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In electrochemical cells, transport of chemical species to/from the electrodes is limited by the mass transfer resistance between the electrode surface and the bulk electrolyte. This mass transfer resistance thus contributes to voltage losses, referred to asmass transport losses or concentration overpotential, compared to the reversible potential of cell. In this paper, we derived analytical expressions for estimating the mass transport losses in all-vanadium redox flow batteries. A step-by-step analysis allows us to relate the surface and bulk concentrations and then, identify the voltage losses due to mass transport from the Nernst equation and the Butler-Volmer kinetics. A zero-dimensional (0D) model with the derived expressions for the concentration overpotential is calibrated and validated with experimental data; good agreement is obtained. The mass transport losses from the Butler-Volmer kinetics are found to be approximately twice of that from the Nernst equation. [ABSTRACT FROM AUTHOR]

A steady-state isothermal model is presented for the electrochemical reduction of CO2 to CO in a microfluidic flow cell. The full cell model integrates the transport of charge, mass, and momentum with electrochemistry for both the cathode and anode. Polarization curves obtained from experiments conducted at different flow rates with varying applied cell potentials are used to determine the kinetic parameters in the electrochemical reaction rate equations. The parameterized model is validated using a different set of experimental results. Good agreement is observed, especially at high cell potentials (-2.5 to -3 V). The model is further used to analyze the effects of several operating parameters, such as applied cell potential, CO2 concentration of the feed and feed flow rates. The use of the model to analyze the effect of design parameters, such as channel length and porosity of the gas diffusion electrodes, is also demonstrated. [ABSTRACT FROM AUTHOR]

An isothermal model for an electrochemical capacitor is presented, analyzed and discussed. In essence, the model accounts for the transient conservation of species and charge in the solid and the electrolyte phase; two main length scales are considered: one corresponding to the entire cell (macroscale) and the other for the active material in the porous electrodes (microscale). Based on an electrochemical capacitor with Ruthenium dioxide electrodes, a scaling analysis is carried out after calibration and validation with experiments, for which good agreement is found. The analysis allows us to not only secure the relevant scales and nondimensional numbers characterizing an electrochemical capacitor, but also to identify limits at which the model can be reduced to a one-dimensional counterpart on the macroscale. Furthermore, a quasi-steady state can be achieved under certain conditions at the microscale, which leads to the elimination of the radial coordinate from the system of governing equations. These findings, in turn, lead to reduced model formulations that are computationally efficient and promising for inclusion in detailed stack models. The latter is explored by emulating stacks of ten and hundred cells. Finally, the inclusion of the equation of change for energy and heat generation is discussed. [ABSTRACT FROM AUTHOR]

A two-dimensional, steady-state, isothermal, and single-phase model considering the conservation of mass, momentum, and species of a direct liquid fuel cell (DLFC) is presented, solved analytically, and demonstrated for a DLFC running on methanol or ethanol. For the anode, approximate analytical solutions that capture the local leading-order physical and electrochemical phenomena are obtained with Taylor series expansions, homogenization, and separation of variables; for the cathode, a closed-form, integrable expression is secured for the local and parasitic current densities, followed by the introduction of a transformation, and solution of the resulting set of equations with the method of eigenfunction expansion. The full set of equations are calibrated and validated with experiments, after which the approximate analytical solutions are verified with the full set: Overall, good to reasonably good agreement is found for both methanol and ethanol, although the single-phase model is not able to capture high current densities (larger than around 2000 Am-2) that can be obtained with methanol. These closed-form solutions can easily be adjusted to account for other types of liquid fuels and should lend themselves well to, e.g., multi-objective optimization. [ABSTRACT FROM AUTHOR]

We present the derivation of two-dimensional (2D) approximate analytical solutions for the velocities, pressure, and methanol mass fraction in the anode of a direct methanol fuel cell. These are obtained from a steady-state, liquid-phase model that considers conservation of mass, momentum, and species together with the electrokinetics. A narrow-gap approximation and scaling arguments allow for a significant reduction in the mathematical complexity; that is, the partial differential equations (PDEs) reduce to a set of ordinary differential equations and one parabolic PDE. Integration, Taylor-series expansions, homogenization, and separation of variables then allow for approximate analytical solutions. Two typical types of flow fields are considered: porous (e.g., a metallic mesh) and plain (e.g., parallel or serpentine flow channels). For the porous flow field, the 2D approximate analytical solutions can capture the three-dimensional behavior of the anode, whereas the solutions are less accurate for the latter. The analytical solutions are verified with numerical solutions of the full set of equations and validated with experiments for the porous flow field: Good agreement is found. We further highlight how the solutions can be extended to enconipass the whole cell, two-phase transport, and other types of liquid fuel cells such as the direct ethanol fuel cell. [ABSTRACT FROM AUTHOR]