Jacobian elliptic functions describe the properties of the diffuse charge region in narrow electrochemical cells

Diffuse double layers merge in narrow electrochemical cells. The distribution of ions, and the accompanying electrical properties, are predicted under static conditions that are mild enough not to engender electrochemical reactions. The predictions rest on assumptions that are not egregiously unreasonable. The potential and concentration profiles are respectively described by Legendre elliptic integrals and Jacobian elliptic functions. The special case of pure water is examined and the relevance of this study to water desalination is briefly addressed.