Two-Dimensional Approximate Analytical Solutions for the Direct Liquid Fuel Cell

Abstract

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.