Electrochimica Acta 51 (2006) 4067–4079 Importance of the density gradient effects in modelling electro deposition process at a rotating cylinder electrode Ph. Mandin a,∗ , C. Fabian b , D. Lincot a a Laboratoire d’Electrochimie et de Chimie Analytique, UMR CNRS 7575, ENSCP, 11 rue Pierre et Marie Curie, 75231 Paris cedex 05, France b James Cook University, Townsville 4814, Qld, Australia Received 1 September 2005; received in revised form 14 November 2005; accepted 16 November 2005 Available online 4 January 2006 Abstract The rotating cylinder electrode configuration is one of the most used electrochemical configurations for electrochemical processes study. It is often used with turbulent flow regime for industrial application such as intensive corrosion or electro deposition processes. It can also be used for laminar regimes but in this case it can appear superposition between forced convection and natural free convection. This natural free convection is generally due to density gradient from electrode to bulk, due to electro deposition or to evolving bubbles. The hydrodynamic regime is then said mixed. There is few knowledge concerning the mixed hydrodynamic and the main goal of the present work is to show the qualitative and quantitative effects and differences between purely forced convective flow and purely free natural flow. © 2005 Elsevier Ltd. All rights reserved. Keywords: Electro deposition process; Electrochemical engineering; Modelling 1. Introduction The present work is interested in the modelling and numerical simulation of the classical electro deposition process at a ver- tical electrode. This process generally implies hydrodynamic and electrochemical processes coupling. Convective transport always exist in electrochemical cells, because for laboratory and industrial scales configurations the flow is used simply for bulk mixing (magnetic mixing), or to ensure and help the electro active specie transport at working electrode. At laboratory scale, it is possible to create known hydrodynamic conditions using a classical geometrical configuration, like rotating electrode, disk, ring, hemisphere or cylinder. At industrial scale, the configu- rations are often more difficult: three-dimensional multi-jets, paddles, sometimes unsteady and turbulent. The electrochemi- cal phenomenon is usually convective transport dependent and sometimes strongly coupled with. During electrochemical pro- cesses like electro deposition, heterogeneous reactions occur at electrodes and locally change chemical composition from bulk ∗ Corresponding author. Tel.: +33 155426380; fax: +33 144276780. E-mail address: philippe-mandin@enscp.fr (Ph. Mandin). to electrode conditions. The density is then modified, due to heterogeneous reactions, and the coupling between mechanical transport and reactive processes become strong: the chemical composition interacts with the hydrodynamic properties. It is the case, for example, during the copper electro deposition at a vertical electrode [1–3]. Transport coefficients like viscosity or specie diffusivity are also modified but this effect is often like in the present work neglected. Numerous works have been done concerning the electro- chemical processes classical configurations modelling and sim- ulation. The continuous scale, well known in chemical and electrochemical engineering science, have been well investi- gated by Bard and Faulkner [4], Alden [5], Van den Bossche et al. [6] and many others who have developed nice electro- chemical process modelling, simulation and even software tools like Pirode ® (mono-dimensional) or Myotras ® (two- or three- dimensional) from Elsyca ® . For rotating disk electrodes, the mono-dimensional flow modelling is almost rigorous. It is no longer the case with the rotating cylinder electrodes which appear to be actually two-dimensional and very dependent of the electrochemical cell confinement [7–10]. Modelling difficul- ties increases also when the considered electrochemical reaction leads to a density gradient in its vicinity and then to a natural 0013-4686/$ – see front matter © 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2005.11.029