Modelling Hydrodynamic Stability in Electrochemical Cells

Abstract

We review the key points concerning the linear stability of the classical von Karman solution of rotating disk flow, modified by the coupling, through the fluid viscosity, with concentration field of a chemical species. The results were recently published by Mangiavacchi et al. (Phys. Fluids, 19: 114109, 2007) and refer to electrochemical cells employing iron rotating disk electrodes, which dissolve in the 1 M H2SO4 solution of the electrolyte. Polarization curves obtained in such cells present a current instability at the beginning of the region where the current is controlled by the hydrodynamics. The onset of the instability occurs in a range of potentials applied to the cell and disappears above and below this range. Dissolution of the iron electrode gives rise to a thin concentration boundary layer, with thickness of about 4% of the thickness of the hydrodynamic boundary layer. The concentration boundary layer increases the interfacial fluid viscosity, diminishes the diffusion coefficient and couples both fields, with a net result of affecting the hydrodynamics of the problem. Since the current is proportional to the interfacial concentration gradient of the chemical species responsible for ion transport, the instability of the coupled fields can lead to the current instability observed in the experimental setups. This work presents the results of the linear stability analysis of the coupled fields and the first results concerning the Direct Numerical Simulation, currently undertaken in our group. The results show that small increases of the interfacial viscosity result in a significant reduction of the stability of modes existing in similar configurations, but with constant viscosity fluids. Upon increasing the interfacial viscosity, a new unstable region emerges, in a range of Reynolds numbers much smaller than the lower limit of the unstable region previously known. Though the growth rate of modes in the previously known region is larger than the one of modes in the new region, the amplitude of the concentration unstable modes in this one is very large when compared to the amplitude of the associated hydrodynamic unstable modes. In addition, concentration modes are always confined in a rather thin region, leading to the existence of large interfacial concentration gradients. Concentration modes in the new unstable region seem thus to have a combination of properties sufficient to drive detectable current oscillations. The numerical experiments show that a progressive increase in the interfacial viscosity initially reduces the stability of the flow, but an increase beyond a certain limit restores the stability properties of constant viscosity flows.