAh·g−1 at 4.2 V to 260 mAh·g−1 at 4.7 V; this advantage is partly offset by its lower average voltage. Assuming optimized cell materials/design and an area-specific impedance of 12 Ω⋅cm2 for all the materials, the BatPaC results indicate that the specific energies or energy densities of the battery electric vehicle (BEV) and plug-in hybrid electric vehicle (PHEV) battery packs with the LMRNMC and NMC cathodes can exceed 180 (BEV) and 160 (PHEV) Wh·kg−1 at UCV>4.6 V vs. Li/Li+. The costs of these battery packs are lowest at UCV = 4.7 V (vs. Li/Li+); estimated at 135–145 and 210–220 $·kWh−1 for BEV and PHEV packs, respectively.

Increasing lithium-ion battery gravimetric energy density to > 300 Wh/kg, while simultaneously meeting a cost target of $80/kWh, is of paramount importance to increasing the driving range and affordability of electric vehicles. One way to address this goal is to reduce inactive components by increasing electrode areal capacities, but conventional thick electrode designs typically perform poorly at high discharge rates due to Li+ mass transport limitations. Here we compare the rate capability and cycle life of NMC 532/graphite pouch cells made with five different thick cathode and anode designs paired together in 25 combinations. We find that using different particle sizes to structure both the cathode and anode architectures in two-layer configurations results in a 2X capacity improvement over the worst-performing combination at high discharge rates (97 vs. 46 mAh/g at 2C). These different cathode/anode designs also translate to different cycle life performance, with many cells cycled at C/2 achieving ∼80% capacity retention after 1000 cycles, and cells cycled at 2C showing different degrees of capacity fade. Overall, these results demonstrate that simple, scalable changes in electrode design can significantly improve the performance of thick electrodes for high energy density batteries.

Heterogeneous battery performance is a critical issue for maximization of cell lifetime capacity and safety. Using high energy synchrotron X-ray diffraction, the influence of charge rate, voltage limit, uneven stack pressure, and gas generation on the lithium transport properties was quantified in single-layer graphite/LiNi0.5Mn0.3Co0.2O2 pouch cells. A freshly formatted cell tracked in operando during initial fast charge cycles indicated variable position-dependent performances, while lateral mapping showed a significant fast charge (6C) heterogeneity compared to slow charge (C/2). Pressure effects were non-dominant compared to charge rate. Maps of previously aged and rested cells indicate that lateral heterogeneity slowly equilibrates at rest, but regenerates upon further cycling at fast charge rate. Furthermore, an unformatted cell was mapped at charge and discharge during its first formation cycle to analyze the effect of byproduct gases on the heterogeneous lithium transport. Gas was observed as randomly interspersed “bubbles” which locally hindered lithium intercalation and caused significant heterogeneity. Electrode architectures and charging protocols that promote homogeneous intercalation are critical for predictable high-performance and long-life batteries.

The battery technology literature is reviewed, with an emphasis on key elements that limit extreme fast charging. Key gaps in existing elements of the technology are presented as well as developmental needs. Among these needs are advanced models and methods to detect and prevent lithium plating; new positive-electrode materials which are less prone to stress-induced failure; better electrode designs to accommodate very rapid diffusion in and out of the electrode; measure temperature distributions during fast charge to enable/validate models; and develop thermal management and pack designs to accommodate the higher operating voltage.

The ability to charge battery electric vehicles (BEVs) on a time scale that is on par with the time to fuel an internal combustion engine vehicle (ICEV) would remove a significant barrier to the adoption of BEVs. However, for viability, fast charging at this time scale needs to also occur at a price that is acceptable to consumers. Therefore, the cost drivers for both BEV owners and charging station providers are analyzed. In addition, key infrastructure considerations are examined, including grid stability and delivery of power, the design of fast charging stations and the design and use of electric vehicle service equipment. Each of these aspects have technical barriers that need to be addressed, and are directly linked to economic impacts to use and implementation. This discussion focuses on both the economic and infrastructure issues which exist and need to be addressed for the effective implementation of fast charging at 400 kW and above. In so doing, it has been found that there is a distinct need to effectively manage the intermittent, high power demand of fast charging, strategically plan infrastructure corridors, and to further understand the cost of operation of charging infrastructure and BEVs.

To achieve a successful increase in the plug-in battery electric vehicle (BEV) market, it is anticipated that a significant improvement in battery performance is required to increase the range that BEVs can travel and the rate at which they can be recharged. While the range that BEVs can travel on a single recharge is improving, the recharge rate is still much slower than the refueling rate of conventional internal combustion engine vehicles. To achieve comparable recharge times, we explore the vehicle considerations of charge rates of at least 400 kW. Faster recharge is expected to significantly mitigate the perceived deficiencies for long-distance transportation, to provide alternative charging in densely populated areas where overnight charging at home may not be possible, and to reduce range anxiety for travel within a city when unplanned charging may be required. This substantial increase in charging rate is expected to create technical issues in the design of the battery system and the vehicle's electrical architecture that must be resolved. This work focuses on vehicle system design and total recharge time to meet the goals of implementing improved charge rates and the impacts of these expected increases on system voltage and vehicle components.

Battery thermal barriers are reviewed with regards to extreme fast charging. Present-day thermal management systems for battery electric vehicles are inadequate in limiting the maximum temperature rise of the battery during extreme fast charging. If the battery thermal management system is not designed correctly, the temperature of the cells could reach abuse temperatures and potentially send the cells into thermal runaway. Furthermore, the cell and battery interconnect design needs to be improved to meet the lifetime expectations of the consumer. Each of these aspects is explored and addressed as well as outlining where the heat is generated in a cell, the efficiencies of power and energy cells, and what type of battery thermal management solutions are available in today's market. Thermal management is not a limiting condition with regard to extreme fast charging, but many factors need to be addressed especially for future high specific energy density cells to meet U.S. Department of Energy cost and volume goals.

The stability of silicon-containing anodes can, in principle, be extended by constraining these electrodes to limited states of lithiation. Partial utilization of the anode lessens the volume changes experienced by silicon particles during cycling, which can mitigate mechanisms of performance degradation. In full-cells, anode utilization can be modulated by adjusting the relative capacities of the negative and positive electrodes – the N/P ratio. Here, we examine how the N/P ratio affects the long-term stability of Si-based full-cells, and investigate how this parameter would impact the cost and energy of realistic Li-ion cells. We show that, for some configurations, cell failure due to rapid anode degradation can only by avoided at higher N/P ratios. The price of this enhanced stability is accelerated impedance rise at the cathode. Surprisingly, when electrode expansion is taken into account, increasing N/P ratio can actually increase the specific energy and energy density of silicon-rich Li-ion cells.

A combination of cell testing and electrochemical-thermal modeling is used to investigate extreme fast charging (XFC) performance for cells with a low loading of 1.5 mAh.cm−2 and moderate loading of 2.5 mAh.cm−2. Cells with a low loading of 1.5 mAh.cm−2 withstand XFC performance remarkably well even up to 9C constant current (CC) charging with high charge capacity, high coulombic efficiency and very little apparent lithium plating. For a moderate loading of 2.5 mAh.cm−2, the 6C CC charge capacity is poor with significant amounts of visually observed lithium plating. Simulated electrolyte transport properties are revealed to be insufficient and majorly set limitations for XFC performance in case of the moderate and the only simulated higher loadings (>2.5 mAh.cm-2). Charging at elevated temperature is shown to be an effective strategy for moderate loading cells enabling good 10-min charge capacity, high coulombic efficiency, and mitigating lithium plating. Lastly, an electrochemical model is used to investigate strategies for enabling 4–6C CC charging for cells incorporating loading beyond 3 mAh.cm−2. As a result, the combination of an increased cell temperature, reduced electrode tortuosity, and enhanced ion-transport in the electrolyte are most likely required to facilitate XFC for state of the art and future high energy lithium-ion batteries.

Lithium-alloying materials are of great interest to improve the gravimetric and volumetric energy density of lithium-ion batteries, though their associated volume fluctuation with cycling often leads to poor cycling performance. Active–inactive alloys and blending alloys with carbon materials are common strategies to accommodate volume fluctuation. Herein we set out to optimize graphite–SiO blend electrode formulations to eliminate rapid capacity fade. Electrodes with highly stable cycling were prepared by simple planetary mixing procedures, enabled by the use of just a fraction of a weight percent of commercial SWCNTs as the only conductive additive, and by the appropriate choice of binder/stabilizing agent. In fact, the use of SWCNTs allowed for graphite-free SiO electrodes with approximately 74% higher volumetric energy density relative to traditional graphite electrodes, and superior capacity retention in coin-type full-cell testing versus NMC532 cathodes.

In this article we describe efforts to improve performance and cycle life of cells containing Li1.2Ni0.15Mn0.55Co0.1O2-based positive and graphite-based negative electrodes. Initial work to identify high-performing materials, compositions, fabrication variables, and cycling conditions is conducted in coin cells. The resulting information is then used for the preparation of double-sided electrodes, assembly of pouch cells, and electrochemical testing. We report the cycling performance of cells with electrodes prepared under various conditions. Our data indicate that cells with positive electrodes containing 92 wt.% Li1.2Ni0.15Mn0.55Co0.1O2, 4 wt.% carbons (no graphite), and 4 wt.% PVdF (92–4–4) show ∼20% capacity fade after 1000 cycles in the 2.5–4.4 V range, significantly better than our baseline cells that show the same fade after only 450 cycles. Our analyses indicate that the major contributors to cell energy fade are capacity loss and impedance rise. Therefore incorporating approaches that minimize capacity fade and impedance rise, such as electrode coatings and electrolyte additives, can significantly enhance calendar and cycle life of this promising cell chemistry.

Although a variety of cathode and electrolyte materials have been studied and commercialized over the past two decades, nearly all commercial cells have used a graphitic carbon anode. Several reasons exist for this choice—including cost, low insertion voltage, and ease of use in the cell manufacturing process. However as uses for lithium-ion batteries expand, alternative anodes that may offer better energy and power capability are being explored. For transportation-oriented purposes, anodes based on simple lithiated Zintl compounds, e.g. Li17Sn4, or intermetallic insertion anodes offer significant advantages in capacity (volumetric and gravimetric) and stability in the cell environment that make them attractive candidates for future cell chemistries. Within this context, little however is known about how these alternative anode materials perform as a function of temperature, which is important for applications where operation at temperatures as low as −30 °C can be expected. In this study we evaluated a series of intermetallic insertion anodes that operate by a simple metal displacement mechanism. We have found that for Cu6Sn5, Ag/Cu6Sn5, and Cu2Sb, the drop-off in performance with temperature is in line with that observed for a commercial graphite-based anode and indicates that additional variables such as cation diffusion through the electrode passivation film or the electrochemical double layer may be playing an important role that is independent of the underlying anode material. We additionally characterized the NiAs-type mineral Sorosite (CuSn0.9Sb0.1), as various literature reports had indicated that substitution of antimony for tin eliminated the need for interstitial copper, however powder X-ray diffraction studies of samples made by annealing or high energy ball milling indicated mixed phase samples.

In addition to the development of high-energy density electrode materials for lithium-ion (Li-ion) batteries, other engineering approaches, such as electrode optimization, should be considered in order to meet the energy requirements of plug-in hybrid electric vehicles (PHEV). This work investigates the impact of the electrode thickness on the energy density of (Li-ion) batteries. The impedance results from the hybrid pulse power characterization (HPPC) test indicate that the electrode resistance is inversely proportional to the electrode thickness. This feature makes it possible to use thicker electrodes in (Li-ion) batteries to meet PHEV power requirements. The practical electrode thickness is determined to be around 100 μm, if considering the electrode mechanical integrity when using conventional PVDF binders. Furthermore, cycle performance shows that cells with a higher loading density have a similar capacity retention to cells with a lower loading density.

Titanium oxides are an important class of lithium–ion battery electrodes owing to their good capacity and stability within the cell environment. Although most Ti(IV) oxides are poor electronic conductors, new methods developed to synthesize nanometer scale primary particles have achieved the higher rate capability needed for modern commercial applications. In this report, the anionic water stable titanium oxalate anion [TiO(C 2 O 4 ) 2 ] 2− was isolated in high yield as the insoluble DABCO (1,4-diazabicyclo[2.2.2]octane) salt. Powder X-ray diffraction studies show that the titanium dioxide material isolated after annealing in air is initially amorphous, converts to N-doped anatase above 400 °C, then to rutile above 600 °C. Electrochemical studies indicate that the amorphous titanium dioxide phase within a carbon matrix has a stable cycling capacity of ∼350 mAh g −1 . On crystallizing at 400 °C to a carbon-coated anatase the capacity drops to 210 mAh g −1 , and finally upon carbon burn-off to 50 mAh g −1 . Mixtures of the amorphous titanium dioxide and Li 4 Ti 5 O 12 showed a similar electrochemical profile and capacity to Li 4 Ti 5 O 12 but with the addition of a sloping region to the end of the discharge curve that could be advantageous for determining state-of-charge in systems using Li 4 Ti 5 O 12 .

Hybrid-electric vehicles require lithium-battery electrolytes that form stable, low impedance passivation layers to protect the electrodes, while allowing rapid lithium-ion transport under high current charge/discharge pulses. In this article, we describe data acquired on cells containing LiNi{sub 0.8}Co{sub 0.15}Al{sub 0.05}O{sub 2}-based positive electrodes, graphite-based negative electrodes, and electrolytes with lithium hexafluorophosphate (LiPF{sub 6}), lithium tetrafluoroborate (LiBF{sub 4}), lithium bis(oxalato)borate (LiBOB) and lithium difluoro(oxalato) borate (LiF{sub 2}OB) salts. The impedance data were collected in cells containing a Li-Sn reference electrode to determine effect of electrolyte composition and testing temperature on individual electrode impedance. The full cell impedance data showed the following trend: LiBOB > LiBF{sub 4} > LiF{sub 2}OB > LiPF{sub 6}. The negative electrode impedance showed a trend similar to that of the full cell; this electrode was the main contributor to impedance in the LiBOB and LiBF{sub 4} cells. The positive electrode impedance values for the LiBF{sub 4}, LiF{sub 2}OB, and LiPF{sub 6} cells were comparable; the values were somewhat higher for the LiBOB cell. Cycling and impedance data were also obtained for cells containing additions of LiBF{sub 4}, LiBOB, LiF{sub 2}OB, and vinylene carbonate (VC) to the EC:EMC (3:7 by wt.) + 1.2 M LiPF{sub 6} electrolyte. Ourmore » data indicate that the composition and morphology of the graphite SEI formed during the first lithiation cycle is an important determinant of the negative electrode impedance, and hence full cell impedance.« less

An electrochemical model was developed to compare the use of internal and external reference electrodes for the study of lithium-ion cells. The impact of reference electrode placement on electrode measurements was examined using idealized reference electrodes in cells undergoing short-duration pulse currents. The effectiveness of internal reference electrodes with finite size and impedance was also examined.

Lithium-ion batteries are considered to be the next battery system for hybrid electric vehicles (HEVs) due to their high power density. However, their power is severely limited at −30 °C and the concern exists that lithium metal could plate on the negative electrode during regen (charge) pulses. The goal of this work is to determine the reason for this poor low-temperature performance using an in situ Li y Sn micro reference electrode (RE) over a wide temperature range of 30 °C to −30 °C. A variety of negative and positive electrode materials with unique morphologies was used in this work to help elucidate the dominant low-temperature mechanism. In this work, it was observed that the potential of graphite negative electrodes does dip below lithium potentials not only during charge pulses, but also under normal charging if the cell cutoff voltage is not reduced from its room-temperature setting of 4.1 V, whereas hard carbon electrodes do not because they operate further from lithium potential. The most surprising finding from this work was that a second impedance mechanism dominates below 0 °C that affects the positive and negative electrodes almost equally. This suggests that the responsible phenomenon is independent of the active material and is most likely a pure electrolyte-interface effect.

The impedance rise that results from the accelerated aging of high-power lithium-ion cells containing LiNi 0.8 Co 0.15 Al 0.05 O 2 -based positive and graphite-based negative electrodes is dominated by contributions from the positive electrode. Data from various diagnostic experiments have indicated that a general degradation of the ionic pathway, apparently caused by surface film formation on the oxide particles, produces the positive electrode interface rise. One mechanistic hypothesis postulates that these surface films are components of the negative electrode solid electrolyte interphase (SEI) layer that migrate through the electrolyte and separator and subsequently coat the positive electrode. This hypothesis is examined in this article by subjecting cells with LiNi 0.8 Co 0.15 Al 0.05 O 2 -based positive and Li 4/3 Ti 5/3 O 4 -based negative electrodes to accelerated aging. The impedance rise in these cells was observed to be almost entirely from the positive electrode. Because reduction products are not expected on the 1.55 V Li 4/3 Ti 5/3 O 4 electrode, the positive electrode impedance cannot be attributed to the migration of SEI-type fragments from the negative electrode. It follows then that the impedance rise results from mechanisms that are “intrinsic” to the positive electrode.

The C /25 discharge data from 18650-size cells containing LiNi 0.8 Co 0.1 Al 0.1 O 2 cathode and graphite anode laminates were analyzed through the use of the differential voltage, d V /d Q , curves. Using half-cell data, the peaks in the d V /d Q curve of the full cell data were assigned. Analysis of the relative peak shifts allowed for the determination of the source of capacity fade. For cells formed and aged at 45 °C for 40 weeks (capacity fade = 7.5%), the analysis indicated negligible loss of accessible material at the anode and at the cathode. Capacity loss of the cell could be accounted for, largely, by side reactions at the anode. This type of analysis can be used when the introduction of a reference electrode is difficult or impractical.

A reference electrode based on a lithium–tin alloy was used to study electrode potential change during hybrid pulse power characterization (HPPC) and electrochemical impedance spectroscopy (EIS) measurements on lithium-ion cells. The cells contained a LiNi0.8Co0.15Al0.05O2-based positive electrode, a graphite-based negative electrode, and a LiPF6-bearing ethylene carbonate: ethyl methyl carbonate (EC:EMC) electrolyte. The cells were prepared and tested in an argon-atmosphere glove box to minimize the impact of moisture and oxygen. The reference electrode was prepared from a 25 μm-diameter, tin-coated copper wire; in situ lithiation produced a LixSn (x ∼ 4.4) alloy that displayed a relatively stable voltage at room temperature. The impedance data obtained from these measurements were reproducible and self-consistent. Data from cells aged at 55 °C showed that the positive electrode impedance increase was the main contributor to cell impedance rise, especially during the first month of aging.

High-power, 18,650 lithium-ion cells have been designed and fabricated in order to understand the factors limiting the calendar life of the lithium-ion system. Each cell consisted of a LiNi0.8Co0.2O2 positive electrode, a blend of MCMB-6 and SFG-6 carbon negative electrode, and a LiPF6 in EC:DEC (1:1) electrolyte. These cells, which initially meet the power requirement set by the partnership for a new generation of vehicles (PNGV), were subjected to accelerated calendar life and cycle life testing. After testing at elevated temperatures, the cells experienced a significant impedance rise and loss of power. The fade rate of power in these cells was dependent of the state of charge and the temperature of testing. Micro-reference electrode and ac-impedance studies on symmetrical cells have confirmed that the interfacial resistance at the positive electrode was the main reason behind the impedance rise in the high power cell.

Development of physico-chemical or process models for impedance spectra requires consideration of the physics and chemistry associated with the specific system under investigation. In order to be useful for interpretation of experimental data, the model must also account for the chracteristics of the measurement. The procedure for development of physico-chemical models is reviewed, and a method is presented that can be used to identify measurement characteristics such as error structure and degree of stationarity.

Comparisons were made between experimental data and a two-dimensional model for the MOCVD of GaAs from trimethylgallium and arsine in two horizontal air cooled reactor geometries. A unique feature of this work was that comparison was made, not only on the wafer, but over the entire deposition regime. Excellent agreement was achieved for growth at low system pressures. Experimental deposition profiles under atmospheric pressure were much less uniform than those predicted by the model. This difference could not be attributed to a pressure dependence of heterogeneous reactions. Inclusion of thermal diffusion had little effect on the uniformity of the calculated deposition profile but decreased the magnitude of the growth rate by up to 12%. Through model calculations and experiments, it was determined that a channel with a tilted upper wall and a horizontal susceptor has the same growth rate profile as does a standard horizontal upper wall channel with a tilted susceptor. Substrate rotation was predicted to cause growth rate uniformity within less than 4.3% in horizontal channel flow and 3.8% in a channel with tilted walls.