The HER current density was assumed proportional to the concentration of hydronium ions in the OHP and exponential to the electrode potential. The simulation reproduced the features of HER at potentials more positive than the onset of reduction of water (fig. ): in a K + -free solution, the current density of hydronium reduction increased without any limitation as potential went cathodically; in a K + -containing solution, a plateau of current density higher than the limiting diffusion current density based on the Levich equation was observed. Fig. and show the profiles of potential and electric field strength with and without K + ions. The addition of K + ions led to a stronger electric field in the Stern layer and a weaker electric field at >2 nm away from the cathode (inset of fig. ). These effects were due to the accumulation of K + ions at OHP. The electric fields generated by cathode and by K+ ions at OHP were in the same direction in the Stern layer while they were opposite in the diffuse layer (fig. ). Although hydronium ions accumulated at OHP had a similar effect to K + on the electric field distribution, the effect was weak since hydronium ions at OHP were consumed in HER (fig. ). Hence, in K + -free medium, the electric field was not sufficiently confined within a few nm from the cathode and the migration of hydronium ions under electric field facilitated the refilling of hydronium ions to OHP. The concentration of hydronium ions at OHP did not change significantly as the electrode potential shifted cathodically (fig. ), indicating hydronium ions would not be depleted as current density increased. In K + -containing medium, in sharp contrast, the concentration of hydronium ions at OHP decreased as the electrode potential was more negative (fig. ), indicating only in an alkali cation-containing medium, depletion of hydronium ions near the cathode would occur.