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Mathematicians may have revealed the secret of how “forests of stone” are formed

The stone forest (Shilin) ​​in China's Yunnan province could be the result of solids dissolving into liquids in the presence of gravity, producing natural convective flows.
Zoom in / The stone forest (Shilin) ​​in China’s Yunnan province could be the result of solids dissolving into liquids in the presence of gravity, producing natural convective flows.

There are many wonderful geological formations in nature, from the Giant’s Causeway in Ireland to the Castleton Tower in Utah, and the various processes by which such structures are formed are of long-standing interest to scientists. A team of applied mathematicians from New York University has turned its attention to the so-called “stone forests” common in some regions of China and Madagascar. These spiky rock formations, like the famous stone forest in China’s Yunnan province, are the result of solids dissolving into liquids in the presence of gravity, which produces natural convection flows, according to the NYU team. They described their findings in a recent paper published in the Proceedings of the National Academy of Sciences.

Co-author Leif Ristroph told Ars that his group at NYU’s Applied Math Lab has been interested in studying stone forests (technically a type of karst topography) for a rather indirect route. They were using simulations and experiments to explore the interesting shapes that evolve in landscapes due to a series of “modeling” processes, most notably erosion and dissolution.

“We first discovered the spikes formed by the dissolution when we left the candies in a tank of water and returned later to find a needle-like spire,” he said. “The graduate student, first author Mac Huang, even accidentally cut himself while he was admiring the shape. This drew us into the problem, and we were very excited when we made the connection with the stone pinnacles and the stone forests, which are rather mysterious states in their development. We hope our experiments tell a simple “origin story” behind these morphologies. “

To test their simulations in the lab, the team combined granulated table sugar, corn syrup, and water in molds to create blocks and single pillars of hard-cracked candy, an approximation of the soluble rocks that typically form karst topographies. . The mold for the blocks included arrays of vertical metal rods to “seed” the blocks with pores for an even closer approximation. They placed these candy blocks and columns in a plexiglass tank filled with room-temperature degassed water, deep enough so that the dissolved sugars would settle to the bottom, away from the objects to be tested. They captured the dissolution process by taking digital photographs at one-minute intervals.

You can watch an elapsed video of the experiment below, in which a dissolving block of candy turns into a series of sharp spikes that resemble a bed of nails. The block begins with internal pores and is entirely submerged under water, where it dissolves and becomes a “candy forest” before collapsing.

This also occurs in still water. “We found that the dissolution process itself generates the streams responsible for etching the tip shape,” said Ristroph. “Basically, the mineral – or, in our experiments, candy lollipops that act as a ‘mock rock’ – dissolves and the surrounding fluid becomes heavy and then flows downward due to gravity. So our mechanism requires no specials. flow conditions or other external conditions or environmental circumstances: the recipe only provides for dissolution in liquid and gravity. “

Ristroph et al. suggest that a similar mechanism is at work in the formation of stone forests, only on a much longer time scale. Soluble rocks such as limestone, dolomite and gypsum are submerged under water, where the minerals slowly dissolve in the surrounding water. The heavier water then sinks under the pull of gravity downwards and the streams gradually form karst topographies. When the water recedes, pillars and forests of stone emerge.

On the surface, these stone forests look quite similar to “penitentes”: snow-capped ice columns that form in the very dry air found high in the Andean glaciers. Some physicists have suggested that penitents are formed when sunlight evaporates snow directly into vapor, without going through an aqueous phase (sublimation). Tiny ridges and dips form and sunlight gets trapped inside them, creating extra heat that digs even deeper dips and those curved surfaces in turn act like a lens, further speeding up the sublimation process. An alternative proposal adds an additional mechanism to account for the strangely periodic fixed distance of penitents: a combination of vapor diffusion and heat transport that produces a steep temperature gradient and therefore a higher sublimation rate.

Physicists have been able to recreate artificial versions of penitents in the laboratory. But penitents and forests of stone are actually very different in terms of the mechanisms involved in their formation. “I think the similarities are pretty superficial,” Ristroph said. “Certainly, the ‘sculpting’ process is very different in terms of the main driving effects. Mainly, our points are very sculpted by the flows, which I don’t think play an important role in the formation of penitents.”

It is true that the NYU researchers obtained their results under idealized conditions, deliberately thus, according to the authors, better identify and clearly characterize the sharpening process, the underlying mechanism and the mathematical structure. As a result, “this study reveals a minimal set of essential ingredients for needle and nail bed motifs,” the authors wrote. In the future, they hope to further test this formation process under different environmental conditions in the lab, such as precipitation and surface runoff, or being buried under loose sediment, could affect pinnacle formation.

DOI: PNAS, 2020. 10.1073 / pnas.2001524117 (About DOI).

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