Boundary asymptotics for a non-neutral electrochemistry model with small Debye length

Abstract

This article addresses the boundary asymptotics of the electrostatic potential in non-neutral electrochemistry models with small Debye length in bounded domains. Under standard physical assumptions motivated by non-electroneutral phenomena in oxidation–reduction reactions, we show that the electrostatic potential asymptotically blows up at boundary points with respect to the bulk reference potential as the scaled Debye length tends to zero. The analysis gives a lower bound for the blow-up rate with respect to the model parameters. Moreover, the maximum potential difference over any compact subset of the physical domain vanishes exponentially in the zero-Debye-length limit. The results mathematically confirm the physical description that electrolyte solutions are electrically neutral in the bulk and are strongly electrically non-neutral near charged surfaces.