A model is solved based on the Nernst Planck equation to calculate the diffusion and migration currents for a species in a thin layer (about 200 nm) confined between two electrodes. This is proposed to account for the current voltage behaviour of a memristor constructed in a similar fashion. At the working electrode, an electroactive species is oxidised and at the counter electrode, the same species is reduced. Upon application of a simple voltammetric waveform, the migration current exhibits a resistance profile at slow scan rates and hysteresis at faster scan rates, indicative of memristor behaviour.