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| Well, in simple words. The electrolyte (the blue liquid, although you did not say what it is) has its own femi level. The metal and electrolyte in contact and their fermi level is aligned. Depends on the band disgram, electrons are able to travel from one end to the other. That forms the current.
The external circuit is required to complete the current loop. There is no loss in the number of electrons as the charge conservation law remains valid....
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