title: Nonlinear oscillations in an electrolyte solution under ac voltage.
abstract: The response of an electrolyte solution bounded between two blocking electrodes subjected to an ac voltage is considered. We focus on the pertinent thin-double-layer limit, where this response is governed by a reduced dynamic model [L. Højgaard Olesen, M. Z. Bazant, and H. Bruus, Phys. Rev. E 82, 011501 (2010)]. During a transient stage, the system is nonlinearly entrained towards periodic oscillations of the same frequency as that of the applied voltage. Employing a strained-coordinate perturbation scheme, valid for moderately large values of the applied voltage amplitude V, we obtain a closed-form asymptotic approximation for the periodic orbit which is in remarkable agreement with numerical computations. The analysis elucidates the nonlinear characteristics of the system, including a slow (logarithmic) growth of the zeta-potential amplitude with V and a phase straining scaling as V-1lnV. In addition, an asymptotic current-voltage relation is provided, capturing the numerically observed rapid temporal variations in the electric current.
authors.affiliation: Department of Mathematics, Technion - Israel Institute of Technology, Haifa, Israel.
authors.forename: Ory
authors.initials: O
authors.lastname: Schnitzer
authors.affiliation: Department of Mathematics, Technion - Israel Institute of Technology, Haifa, Israel.
authors.forename: Ehud
authors.initials: E
authors.lastname: Yariv