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Interfacial dynamics in transport-limited dissolution.

Martin Z Bazant¹

¹Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|August 16, 2006

Summary

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This study analyzes transport-limited dissolution using conformal maps. It reveals how shapes change during dissolution, with some maintaining form while others dissolve complexly.

Area of Science:

Physical Chemistry
Mathematical Physics
Surface Science

Background:

Transport-limited dissolution is crucial in various natural and industrial processes.
Understanding surface evolution under dissolution requires robust analytical tools.

Purpose of the Study:

To analyze two-dimensional transport-limited dissolution models.
To investigate the dynamics of surface smoothing and solid disappearance.
To explore solutions for diffusion-limited and advection-diffusion dissolution.

Main Methods:

Utilized time-dependent conformal mapping techniques.
Analyzed exact solutions for diffusion-limited dissolution (reverse Laplacian growth).
Considered non-Laplacian dissolution processes and advection-diffusion scenarios.

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Main Results:

Exact solutions were found for surface smoothing in diffusion-limited scenarios.
Continuous analogs of internal diffusion-limited aggregation and diffusion-limited erosion were discussed.
A tilted ellipse maintained its shape during advection-diffusion dissolution, unlike other shapes.

Conclusions:

Conformal maps provide powerful insights into transport-limited dissolution dynamics.
The study clarifies conditions for solid disappearance and shape evolution.
Dissolution dynamics vary significantly based on transport mechanisms and initial geometry.