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Phase-field modeling of two-dimensional solute precipitation∕dissolution: solid fingers and diffusion-limited
1Computational Mathematics Group, Fundamental and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, USA. zhijie.xu@pnl.gov
The Journal of Chemical Physics
|February 2, 2011
Summary
Simulations show that diffusion-limited precipitation forms fractal patterns similar to diffusion-limited aggregation (DLA). This dendritic growth, driven by chemical reactions at interfaces, yields fractal dimensions close to DLA clusters.
Area of Science:
- Materials Science
- Chemical Physics
- Computational Modeling
Background:
- Dendritic growth is a common phenomenon in solidification processes.
- Understanding the mechanisms behind pattern formation is crucial for materials design.
- Phase-field models offer a powerful tool for simulating complex interfacial phenomena.
Purpose of the Study:
- To simulate two-dimensional dendritic growth driven by solute precipitation.
- To investigate the similarities between diffusion-limited precipitation and diffusion-limited aggregation (DLA).
- To determine the fractal dimension of the resulting dendritic structures.
Main Methods:
- Utilized a previously reported phase-field model for simulation.
- Set chemical reaction rates significantly higher than solute diffusion to isolate diffusion effects.
- Compared simulation results with analytical solutions.
Main Results:
- Two-dimensional dendritic growth patterns were successfully simulated.
- Diffusion-limited precipitation exhibits characteristics analogous to DLA.
- Fractal solid fingers were observed with a measured fractal dimension of d(f)=1.68.
- This dimension is comparable to that of large square lattice DLA clusters (d(f)=1.64).
Conclusions:
- Phase-field simulations accurately capture diffusion-limited precipitation phenomena.
- Dendritic growth via diffusion-limited precipitation shares fundamental similarities with DLA.
- The formation of fractal structures is a key characteristic of this process.
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