Diffusion-Limited Aggregation
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The document discusses diffusion-limited aggregation, focusing on the formation of mineral dendrites in rock fissures through the percolation of manganese and iron solutions. It explains the processes of branched electrodeposition and provides insights into simulations that model the aggregation of particles. Key questions addressed include the reasons behind the branching structure and its retention during the aggregation process.
Diffusion-Limited Aggregation
- 1. Diffusion - Limited Aggregation Abhranil Das SPRING 2012
- 2. Mineral Dendrites Dendron = plant. Naturally occurring fissures in limestone and other rock are percolated by manganese and iron solutions. Often mistaken for fossils.
- 3. Branched Electrodeposition Dendritic structures also form when materials freeze or crystallize out of equilibrium. e.g: high voltage metal electrodeposition. Picture: Copper aggregate in copper sulphate solution
- 4. Simulation The first computer model was given by Tom Witten at the College dé France and Len Sander at the University of Michigan (~2000 citations), to describe how dust particles form clumps in the air.
- 5. Simulation: Point Seed Brownian Tree
- 6. Simulation: Point Seed Snapshot with 944 drifters and 1131 aggregates, each of radius 0.005 units.
- 7. Why this shape? • Why do the branches form? • Why are they retained? Why doesn’t the shape get filled in?
- 10. Simulation: Line Seed Snapshot at dynamic equilibrium with about 250 drifters and 1300 aggregates, each of radius 0.005 units.
- 11. Formation of Mineral Dendrites Solutions of metal and oxide ions diffuse through rock cracks. When they meet, they produce a soluble compound. Beyond a concentration, the compound forms a coloured precipitate. On meeting a precipitate molecule, a dissolved compound molecule sticks to it and adds to the precipitate. Therefore, the mechanism is the same as electrodeposition.
- 13. Sources • Branches, Philip Ball, Oxford University Press 2009 • Diffusion-limited aggregation, T.A. Witten, L.M. Sander, Physical Review B 1983 • classes.yale.edu/fractals