Mathematicians May Have Figured Out How ‘Stone Forests’ Form

There are many wondrous geologic formations in nature, from Giant’s Causeway in Ireland to Castleton Tower in Utah, and the various processes by which such structures form is of longstanding interest for scientists. A team of applied mathematicians from New York University has turned its attention to the so-called “stone forests” common in certain regions of China and Madagascar. These pointed rock formations, like the famed Stone Forest in China’s Yunnan Province, are the result of solids dissolving into liquids in the presence of gravity, which produces natural convective flows, according to the NYU team. They described their findings in a recent paper published in The Proceedings of the National Academy of Sciences.

Coauthor Leif Ristroph told Ars that his group at NYU’s Applied Math Lab became interested in studying stone forests (technically a type of karst topography) by a somewhat indirect route. They were using simulations and experiments to explore the interesting shapes that evolve in landscapes due to a number of “shaping” processes, most notably erosion and dissolving.

“We first discovered the spikes formed by dissolution when we left candy in a water tank and came back later to find a needle-like spire,” he said. “The grad student, first author Mac Huang, even accidentally cut himself when he was admiring the shape. This drew us into the problem, and we were very excited when we realized the connection to stone pinnacles and stone forests, which have been quite mysterious in their development. We hope our experiments tell a simple ‘origin story’ behind these landforms.”

In order to test their simulations in the lab, the team combined granulated table sugar, corn syrup, and water in molds to make blocks and single pillars of solidified (hard-crack) candy—an approximation to the soluble rocks that typically form karst topographies. The mold for the blocks included arrays of upright metal rods to “seed” the blocks with pores for an even closer approximation. They placed these candy blocks and pillars in a plexiglass tank filled with room-temperature degassed water—deep enough so that the dissolved sugars settled at the bottom, away from the objects being tested. They captured the dissolving process by taking digital photographs at one-minute intervals.

You can watch a time-lapsed video of the experiment here, in which a dissolving block of candy morphs into an array of sharp spikes resembling a bed of nails. The block starts out with internal pores and is entirely immersed under water, where it dissolves and becomes a “candy forest” before collapsing.

This occurs even in still water. “We found that the dissolving process itself generates the flows responsible for carving the spike shape,” said Ristroph. “Basically, the mineral—or, in our experiments, lollipop candy serving as ‘mock rock’—dissolves and the surrounding fluid gets heavy and then flows downward due to gravity. So our mechanism doesn’t require any particular flow conditions or other external or environmental circumstances: The recipe involves just dissolving into liquid and gravity.”

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

On the surface, these stone forests look rather similar to “penitentes“: snowy pillars of ice that form in very dry air found high in the Andean glaciers. Some physicists have suggested that penitentes form when sunlight evaporates the snow directly into vapor, without passing through a water phase (sublimation). Tiny crests and troughs form, and sunlight gets trapped within them, creating extra heat that carves out even deeper troughs, and those curved surfaces in turn act as a lens, speeding up the sublimation process even more. An alternative proposal adds an additional mechanism to account for the oddly periodic fixed spacing of penitentes: a combination of vapor diffusion and heat transport that produces a steep temperature gradient, and hence a higher sublimation rate.