Consider the electrochemical cell shown below. Develop a one dimensional model for the current distribution by 1) assuming potential variations only in the y direction (along the length of the electrode), 2) solving for conservation of charge in the electrolyte phase to obtain the variation of current density flowing through the electrolyte in the y direction 3) using Ohm/s law (because there are no concentration variations) in the electrolyte to eliminate i.
a. write the governing equation and boundary conditions, assuming linear kinetics.
b. make dimensionless and give independent dimensionless parameters. comment on the meaning of the parameters.
c. solve for in(y)/iavg
d. assume that the electrode is decorated with Pt particles and cost is a factor. Discuss how you may use the solution to part c to control costs.
Refer attached file.