Numerical simulation of MHD in thin cell electrodeposition : influence of concentration

International audienceNumerical investigations of the magneto-hydrodynamic convection in thin cell electrochemical deposition under normal magnetic field were undertaken with the aim of understanding the peculiarities of the patterns found out in experimental growth

Characterization of MHD convection in thin cell electrodeposition

International audienceWe are studying the effect of a magnetic field normal to the cell in electrodeposition of zinc arborescences. When the cell thickness is reduced, the MHD convection, responsible for morphology changes, spiraling, etc. is suppressed, but in a high magnetic field there is still an effect maybe due to small-scale hydrodynamic convection or to the Lorentz force on the growing metallic branches, the "Laplace" force

Model for the growth of electrodeposited ferromagnetic aggregates under an in-plane magnetic field

International audienceThe quasi-two-dimensional deposition of ferromagnetic materials by electrochemical process under the influence of a magnetic field applied in the plane of the growth leads to a surprising symmetry breaking in the dendritic structures found. The reasons for these features are still not completely understood. The original dense circular envelope becomes rectangular, as well as the sparse figures have their shapes elongated. This paper reports the results of a diffusion-limited aggregation DLA -like simulation. The model proposed here, a modification of the original DLA model, can deal with ferromagnetic particles under the influence of an electric field and the dipolar interactions between particles, submitted to an applied magnetic field in the plane of growth of such structures. The results were produced varying the applied magnetic field and the magnetic moment of the particles and show that the balance between these interactions is an important mechanisms that can be responsible for the changes in shape of the aggregates observed in the experiments

Morphometric methods.

<p>(A) A skeleton graph with the increased level of occlusion of the volumetric data in the background, (B–C) Visualization of spheres used for calculating morphometric traits - diameter of a sphere at the terminal branch is defined as terminal branch thickness –<i>dc</i>, (D) A visualization of the volumetric data of TS_002 coral (See <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002849#pcbi-1002849-t001" target="_blank">Table 1</a> for label), (E) Visualization of symmetry angles <i>h_angle</i> and <i>v_angle</i> , (F) Visualization of the associated vectors used for calculation of symmetry vector <i>sm_mag</i>.</p

The simulated growth forms.

<p>(A) Simulated coral in a no-flow condition. (B–F) Simulated corals from various flow simulations (B) <i>Pe_branch</i> = 0.00113, (C) <i>Pe_branch</i> = 0.0105, (D) <i>Pe_branch</i> = 0.0970, (E) <i>Pe_branch</i> = 1.13, (F) <i>Pe_branch</i>∼11.3, Arrow indicates flow direction. The labels of the simulated corals are located on the bottom of each figure (See <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002849#pcbi-1002849-t001" target="_blank">Table 1</a> for labels).</p

Parameters used for simulations and parameters used to calculate <i>Pe</i> number, surface/volume ratio and symmetry magnitude.

<p>Parameters used for simulations and parameters used to calculate <i>Pe</i> number, surface/volume ratio and symmetry magnitude.</p

An example of three consecutive accretive growth steps.

<p>(A–C) Accretive growth steps; vertex v_i represents a simulated corallite. The new layer is constructed along the direction of normal vector n_i of the vertex v_i. A, B and C are three consecutive growth steps where triangles are inserted once the surface of the object increases.</p

Mean values of symmetry magnitude <i>sm_mag</i> versus <i>Pe_branch</i> for simulated corals (A) and CT-scanned (B) corals.

<p>Error bars indicate 95% confidence interval. (C-D) surface/volume ratio of simulated and CT-scanned corals versus <i>Pe_branch</i>.</p

Visualization of the volume rendering of the CT-scanned corals with their associated histograms of the local morphometric traits.

<p>Red lines indicate projected branches vector on the substratum plane (visualized from the bottom up perspective). For the <i>in situ</i> flow-controlled corals, flow direction is from right to left. The morphometric traits measured here are as follow: symmetry angles <i>h_angle</i> and <i>v_angle</i>, and the symmetry attitude <i>sm_mag</i> (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002849#pcbi-1002849-t001" target="_blank">table 1</a> for labels). (A) controlled coral CT_456, <i>Pe_branch</i> = 0.136, (B) reduced flow coral (TS_002), <i>Pe_branch</i> = 0.0163 (C), enhanced-flow coral TS_001, <i>Pe_branch</i> = 0.188, (D) enhanced-flow coral TS_003, <i>Pe_branch</i> = 0.227, and (E) enhanced-flow coral CT455, <i>Pe_branch</i> = 0.288.</p

Schematic diagram of the simulation.

<p>(A) A spherical object represents an initial growth state of the simulation (first growth step) (B) A simulation phase involves solving the Navier-Stokes equations (i) and the advection-diffusion equation (ii). (C) Accretion phase translocates absorbed nutrients from previous simulation phase to a new growth layer hence, after a few consecutive growth steps, spontaneous branching occurs.</p