Modeling of the anode side of a direct methanol fuel cell with analytical solutions

TL;DR

This paper derives analytical solutions for methanol concentration and current density profiles in a direct methanol fuel cell's anode, linking overpotential with cell current and transport parameters, enhancing understanding of cell performance.

Contribution

It introduces a comprehensive analytical model for the anode side of a direct methanol fuel cell, including new expressions for the Thiele modulus and overpotential as functions of current and parameters.

Findings

Thiele modulus varies quadratically with cell current density at high currents

Analytical profiles for methanol concentration and current density are derived

New semi-empirical equations for overpotential are proposed

Abstract

In this work, analytical solutions were derived (for any methanol oxidation reaction order) for the profiles of methanol concentration and proton current density by assuming diffusion mass transport mechanism, Tafel kinetics, and fast proton transport in the anodic catalyst layer of a direct methanol fuel cell. An expression for the Thiele modulus that allows to express the anodic overpotential as a function of the cell current, and kinetic and mass transfer parameters was obtained. For high cell current densities, it was found that the Thiele modulus ($\phi^2$) varies quadratically with cell current density; yielding a simple correlation between anodic overpotential and cell current density. Analytical solutions were derived for the profiles of both local methanol concentration in the catalyst layer and local anodic current density in the catalyst layer. Under the assumptions of the model presented here, in general, the local methanol concentration in the catalyst layer cannot be expressed as an explicit function of the position in the layer. In spite of this, the equations presented here for the anodic overpotential allow the derivation of new semi-empirical equations.