Say that title five times fast, I dare you. But seriously, folks, a pair of physicists from the University of Illinois recently published research concerning the formation of limestone structures in the thermal springs of Yellowstone National Park. While their discussion also touched on the terraces, I’m sticking to domes and stalactites. If you want to know more, the article will be published soon in Physical Review E.
Making Travertine
The particular type of limestone is a porous calcite called travertine. Water seeps downward through the soil, eventually coming into contact with hot gasses rising from a magma chamber. These gasses heat the water and infuse it with carbon dioxide (CO2). Combining with water (H2O), carbonic acid forms (H2CO3).
Rising up through limestone layers, the weakly acidic water dissolves the limestone and gathers calcium ions. The carbonic acid loses a positive hydrogen ion and begins to react with the calcium in the water, forming calcium carbonate (CaCO3), water, and carbon dioxide. When the hot water flows through a vent, it begins to release carbon dioxide, and the calcium carbonate forms a precipitate (falls out of the water), depositing itself on convenient surfaces.
Stalactites occur in caves, where water stuck to the ceiling through adhesive properties follows a slope to find a low point. There it deposits travertine as it waits for more water to collect until a droplet large enough to break the surface tension forms and falls. At Yellowstone, stalactites can grow as fast as an inch per year (fast for stalactites, but much slower than the domes and terraces).
Domes can form around the vents that spill hot spring water where the surrounding ground is flat. A thin layer of water deposits circular layers of travertine, building up into a dome shape. Near the edges, the water becomes too thin and begins to form rivulets, resulting in the fluting visible in the sides of the domes pictured. They grow as much as 1-5 mm a day.
Modeling Domes
Past research has focused on the small processes involving microbes and and crystal lattices. The work of Pak Yuen Chan and Nigel Goldenfeld tries to take in whole structures, investigating domes and stalactites macroscopically.
There are two ways to mathematically describe a system. One is a top-down method in which the scientists examine the system, gather data, and use statistics to make an equation that fits the data. The other is a ground-up method in which scientists use the equations that describe the processes that work together in the system. Then they figure out how to merge these processes into one big equation that describes the whole system.
The researchers had used the top-down method in the past and successfully described the building of domes and stalactites. Now, trying the ground-up method, the physicists did not find the fluting that occurs on the edges of domes. More problematic, they found that domes should be “unstable” structures, meaning that they should not arise spontaneously, and thus we should not find them in nature. Considering that the researchers probably wouldn’t be studying the domes if they weren’t found in nature, this is rather a serious problem. Why the wrong result?
Approximation. If physicists included every little detail of a system, the equations would be too large and unwieldy. Instead, they simplify or get rid of the factors that don’t matter as much or would complicate the equation beyond usefulness. One of the factors that the scientists threw out, in calculating the formation of domes and stalactites, is surface tension. Unfortunately, surface tension turned out to be critical in the formation of the domes.
More Success with Stalactites
Making the same approximation in trying to describe the growth of stalactites, they found that stalactites should indeed arise naturally. Surface tension only affects the speed at which the stalactites build. Surface tension obviously doesn’t affect domes and stalactites equally.
In domes, the spring water spreads out over a growing area. The layer of water becomes thinner and thinner until forces between the water molecules pull it into tiny rivulets. These rivulets cause the fluting on the edges of the domes. As you may see in the image, the “analytical” or ground-up model matches the actual dome up until the fluting occurs.
As water flows down stalactites, it covers a smaller and smaller surface. Since the layer grows thicker rather than thinning out, the water doesn’t separate into rivulets. In fact, surface tension only matters at the tip where droplets of water accumulate and fall.
The moral of the story is, surface tension plays a critical role in the formation of the domes but not stalactites.
Image Credits:
Mammoth Springs — Wendy Seltzer, flickr’s wseltzer
Stalactites — Tom Hodgkinson, flickr’s hodgers
Dome images — the researchers, Pak Yuen Chan and Nigel Goldenfeld