Morphological Attractors in Natural Convective Dissolution

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.

Automated summary

Recent experiments have shown that a soluble body placed in a fluid can spontaneously form a dissolution pinnacle, which resembles naturally occurring karst pinnacles found in stone forests. These pinnacles are the result of the interaction between interface motion and natural convective flows driven by the descent of relatively heavy solute. Previous research suggested that these structures are associated with shock formation in the underlying evolution equations and require the regularizing Gibbs-Thomson effect for finite tip curvature. However, this study has discovered a class of exact solutions that act as attractors for shape dynamics in two and three dimensions. These solutions exhibit large but finite tip curvature without the need for any regularization and match experimental measurements accurately. The relationship between the dimensions of the initial shape and the final state of dissolution may provide a principle for estimating the age and environmental conditions of geological structures.