A publication in Proceedings of the Royal Society A

A single drop that falls into the air has a random trajectory, and this determines the shape of stalagmites

A ULiège research team examined the formation of stalagmites. To do this, the researchers visited several caves in the South of France to study this strange phenomenon. Their study has just been published in the scientific journal Proceedings of the Royal Society A (1).


talactites, stalagmites and other speleothems decorate the cave rooms explored each year by millions of visitors. While these elegant sculptures often fascinate people, they are also of great interest to Earth Sciences researchers. Indeed, stalagmites contain information on past climate. They result from the slow precipitation of limestone contained in the water drops impacting them (growth of about 1 mm per year). Their isotopic composition - the proportion of each variety of a chemical element - provides information on the climate conditions and vegetation contemporary to the rainwater that has infiltrated the soil over the years. A vertical cut of a stalagmite reveals its growth over the years, and hints at the corresponding climate.

While existing physical models explain the vertical growth of stalagmites well, their horizontal extension - and therefore their shape - remains poorly understood. Why are some stalagmites five times wider than others when they are not higher? The Microfluidics Lab research team (A&M Research Unit / School of Engineering) of the University of Liège tried to answer this question. With the help of experts in cave geology, they visited several caves in the South of France (including l'Aven d'Orgnac, la Salamandre and Clamouse), known for the variety of their stalagmites. "We were able to take measurements on more than 60 stalagmites, each fed by a single stalactite," explains Justine Parmentier, a researcher at the Microfluidics Lab and the first author of the scientific publication. These measurements revealed that the width of a stalagmite is strongly correlated with the vertical distance to the stalactite that feeds it. Wider stalagmites are often found in higher ceiling rooms. This led us to wonder if the width of the stalagmites would be related to the way the drops fall and impact them. »

To test this hypothesis, the team set up a very high speed camera in the cave, to record thousands of images per second, thus allowing to see the drop fall and impact on the top of the stalagmites. "We have collected more than 500 videos on 13 different stalagmites," says Tristan Gilet, head of the ULiège laboratory. To our great surprise, we observed that the drops impact the stalagmite in different places though they come from the same overlying stalactite. This effect is more pronounced for larger stalagmites, where the impact point can be dispersed over the entire surface, namely over a distance of more than 10 cm!»


The drops that form the base of the stalagmites have a random trajectory

A ULiège research team focused on the formation of the stalagmite base. A much more complex training than it seems. To do this, the researchers visited several caves in the south of France to study this strange phenomenon. This study has just been published in the scientific journal Proceedings of the Royal Society A.

The analysis of the videos showed that the drops did not systematically fall along a straight vertical trajectory, but experienced slight horizontal deviations. At first, the team thought that these deviations could be due to draughts induced by the ventilation of the cave. "We then carried out laboratory tests in a controlled space protected from any air currents," explains Justine Parmentier, "by releasing drops from the lab ceiling, we nevertheless observed the same behaviours as those observed in the cave. "The team then concluded that the drops were themselves responsible for their random deviations. But how could they be?

DeltaOfZ illustrationThe team called on the expertise of their colleagues at the Multiphysics & Turbulent Flow Computation Laboratory (MTFC / A&M Research Unit / Faculties of Applied Sciences) to better understand this phenomenon. "Any object moving quickly in a fluid (like a millimetre drop moving at 7 metres per second) generates a multitude of eddies in its wake," explains Vincent Terrapon, head of the MTFC Laboratory. "Each of these vortices, at the time of its creation, exerts a lift force on the drop - in a random horizontal direction - which slightly pushes the drop away from its initial trajectory. " By applying this physical model to drops that form stalagmites, the researchers have proven that the dispersion of the drop impact point directly results from this random motion, induced by the wake vortices during the fall. The higher the drops fall, the more they deviate from a vertical trajectory, which ultimately determines the width of the stalagmite.

Research team

ULiège researchers : Justine Parmentier, Sophie Lejeune and Tristan Gilet (Microfluidics Lab) Vincent Terrapon (MTFC)

Experts in cave geology : Dominique Genty (EPOC, U. Bordeaux), François Bourges (Géologie-Environnement-Conseil, St. Girons) and Jean-Christophe Maréchal (BRGM, U. Montpellier)

Scientific reference

Parmentier, S. Lejeune, M. Maréchal, F. Bourges, D. Genty, V. Terrapon, J.-C. Maréchal and T. Gilet, A drop does not fall in a straight line: a rationale for the width of stalagmites, Proceedings of the Royal Society A, 20 Nov. 2019

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