Morphological attractors in natural convective dissolution

TL;DR

This paper identifies exact solutions describing the formation of natural-like dissolution pinnacles driven by convective flows, matching experiments without regularization and offering insights into geological structure evolution.

Contribution

It introduces a class of exact attractor solutions for dissolution shapes that naturally develop finite tip curvature without regularization, aligning with experimental observations.

Findings

Exact solutions act as shape attractors in dissolution processes.

Solutions exhibit finite tip curvature without regularization.

Model matches experimental measurements of natural pinnacles.

Abstract

Recent experiments demonstrate how a soluble body placed in a fluid spontaneously forms a dissolution pinnacle -- a slender, upward pointing shape that resembles naturally occurring karst pinnacles found in stone forests. This unique shape results from the interplay between interface motion and the natural convective flows driven by the descent of relatively heavy solute. Previous investigations suggest these structures to be associated with shock-formation in the underlying evolution equations, with the regularizing Gibbs-Thomson effect required for finite tip curvature. Here, we find a class of exact solutions that act as attractors for the shape dynamics in two and three dimensions. Intriguingly, the solutions exhibit large but finite tip curvature without any regularization, and they agree remarkably well with experimental measurements. The relationship between the dimensions of the initial shape and the final state of dissolution may offer a principle for estimating the age and environmental conditions of geological structures.