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

Ag fractal structures in electroless metal deposition systems with and without magnetic field

Metal electrodeposition systems display tree-like structures with extensive ramification and a fractal character. Electrolysis is not a necessary route for the growth of such dendritic metal deposits. We can grow beautiful ramification patterns via a simple redox reaction. We present here a study of silver (Ag) deposits from the reduction of Ag⁺ in (AgNO₃) solution by metallic copper. The experiments are carried out in discotic geometry, in a Petri dish hosting a thin AgNO₃ solution film. A variety of deposited structures and patterns is obtained at different Ag⁺ concentrations, yet with essentially the same fractal dimension averaged at 1.64, typical of diffusion-limited aggregation (DLA). A linear magnetic field of low induction (0.50-1.0 T) applied across the medium causes a notable transformation in the morphology of the deposits. In both the field off and the field on cases, the effect of vertical (hence 3D) heaving seems to be dominant, perhaps explaining the nearly constant fractal dimension.

Modeling biosilicification at subcellular scales

Biosilicification occurs in many organisms. Sponges and diatoms are major examples of them. In this chapter, we introduce a modeling approach that describes several biological mechanisms controlling silicification. Modeling biosilicification is a typical multiscale problem where processes at very different temporal and spatial scales need to be coupled: processes at the molecular level, physiological processes at the subcellular and cellular level, etc. In biosilicification morphology plays a fundamental role, and a spatiotemporal model is required. In the case of sponges, a particle simulation based on diffusion-limited aggregation is presented here. This model can describe fractal properties of silica aggregates in first steps of deposition on an organic template. In the case of diatoms, a reaction-diffusion model is introduced which can describe the concentrations of chemical components and has the possibility to include polymerization chain of reactions.

Nature of inclined growth in thin-layer electrodeposition under uniform magnetic fields

Electrochemical deposition (ECD) in thin cells in a vertical position relative to gravity, subject to an external uniform magnetic field, yields a growth pattern formation with dense branched morphology with branches tilted in the direction of the magnetic force. We study the nature of the inclined growth through experiments and theory. Experiments in ECD, in the absence of magnetic forces, reveal that a branch grows by allowing fluid to penetrate its tip and to be ejected from the sides through a pair of symmetric vortices attached to the tip. The upper vortices zone defines an arch separating an inner zone ion depleted and an outer zone in a funnel-like form with a concentrated solution through which metal ions are carried into the tip. When a magnetic field is turned on, vortex symmetry is broken, one vortex becoming weaker than the other, inducing an inclination of the funnel. Consequently, particles entering the funnel give rise to branch growth tilted in the same direction. Theory predicts, in the absence of a magnetic force, funnel symmetry induced through symmetric vortices driven by electric and gravitational forces; when the magnetic force is on, it is composed with the pair of clockwise and counterclockwise vortices, reducing or amplifying one or the other. In turn, funnel tilting modifies particle trajectories, thus, growth orientation.