Transition from gravito- to electroconvective regimes in thin-layer electrodeposition G. Gonzalez, 1,2 G. Marshall, 2 F. Molina, 1 and S. Dengra 2 1 INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina 2 Laboratorio de Sistemas Complejos, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina ~Received 13 January 2002; published 21 May 2002! The transition from gravitoconvective to electroconvective prevailing regimes in thin-layer electrochemical deposition is analyzed through variations of electrolyte viscosity at constant cell thickness. The distribution of velocity directions at the deposit front is a measure of the relative weight of electroconvection versus gravi- toconvection, and a signature of that transition. The experiments are carried out under galvanostatic conditions in convection prevailing regimes. Particle image velocimetry reveals that at low viscosities, buoyancy driven convection dominates; as viscosity increases, electrically driven convection becomes more important, eventu- ally prevailing. The transition is observed at 1.5 times the viscosity of water. The theoretical model presented reveals that an increase of the Poisson and Reynolds numbers and a decrease of the Peclet and electric Grashof numbers, when viscosity increases, makes the electroconvective motion relatively more important. The model predicts a transition at approximately two times the viscosity of water. We may conclude that, in a physico- chemical hydrodynamic flow involving ions, under galvanostatic conditions, increasing viscosity damps gravi- toconvection and enhances electroconvection. DOI: 10.1103/PhysRevE.65.051607 PACS number~s!: 82.45.Qr, 47.20.Bp, 89.90.1n I. INTRODUCTION In electrochemical thin-layer electrodeposition ~ECD!, the use of relatively high current densities, along with the ab- sence of support electrolyte, give rise to complex, branched growth morphology @1#. In this situation, the transport of ions in the electrochemical cell is due to a combination of migration, diffusion, and convection. The relevance of con- vection, relative to migration and diffusion, in ion transport and growth morphology in ECD, for cells with thickness larger than 50 mm, has been demonstrated by a number of researchers @2–21#. In cells with thickness less than 50 mm, diffusion and migration are the dominant modes in ion trans- port as shown by Leger et al. @17#. Convection is driven mainly by Coulombic forces due to local charges @8,9,15#, and by buoyancy forces due to concentration gradients that lead to density gradients @14,15#. When ramified deposits form, they interact with gravity driven vortex tubes and elec- tric driven vortex rings, yielding a complex three- dimensional helicoidal fluid motion. The only way to assess quantitatively those interactions is through fluid velocity di- rection measurements. In this way, the relative weight of gravity to electroconvection can be determined. The study of the relative weight of electroconvection against gravitocon- vection in ECD is relevant because it determines the flow regime and thus ion transport and growth morphology. One way to analyze this problem is through variations in cell thickness @15,22#; an alternative shown below, is through electrolyte viscosity variations. The former was addressed in the works of Huth et al. @15#, and Marshall et al. @22#. In Ref. @22#, a theoretical analysis was performed in which the equations describing ECD are written in terms of dimension- less quantities. In particular the gravity Grashof Gg and the electric Grashof Ge numbers represent the relative strength of the electric and gravity forces, respectively. The ratio l5 Gg/Ge was introduced to express the importance of gravitoconvection as compared to electroconvection. It was found that the variations of l correlate well with the changes in the relative importance of both modes when the thickness was varied. Viscosity is a key parameter to analyze the in- fluence of convection. In a typical hydrodynamic flow, in- creasing viscosity produces a general damping of the flow pattern. In a physicochemical hydrodynamic flow involving ions, the situation is more complex as shown below. In a recent paper, Gonzalez et al. @23# presented an extensive ex- perimental and theoretical study of the role of viscosity in ECD under galvanostatic conditions, where viscosity was changed through glycerol additions. Experiments revealed that increasing viscosity, convection decreased and concen- tration gradients were more pronounced, while electric resis- tance and voltage increased. Concentration and convective fronts slowed down with viscosity, but their time scaling followed the same law as for solutions without glycerol, only differing by a constant. The theoretical model presented, based on that introduced by Marshall et al. @22#, describes diffusive, migratory and convective ion transport in a fluid subject to an electric field. It is shown theoretically that, under galvanostatic conditions, while the gravity Grashof number remains constant, the electric Grashof number in- creases with viscosity. This fact demonstrates that electric forces increase relative to gravity ones as viscosity increases, thus motivating the present work. In this paper we study through experiments, theory and computational modeling, the relative importance of gravitoconvection vis-a-vis elec- troconvection in ECD. The transition from gravity to electro- convective prevailing regimes is analyzed through variations of electrolyte viscosity at constant cell thickness and under galvanostatic conditions. In particular we measure fluid ve- locities by means of particle image velocimetry ~PIV! using micron sized particles. Viscosity variations are achieved by means of glycerol addition. The distribution of velocity di- rections at the deposit front is a measure of the relative PHYSICAL REVIEW E, VOLUME 65, 051607 1063-651X/2002/65~5!/051607~8!/$20.00 ©2002 The American Physical Society 65 051607-1