Modeling of Diffuse Charge Effects in a Microfluidic Based Laminar Flow Fuel Cell

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A mathematical model for laminar flow fuel cells including electrical double layer and ion transport effects is developed. The model consists of the Poisson-Nernst-Plank equations and the modified Navier-Stokes equations to account for the advection of species in the downstream direction. The generalized Frumkin-Butler-Volmer equation is used for the fuel cell kinetics. The finite-volume method is used to develop a system of algebraic equations from the governing partial differential equations, and a numerical algorithm is developed to obtain the results. The accuracy of the 2-D numerical simulation is validated against published results using a 1-D analytical solution. Numerical results show that the concentration distributions for both the neutral species and ions change in both the cross-stream and streamwise directions. An especially interesting result is the change in positive ion concentration within the electrical double layer along the streamwise direction. A study on the importance of the electric body force in the momentum conservation equations is also presented. It is found that the flow results are only affected by the electric body force term at the start of the electrodes and has a negligible impact on device performance results. This model allows us to study both kinetically active (electrodes) and inactive (insulated wall) regions for a microfluidic fuel cell. The mathematical model and numerical simulation will be particularly useful in analyzing the complex behavior that occurs in laminar flow electrochemical devices where a minimum of two spatial dimensions must be considered and the electrical double layer and ion transport cannot be neglected.