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I'm curious whether the dimensions of the cathode and anode matter in an electrochemical process. Let's take copper electrorefining as an example. For instance, should the cathode and anode be of the same length and be in alignment with each other or does the process not care?

From my perspective, the cathode doesn't 'see' the anode, it only sees the $\text{Cu}^{2+}$ ions and therefore the anodes dimensions and placement relative to the cathode don't have an effect. Note, let's ignore the increase in resistance as the cathode and anode are placed further away and other similar effects. The essence of what I'm trying to understand is how their placement/alignment effects the occurrence of the reaction.

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  • $\begingroup$ It depends $ $. $\endgroup$
    – Mithoron
    Aug 28, 2018 at 22:25
  • $\begingroup$ Dimensions - no; curvature - yes. $\endgroup$
    – A.K.
    Aug 28, 2018 at 22:45

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The dimensions of your electrodes should not effect the open circuit voltage, since this is determined solely by the identity and concentrations of the redox species.

Once the cell is running, the dimensions may affect how much the voltage drops off as you draw current, known as "overpotential". If your cell is limited by its ability to deliver ions to the surface of the electrode, or to transfer charge into the electrode, then the higher surface area of a large electrode is likely to result in a more efficient battery.

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If you examine the Nernst Equation, there is no indication that the cathode or anode have any effect. What does effect the current is the resistivity of the solution. The further apart the electrode are, the more resistance the solution offers to the current. If the electrodes get too close, a short can occur.

Also, a high current between the electrodes can deplete the carriers due to a lack of diffusion or electrostatic repulsion.

At lower currents, you will see the same amount of current for any electrodes with the same surface area at the same distance.

If the electrodes are not aligned, then the electrodes look like tapered cones due to the increasing resistance from the closest point to the ends.

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