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.