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I've never seen this discussed so I wanted to ask here. Consider the electrolysis of water with inert electrodes and electrolytes that won't be oxidized or reduced, such as sodium sulfate. Since the migration of electrolytes in an electrolytic cell is responsible for the electrical current, does the gradual sequestering of electrolytes at the electrodes decrease the electrolyte concentration in the middle (between the electrodes), and cause a decrease in conductivity?

A couple thoughts occur to me:

  1. the $\ce{H+}$ and $\ce{OH-}$ will diffuse from the electrodes into the cell water. As the $\ce{H+}$ and $\ce{OH-}$ diffuse back into bulk they could carry the electrolytes with them.

  2. the battery could be disconnected momentarily to mix the electrolyte solution.

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    $\begingroup$ If anything, gradual buildup of $\ce H^+$ and $\ce{OH}^{-}$ in their corresponding areas should increase the conductivity. $\endgroup$ – Ivan Neretin Feb 1 '16 at 5:47
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...does the gradual sequestering of electrolytes at the electrodes decrease the electrolyte concentration in the middle (between the electrodes), and cause a decrease in conductivity?

In a word, no. But, it is actually very complicated. The electrolyte in most simple lab electrolytic cells for water is not very viscous. This means that convective transport dominates over diffusion, except very very close to the electrode surfaces, i.e. at the boundary layer, which is hundreds of nanometers to maybe a few hundred micrometers thick, depending on conditions. Outside the boundary layer, i.e. in the vast majority of the space "between the electrodes", no, the concentration of the electrolyte will not decrease. In fact it may build up to higher concentrations, since water electrolysis involves loss of water, leaving more electrolyte per unit of solvent.

Inside the boundary layer, a phenomenon that does distort the bulk concentration of electrolyte can happen. This phenomenon is called concentration polarization. For water electrolysis, this means that the cathode (which generates hydrogen gas and consumes aqueous protons) would be depleted in protons, i.e. would be more alkaline than the bulk solution. The anode's boundary layer, which generates protons from water while evolving oxygen) would have an excess of protons. The cathode boundary layer would have excess sodium cation and the anode excess sulfate anion to maintain electrical neutrality.

The formation of the boundary layer is very fast, taking less than a second, not gradual. But the boundary layers are very small.

So in the end, you had it right with your first idea:

  1. the $\ce{H+}$ and $\ce{OH-}$ will diffuse from the electrodes into the cell water. As the $\ce{H+}$ and $\ce{OH-}$ diffuse back into bulk they could carry the electrolytes with them.
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