Boundary Layer Analysis of Membraneless Electrochemical Cells (original) (raw)
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Theory of Membraneless Electrochemical Cells
2013
A mathematical theory is presented for the charging and discharging behavior of membraneless electrochemical cells, such as flow batteries and electrolyzers, that rely on slow diffusion in laminar flow to separate the half reactions. Ion transport is described by the Nernst-Planck equations for a flowing quasineutral electrolyte with heterogeneous Butler-Volmer kinetics. Analytical approximations for the current-voltage relation and the concentration and potential profiles are derived by boundary layer analysis (in the relevant limit of large Peclet numbers) and validated against finite-element numerical solutions. Both Poiseuille and plug flows are considered to describe channels of various geometries, with and without porous flow channels. The tradeoff between power density and reactant crossover and utilization is predicted analytically. The theory is applied to the membrane-less Hydrogen Bromine Laminar Flow Battery and found to accurately predict the experimental and simulated ...
On the mass transport in membraneless flow batteries with flow-by configuration
International Journal of Heat and Mass Transfer, 2018
Progress on the analysis of the mass transport phenomena in a membraneless redox flow battery with porous electrodes in flow-by configuration is here reported. A species transport model for a typical redox reactant interacting with a porous electrode is proposed. A hybrid numerical-analytical solution is obtained through the Generalized Integral Transform Technique (GITT), adopting a single domain formulation that includes both the porous and pure fluid regions. The influence of the Reynolds number and the thickness of the electrode on the parameters of interest is theoretically examined. The importance of considering the simultaneous development of flow and mass transport is analyzed, and the presence of the transversal convective flux of species proves to have a significant role on the generation of current inside the electrode. A scaling of the limiting current density with $Re 0.41 is demonstrated and some physical conclusions are drawn. Guidelines for the prevention of crossover are also offered, with increasing Reynolds number and decreasing relative thickness of the electrode having a positive effect, as far as avoiding the mixed potentials effects is concerned. The physical insights attained through the present analysis should add to the efforts in achieving membraneless redox flow batteries with performances comparable to membrane-based devices of similar size.
Flow, 2022
Redox flow batteries (RFBs) are an emerging electrochemical technology envisioned towards storage of renewable energy. A promising sub-class of RFBs utilizes single-flow membraneless architectures in an effort to minimize system cost and complexity. To support multiple functions, including reactant separation and fast reactant transport to electrode surfaces, electrolyte flow must be carefully designed and optimized. In this work, we propose adding a secondary channel adjacent to a permeable battery electrode, solving for the flow field and analysing the effects on the reactant concentration boundary layer at the electrode. We find that an adjacent channel with gradually changing thickness leads to a desired nearly uniform flow through the electrode to the adjacent channel. Consequently, the thickness of the concentration boundary layer is significantly reduced, increasing reactant transport to the electrode surface to 140 % of the rate of a battery with a constant width adjacent channel, and 350 % of the rate with no adjacent channel. Overall, this theory provides insight into the important role of flow physics for this promising sub-class of flow batteries, and can pave the way to improved energy efficiency of such flow batteries. Impact Statement An important contemporary engineering challenge is the development of inexpensive and high-performance renewable energy storage systems. Such systems support the penetration of intermittent sources, such as solar and wind energy, reducing dependence on fossil fuels. Flow batteries are promising due to their use of inexpensive, Earth-abundant reactants, and ability to readily upscale because of a spatial decoupling of energy storage and power delivery. To reduce system capital costs, single-flow membraneless flow batteries are under intense investigation, but require intricate flow engineering. In this work, we analytically and numerically model the flow and chemical species transport for a novel single-flow geometry, and show enhancement of reactant transport and separation. Thus, such geometries promise to increase battery performance and efficiency while reducing cost.
Single-flow multiphase flow batteries: Theory
Electrochimica Acta, 2021
Redox flow batteries are an emerging technology for stationary, grid-scale energy storage. Membraneless batteries in particular are explored as a means to reduce battery cost and complexity. Here, a mathematical model is presented for a membraneless electrochemical cell employing a single laminar flow between electrodes, consisting of a continuous, reactant-poor aqueous phase and a dispersed, reactant-rich nonaqueous phase, and in the absence of gravitational effects. Analytical approximations and numerical solutions for the concentration profile and current-voltage relation are derived via boundary layer analysis. Regimes of slow and fast reactant transport between phases are investigated, and the theory is applied to a membraneless zinc-bromine single-flow battery with multiphase flow. The regime of fast interphase reactant (bromine) transport is characterized by the negligible effect of advection within the cathode boundary layer, leading to a thin boundary layer whose size is largely independent of position, and by relatively high battery current capability. Increasing the nonaqueous (polybromide) phase volume fraction is shown to significantly improve battery performance, as has been observed in recent experiments. For the case of spherical polybromide droplets, the contribution of bromine release from the polybromide phase on the limiting current density becomes negligible for diameters above a critical droplet diameter, when the system can be characterized as having a slow interphase bromine transport. Overall, we show that our analytical approximations agree well with numerical solutions and thus establish a useful theoretical framework for single-flow batteries with multiphase flow .
A Model of An Electrochemical Flow Cell With Porous Layer
2009
In this paper we discuss three different mathematical models for fluid-porous interfaces in a simple channel geometry that appears e.g. in thinlayer channel flow cells. Here the difficulties arise from the possibly different orders of the corresponding differential operators in the different domains. A finite volume discretization of this model allows to calculate the limiting current of the H 2 oxidation in a porous electrode with platinum catalyst particles.
Electrical Model of a Membraneless Micro Redox Flow Battery—Fluid Dynamics Influence
IEEE Access, 2023
Membraneless micro redox flow batteries are an incipient technology that has been shown to extend some properties of traditional redox flow batteries. Due to their microfluidic scale and the absence of membrane, the fluid dynamics operation is critical in the electrical response. In this work, an electrical model is established to evaluate the influence on three battery performance metrics: steady-state power, power transient dynamics, and mixing and self-discharge losses. First, an equivalent electrical circuit, derived from a state-of-the-art regular battery equivalent circuit, is defined by studying the influence of flow changes on its impedances and source, aggregating it as a variable. Then, empirical data are used to demonstrate the proposed equations defining the variation of the electrical response relative to fluid dynamics, and their parameters are identified with grey box methods. The steady-state power model incorporates the interphase position, extending conventionally used redox flow batteries expressions, such as Faraday´s Law and Nersnt´s equation, for the membraneless analysis. A transient response model is built, which becomes effectively relevant in intermittent power applications (such as many renewable energy storage ones). Finally, mixing and self-discharge losses are evaluated with the variation state of charge at the outputs of the cell, using spectrophotometry measurements, and compared with flowmeter mixing values. This demonstrates that flow-rate values can provide a precise quantification of these losses. The electrical model with dependent parameters from the three fluid dynamics analyses can be used to evaluate the performance of micro membraneless redox flow batteries and their response to fluidic operation. INDEX TERMS Battery efficiency, electric equivalent model, grey box identification, microfluidics, redox flow battery.
Membrane-less hydrogen bromine flow battery
Nature Communications, 2013
In order for the widely discussed benefits of flow batteries for electrochemical energy storage to be applied at large scale, the cost of the electrochemical stack must come down substantially. One promising avenue for reducing stack cost is to increase the system power density while maintaining efficiency, enabling smaller stacks. Here we report on a membraneless hydrogen bromine laminar flow battery as a potential high-power density solution. The membrane-less design enables power densities of 0.795 W cm À 2 at room temperature and atmospheric pressure, with a round-trip voltage efficiency of 92% at 25% of peak power. Theoretical solutions are also presented to guide the design of future laminar flow batteries. The high-power density achieved by the hydrogen bromine laminar flow battery, along with the potential for rechargeable operation, will translate into smaller, inexpensive systems that could revolutionize the fields of large-scale energy storage and portable power systems.
Physical review. E, 2017
Linear sweep and cyclic voltammetry techniques are important tools for electrochemists and have a variety of applications in engineering. Voltammetry has classically been treated with the Randles-Sevcik equation, which assumes an electroneutral supported electrolyte. In this paper, we provide a comprehensive mathematical theory of voltammetry in electrochemical cells with unsupported electrolytes and for other situations where diffuse charge effects play a role, and present analytical and simulated solutions of the time-dependent Poisson-Nernst-Planck equations with generalized Frumkin-Butler-Volmer boundary conditions for a 1:1 electrolyte and a simple reaction. Using these solutions, we construct theoretical and simulated current-voltage curves for liquid and solid thin films, membranes with fixed background charge, and cells with blocking electrodes. The full range of dimensionless parameters is considered, including the dimensionless Debye screening length (scaled to the electro...
Theory of Flow Batteries with Fast Homogeneous Chemical Reactions
Journal of The Electrochemical Society, 2018
Redox flow batteries are widely investigated toward cost-effective storage of energy generated via intermittent renewable sources. Many redox chemistries have been proposed for flow batteries, possessing various attractive features such as low-cost reactants, fast electrochemical reaction kinetics without precious metal catalysts, negligible thermal runaway risk, and low toxicity. While all flow batteries rely on heterogeneous electrochemical reactions occurring at electrode surfaces, in a subset of chemistries homogeneous chemical reactions occur in the electrolyte. A prominent example are batteries employing halogen-based catholytes, where halogen molecules complex with halide ions in the catholyte, forming redox-active polyhalide ions. However, state-of-the-art models capturing flow battery performance for halogen systems typically neglect the presence of such homogeneous reactions and polyhalide ions. The latter assumption allows for simpler models, but at the cost of accurately predicting battery chemical state and performance. We here present a generalized flow battery theory extended to include fast homogeneous reactions, which employs a technique known as the method of families to simplify the governing equations. We then apply and solve the model for the specific case of a membraneless hydrogen-bromine flow battery, illustrating the predicted effect of the homogeneous complexation reaction in the catholyte on flow battery performance.
Prospects of recently developed membraneless cell designs for redox flow batteries
When the membrane in a flow battery or fuel cell is removed, the result is a fluid-fluid interface across which selective ion exchange must occur with minimal reactant crossover. Here, we review five major approaches to the design of membraneless cells reported in the recent literature (from 2004 to mid-2016), including our own contributions. Although most of the reviewed designs were originally developed for microfluidic fuel cells, we proceed to discuss the potential applicability of these designs as membraneless redox flow batteries, given their similarity to fuel cells. The various designs exhibit noticeable performance differences due to differences in their redox couple chemistries, electrolyte compositions, and flow architectures. Therefore, we discuss eight performance metrics that can be determined from cell operation data and electrolyte cost indices and can be used for systematic comparison of various designs. Using these metrics, we present an outlook for promising designs in terms of their potential for wide acceptance or commercialization, with the aim of directing future research.