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Emergence of tip singularities in dissolution patterns.

Martin Chaigne1, Sabrina Carpy2, Marion Massé2

  • 1Matière et Systèmes Complexes, Université Paris Cité, CNRS (UMR 7057), Paris 75013, France.

Proceedings of the National Academy of Sciences of the United States of America
|November 21, 2023
PubMed
Summary
This summary is machine-generated.

Chemical erosion dissolves soluble rocks, forming unique patterns like spikes. This study uses a geometrical approach to explain how these sharp shapes emerge from surface geometry and dissolution dynamics, applicable to various ablation processes.

Keywords:
dissolutionfluid–solid interfacegeomorphologypattern formationsingularities

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Area of Science:

  • Geomorphology
  • Fluid Dynamics
  • Materials Science

Background:

  • Chemical erosion, alongside mechanical erosion, shapes landscapes by dissolving soluble rocks like gypsum and limestone.
  • Dissolution processes, influenced by rock geometry, mass transfer, and water flow, create intricate patterns such as cave scallops.
  • Sharp shapes and spikes are commonly observed in dissolution patterns across diverse conditions, yet a unified explanation is lacking.

Purpose of the Study:

  • To provide a generic geometrical explanation for the emergence of sharp spikes in chemical dissolution patterns.
  • To model the surface evolution during dissolution and understand the formation of cellular structures.
  • To validate theoretical predictions with experimental observations of dissolution patterns.

Main Methods:

  • Analysis of natural dissolution-shaped interfaces to identify singular structures.
  • Development of surface evolution models of increasing complexity to simulate spike and cellular pattern formation.
  • Experimental investigation of dissolution patterns driven by solutal convection.

Main Results:

  • Demonstrated the presence of singular structures in naturally eroded surfaces.
  • Surface evolution models successfully predicted the emergence of spikes and long-term cellular structures.
  • Experimental results showed cellular patterns consistent with model predictions.

Conclusions:

  • Geometrical arguments based on surface evolution provide a generic explanation for characteristic spikes in dissolution patterns.
  • The findings offer insights into pattern formation in chemical erosion and other ablation processes.
  • While full hydrodynamic studies are needed for precise shape prediction, geometry plays a key role in emergent features.