Example: Maxwell-Stefan Diffusion in a Proton Exchange Membrane Fuel Cell

This example models the cross-section of a proton exchange membrane fuel cell cathode. The cross-section includes equal parts of the current collector and the channel in the bipolar plate as upper boundary. The active layer defines the lower boundary. Maxwell-Stefan diffusion in a fuel cell - Geometry

Mass balance; divergence of the mass flux through diffusion M - total molar mass of the mixture M j - molar mass of species j  j - mass fraction of species j Equation: Maxwell-Stefan diffusion in a fuel cell - Equation

The symmetric diffusivities are strongly dependent on the composition and are given by the following expressions: x j is the molar fraction of species j D ij is the Maxwell-Stefan diffusivity for the pair ij Subsequent entries can be obtained by permutation of the indices Maxwell-Stefan diffusion in a fuel cell - Equation

The Maxwell-Stefan diffusivities can be described with a semi- empirical equation based on kinetic gas theory: Resulting diffusivities, in m 2 s -1, at T=353 K and p=101 kPa are: D O2N2 = D N2O2 = 9.7e-6 D O2H2O = D H2OO2 = 1.20e-5 D H2ON2 = D N2H2O = 1.24e-5 Maxwell-Stefan diffusion in a fuel cell - Diffusivities

At the reactive boundary, oxygen is consumed according to the following expression Subscript 0 in the mass fraction for oxygen represents the reference state, and k is the reaction rate given by the Tafel expression: Combining all constants, the flux can be written as: *wO2 Maxwell-Stefan diffusion in a fuel cell - BC’s

Results – mass fraction of oxygen, wO2. Oxygen transport limits the rate of the reaction. The concentration of oxygen in the active layer is less than 50% of the concentration at the position of the channel. Maxwell-Stefan diffusion in a fuel cell - Results

Results – concentration dependent diffusion coeficcients Large variations in concentration have a direct influence on the value of the diffusion coefficients. DD11, reflects the interaction between oxygen molecules. Maxwell-Stefan diffusion in a fuel cell - Results