Hydrodynamic Stability in Electrochemical Cells

Abstract

We consider the stability of rotating disk flow coupled, through the fluid viscosity, to the mass concentration field of a chemical species. This configuration refers to an electrochemical cell where the working electrode consists of an iron rotating rod, which is dissolved in the 1 MH SO solution of the electrolyte. Polarization curves obtained in these cells present a 2 4 current instability at the beginning of the region where the current is controlled by the mass transport. The instability appears at a certain value of the applied potential and is suppressed beyond another value. Dissolution of the electrode gives rise to a thin concentration boundary layer, due to a Schmidt number Sc = 2000 of the setup. This boundary layer, together with the potential applied to the electrode, leads to an increase in the fluid viscosity and to a decrease in the diffusion coefficient, both affecting the chemical species field. Since the current is proportional to the normal derivative of the species concentration at the interface, an instability of the coupled fields at sufficiently low Reynolds numbers may result in a current instability. In this work we review the main points related to the joint work conducted in the last ten years by the Metalurgy and Materials Engineering Dept./Program at the Federal University of Rio de Janeiro, togeteher with the Mechanical Engineering Graduate Program/GESAR Group, at the State University of Rio de Janeiro, related to the linear stability analisys of the hydrodynamic field close to the rotating disk electrode. in addition, we report the first steps towards a direct numerical simulation of the problem. The linear stability analysis shows that the coupling of the hydrodynamics to the cocentration field of a representative chemical species strongly reduces the stability of both. In addition, the coupling gives raise to a new unstable region of modes at even lower Reynolds numbers, of same order of those attained in the experimental setup. The amplitude of the concentration component of unstable modes in this new region is much larger than the amplitude of the hydrodynamic variables. Furthermore, the concentration unstable modes are confined to a boundary layer 20 times thinner than the hydrodynamic boundary layer. The combination of these two properties point to the existence of oscillations of the interfacial concentration gradient at levels sufficient high to induce detectable current oscillations. In addition, numerical experiments show that the new unstable regions collpase andtheconstant viscosity stability properties are recovered if a too high interfacial viscosity is attained, suggesting that this mechanism could be responsiblefor the collpase of the current oscillations. As a follow up of the stabilityanalysis, a FEM-DNS code isunder developmentatour group. The numerical solutions adopted are discussed and validation results of the proposed algorithm are presented.