Alcohol-based fuel cells offer a possibility of using renewable fuels derived from biomass  to be used for power generation. In this context, direct ethanol fuel cells (DEFC), in which ethanol in liquid form is fed as the proton source in a regular proton exchange membrane-based fuel cell (PEMFC), offers the treble advantages of a renewable, environmentally friendly and easily transportable fuel to produce electrical power , while with respect to methanol it has higher energy density and is non-toxic . However, as in all alcohol-based PEMFCs, fuel permeation through the proton exchange is a problem. This “cross-over” of ethanol from the anode through the membrane electrode assembly (MEA) to the cathode side results in two disadvantages: it burns up chemically on the cathode side in the presence of platinum catalyst without producing any protons, and it also competes with electricity-producing protons for oxygen. The extent of ethanol cross-over can have an important bearing on the usefulness of DEFCs as a power provider .
The cross-over of ethanol is primarily a mass transfer phenomenon with add-on effects of electrochemistry. In the present study, a comprehensive mathematical model is presented to calculate the extent of fuel cross-over in a DEFC. The model is based on a similar model  for direct methanol fuel cell but differs from it in the treatment of the oxidation-reduction reaction kinetics on the anode side. The model takes account of all the important ethanol transport mechanisms in a DEFC. While ethanol permeation through the “gas diffusion layer” is by concentration-gradient-driven diffusion, ethanol cross-over across the PEM takes place by diffusion and convection . Convective transport in the membrane is driven by electrostatic potential gradient and pressure gradient. All these effects are included in the present model. The electrochemical ethanol oxidation at the anode side of the DEFC is modelled using Tafel kinetics with a first order dependence.
Using the mathematical model, the effect of important cell operating parameters such as current density, ethanol feed concentration, cell temperature and cathode side pressure on the ethanol cross-over rate is investigated. The results obtained show that at low concentrations, the ethanol cross-over flux decreases as the current density increases. However, as the feed concentration increases, the ethanol cross-over flux remains constant or increases  with the current density and it poses serious problem to DEFC performance. At the same time, the permeated ethanol and its oxidation of intermediate products could poison the cathode catalyst and declines the active nature of platinum. For low ethanol feed concentrations, the potential gradient driven electro-osmotic cross-over flux is small, and as the current density increases, the ethanol concentration at the interface between anode catalyst layer and PEM decreases and becomes zero at limiting current density values. Thus, for low feed ethanol concentrations, the ethanol cross-over flux across PEM is purely by diffusion mode of transport. For higher ethanol concentrations, over a range of current densities, no sharp drop or any significant change in diffusive cross-over flux but the net cross-over rate increases because of the enhanced electro-osmotic cross-over flux with current density.
The effect of temperature on the ethanol cross-over is related to the diffusivity of the PEM. So, decreasing the cell temperature decreases the diffusivity of ethanol through PEM and hence the cross-over rate. It is also found that the ethanol cross-over flux can be slightly reduced by increasing the cathode side pressure which is attributable to the increased negative effect of the pressure gradient driven ethanol cross-over flux that takes place in the opposite direction i.e., from the cathode side to the anode side.
The model is thus able to capture the effect of important parameters on ethanol cross-over and it can be used for optimizing the design and operating parameters of a DEFC.
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