M.Sc.
Current instabilities in electrochemical cells is a research subject of
the Applied Electrochemistry Group in the Metallurgy and Materials
Program – COPPE/UFRJ. Electrochemical cells containing a 1M sulfuric
acid electrolyte and an iron rotating disk electrode are used by the
group and present this instability.
A possible reason for the phenomena
is a reduction of the stability of the flow, induced by the existence
of a thin mass concentration boundary layer, produced by the dissolution
of the electrode. The group has addressed the problem by performing
linear stability analysis of the flow for electrolytes with a viscosity
profile depending on the axial coordinate z only and, subsequently, by
coupling the hydrodynamic and the mass concentration field produced by
the dissolution of the electrode, through the fluid viscosity. The
results suggest a significant reduction of the stability of the flow,
due to the coupling of fields. The purpose of this work is to develop a
computational platform for further studying the hydrodynamic field close
to the rotating disk electrode, through a 3D Direct Numerical
Simulation using the Finite Element Method. Viscous and pressure terms
are discretized through the Galerkin method and the convective term is
treated through a semi-Lagrangean method. Time derivatives are
discretized by a first-order backward Euler implicit scheme. Velocity
and pressure are decoupled through a projection method based on LU
decomposition. The resulting linear system is solved by the
pre-conditioned conjugate gradient method. A hydrodynamic field, very
close to the generalized von Kármán solution for the rotating disk
flow was obtained, validating the code. The code, developed within the
object oriented paradigm, constitutes a platform for the study of 3D
perturbations in electrochemical cells in the linear regimen and in the
saturation and the modes interaction in the non-linear regimen.