Hall effect in electrolyte solutions: Self-consistent Debye-Hückel-Onsager theory

A self-consistent statistical-mechanical theory of the Hall effect in electrolyte solutions is developed by extending the self-consistent Debye-Hückel-Onsager (SCDHO) framework to crossed electric and magnetic fields. The theory incorporates non-local ionic charge distributions via Slater-type form factors, regularizing the Coulomb interaction at short range, and accounts for dielectric friction through ion-specific coefficients, employing experimental values for protons and hydroxide ions. Within the random-phase approximation, closed-form expressions for mean-field, correlation, and electrophoretic contributions to the Hall conductivity are derived, recovering the classical Debye-Hückel-Onsager limiting law in the point-charge limit. Validated against available experimental Hall data for aqueous solutions of simple salts, strong acids, and alkali hydroxides and against conductivity data for aqueous imidazolium-salt solutions up to 1 M, the theory reproduces the sign and magnitude of the Hall number with typical deviations of 10%-20% where Hall data are available. The analysis reveals a rich interplay of transport channels: correlation dominates in acids with large mobility contrast, electrophoretic and correlation terms are comparable in moderately asymmetric salts, and a crossover occurs in hydroxides. The non-local charge distribution is shown to be essential for quantitative predictions, even reversing the sign of individual contributions at moderate concentrations. The SCDHO Hall theory thus provides a physically transparent and predictive tool for magnetotransport in liquid electrolytes, with direct relevance to nanofluidics, iontronics, and magneto-electrochemistry.