In an electrolytic cell, does current flow from
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The cathode is defined as the electrode at which reduction happens. The anode is the electrode at which you oxidise. This is always true. I remember it by saying ‘anodic oxidation is the alpha and omega.’
In a galvanic cell, the anode will produce ‘electron pressure’: the compounds being oxidised leave there electrons there until the electron density is too high. These electrons flow through the circuit from the anode to the cathode and are consumed in reductions on the other end.
In an electrolytic cell, the battery creates an ‘electron pull’ from its positive pole. This pole is connected to the anode and therefore electrons are pulled away from the anode into the battery. On the cathodic side, the battery produces an electron pressure again to drive the reduction.
So in both cases electrons flow from the anode to the cathode.
(This analysis is complicated by something I learnt in school as the technical current flow definition. According to Bavarian textbooks, technicians defined current as flowing from plus to minus which is exactly the opposite of the flow of electrons. In that case (only), the direction of current is reversed but due to a different definition.)