Ultra-sharp pinnacles sculpted by natural convective dissolution

Abstract

The evolution of landscapes, landforms, and other natural structures involves highly interactive physical and chemical processes that often lead to intriguing shapes and recurring motifs. Particularly intricate and fine-scale features characterize the so-called karst morphologies formed by mineral dissolution into water. An archetypal form is the tall, slender, and sharply tipped karst pinnacle or rock spire that appears in multitudes in striking landforms called stone forests, but whose formative mechanisms remain unclear due to complex, fluctuating, and incompletely understood developmental conditions. Here, we demonstrate that exceedingly sharp spires also form under the far-simpler conditions of a solid dissolving into a surrounding liquid. Laboratory experiments on solidified sugars in water show that needlelike pinnacles, as well as bed-of-nails-like arrays of pinnacles, emerge robustly from the dissolution of solids with smooth initial shapes. Although the liquid is initially quiescent and no external flow is imposed, persistent flows are generated along the solid boundary as dense, solute-laden fluid descends under gravity. We use these observations to motivate a mathematical model that links such boundary-layer flows to the shape evolution of the solid. Dissolution induces these natural convective flows that, in turn, enhance dissolution rates, and simulations show that this feedback drives the shape toward a finite-time singularity or blow-up of apex curvature that is cut off once the pinnacle tip reaches microscales. This autogenic mechanism produces ultra-fine structures as an attracting state or natural consequence of the coupled processes at work in the closed solid-fluid system.

The convective Stefan problem: shaping under natural convection

“…This work complements a recent study demonstrating that a dissolving block of candy containing vertical cavities evolves into a series of upwards-pointing spikes (Huang et al. 2020) reminiscent of the remarkable stone forests of China and Madagascar, further emphasising the real-world applications of this research. Their model predicts that the tip curvature always increases to infinity in a finite time, contradicting the potential for blunting implied by our full model solutions (e.g.…”

Alcove formation in dissolving cliffs driven by density inversion instability

“…The solids used in our study are prepared with 5 part sucrose, 3 part light corn syrup, and 2 part distilled water by volume, similar to recipes in other studies [10,13]. These ingredients are stirred and heated together, while keeping the temperature at approximately 160 • C, until 7/8th of the original volume remains after evaporation corresponding to a density 1.3 ± 0.1 g/cm 3 .…”

“…Opacity of the medium only allowed intermittent and indirect inferences to be drawn in these studies. Recent studies of two-phase model systems with rapidly dissolving non-crystalline hard candy have illuminated the formation of pinnacles in karsts, furrows in sandstone, and ice scallops [10][11][12][13][14][15][16][17]. Significant progress has been made in describing the observed outer envelops of the structures with counter-intuitive growth of singularities versus blunting of sharp tips depending on the shapes of the initial surfaces and flow conditions [15].…”

Elastic amplification of the Rayleigh–Taylor instability in solidifying melts

“…Yet, mechanical instabilities and the patterns they generate are primarily studied using fixed material properties, whether in liquids (1), elastic solids (21)(22)(23)(24), viscoelastic materials (25), or multiphase problems (26,27). Conversely, there are examples of complex natural structures formed by successive far-from-equilibrium nonlinear processes, e.g., in biology (28,29) and geomorphology (30). Porting multistep pattern formation to comparatively simpler model systems, e.g., melts, could unveil additional physics and open more possibilities in engineering.…”