ECD

Electrodeposition (ECD) in thin cells with different orientations relative to gravity leads to complex stable and unstable physicochemical hydrodynamic flows. Here we study the impact of gravity in these flows through a theoretical macroscopic 3D model and its numerical simulation. The model describes the diffusive, migratory and convective motion of ions in a fluid subject to an electric field through the Nernst-Planck, Poisson and Navier- Stokes equations, respectively. The equations are written in terms of dimensionless quantities, in particular, the gravity Grashof number, revealing the importance of gravitoconvection. The nonlinear system of partial differential equations is solved in a uniform grid using finite differences and a strongly implicit iterative scheme. In ECD in a cell in a horizontal position, our model predicts the evolution of two gravity driven convective rolls and concentration shells attached to each electrode: their birth, growth, expanding towards one another, collision and merging into a single roll invading the whole cell. In ECD in a cell in vertical position, cathode above anode, our model predicts that gravity induced rolls and concentration shells remain locally attached to downwards growing fingers, thus global invasion of the cell by gravity induced rolls is suppressed leading to a stable stratified flow. In ECD in a cell in a vertical position, cathode below anode, our model predicts the detachment of rolls and concentration shells from each electrode in the form of plumes, expanding towards one another, mixing, invading the whole cell and leading to an unstable stratified flow. For ECD whether in horizontal or vertical position, in the presence of growth, our model predicts the existence of an electrically driven vortex ring at the dendrite tip interacting with concentration shells and rolls, leading to complex helicoidal flows. Such structures are experimentally observed suggesting that ion transport underlying dendrite growth is remarkably well captured by our model.

Publications:

G. Marshall and P. Mocskos, A Growth Model for Ramified Electrochemical Deposition in the Presence of Diffusion, Migration and Electroconvection, Phys. Rev. E 55 (1997) 549.

G. Marshall, P. Mocskos, H. L. Swinney and J. M. Huth, Buoyancy and Electrical Driven Convection Models in Thin-layer Electrodeposition, Phys. Rev. E 59 (1999) 2157.

S. Dengra, G. Marshall and F. Molina, Front tracking in thin-layer electrodeposition, J. of the Physical. Society of Japan 69 (2000) 963.

G. González, G. Marshall, F. V. Molina, S. Dengra and M. Rosso, Viscosity effects in thin-layer electrodeposition, J. of the Electrochemical Society, 148 (2001) C479.

G. Gonzalez, G. Marshall, F. V. Molina and S. Dengra, Transition from gravito- to electroconvective regimes in thin-layer electrodeposition, Phys. Rev. E 65 (2002) 051607

G. Marshall, E. Mocskos, F. V. Molina and S. Dengra, The Three-Dimensional Nature of Ion Transport in Electrochemical Deposition, Phys. Rev., E 68 (2003) 021607.

G. Marshall, A. Soba and F. V. Molina , Ion transport in thin-cell electrodeposition: modelling three-ion electrolytes in dense branched morphology under constant voltage and current conditions, Electrochimica Acta, Vol 50/16-17 (2005) 3436.

G. Marshall, E. Mocskos, G. Gonzalez, S. Dengra, F. V. Molina and C. Iemmi, Stable, quasi-stable and unstable physicochemical hydrodynamic flows in thin-layer cell electrodeposition, Electrochimica Acta, Volume 51, Issue 15 (2006) 3058

E. Mocskos and G. Marshall, Impact of gravity in thin-layer cell electrodeposition, Electronic Transactions in Numerical Analysis, ETNA, Vol. 34 (2008-2009) 90.