There are many wondrous geological formations in nature, from Ireland’s Giant’s Causeway to Utah’s Castleton Tower, and the various processes that create such structures have historically been of interest to 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 jagged rock formations, like the famous Stone Forest in China’s Yunnan province, result from the dissolution of solids in liquids in the presence of gravity, producing natural convective currents, according to the NYU team. They detailed 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 became interested in studying rock forests (technically a type of karst topography) through a somewhat indirect route. They used simulations and experiments to investigate the interesting shapes that evolve in landscapes as a result of a number of “forming” processes, most notably erosion and dissolution.
“We first discovered the spikes formed by decomposition when we left candy in a water tank and later came back to find a needle-like spire,” he said. The graduate student, first author Mac Huang, even accidentally cut himself while admiring the shape. This drew us into the problem, and we were very excited when we realized that there was a connection with stone pinnacles and stone forests, which were quite mysterious in their development. We hope our experiments tell a simple ‘origin story’ behind these landforms.”
To test their simulations in the lab, the team combined granulated sugar, corn syrup and water in molds to create blocks and single pillars of solidified (hard-crack) candy — an approximation of the soluble rocks that typically form karst topographies. The mold for the blocks included sets of upright metal rods to “seed” the pored blocks for an even better approach. They placed these candy blocks and pillars in a Plexiglas tank filled with room temperature degassed water — deep enough so that the dissolved sugars settled to the bottom, away from the objects being tested. They recorded the dissolution process by taking digital photos at one-minute intervals.
You can watch a time-lapse video of the experiment below, in which a dissolving block of candy turns into a series of sharp points that resemble a bed of nails. The block begins with internal pores and is completely submerged under water, where it dissolves and becomes a “candy forest” before collapsing.
This even happens in standing water. “We found that the dissolution process itself generates the currents responsible for cutting the point shape,” Ristroph said. “Basically, the mineral – or, in our experiments, lollipop candies that act as ‘mock rocks’ – dissolves and the surrounding liquid becomes heavy and then flows downwards due to gravity. So our mechanism does not require specific flow conditions or other external or environmental conditions: the recipe involves simply dissolving in liquid and gravity.”
Ristropho et al. suggest that a similar mechanism is at work in rock forest formation, only on a much longer timescale. Soluble rocks such as limestone, dolomite, and gypsum are submerged underwater, 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 are quite similar to “penitentes”: snow-covered ice pillars that form in very dry air found high in the Andean glaciers. Some physicists have suggested that penitentes are formed when sunlight evaporates the snow directly into vapor, without passing through an aqueous phase (sublimation). Tiny peaks and troughs are formed and sunlight is trapped in them, creating extra heat that cuts 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 strangely periodic fixed distance of penitentes: a combination of vapor diffusion and heat transport that produces a steep temperature gradient, and thus a higher sublimation rate.
Physicists have been able to simulate artificial versions of penitentes in the lab. But penitentes and stonewoods 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. Our spikes are mainly formed by currents, which I don’t think play a major role in penitentes formation.”
Admittedly, the NYU researchers achieved their results under idealized conditions — intentionally, according to the authors, to clearly identify and characterize the sharpening process, underlying mechanism and mathematical structure. As a result, “This study reveals a minimal set of ingredients essential to the needle and nail bed motifs,” the authors wrote. In the future, they hope to further test this formation process under various environmental conditions in the lab, such as how precipitation and surface runoff, or burial under loose sediment, can influence peak formation.
DOI: PNAS, 2020. 10.1073/pnas.2001524117 (About DOIs).