A drop does not necessarily fall vertically

Drops falling from a single stalactite do not always reach the same point on the underlying stalagmite. High-speed imaging revealed that their impact positions can be scattered over several centimetres.

This dispersion is not explained by cave air currents or other external disturbances. The same behaviour was observed under controlled laboratory conditions.

The apparent randomness is generated by the falling drop itself.

What determines the width of a stalagmite?

Stalagmites grow as calcium-rich droplets impact a thin water film and deposit calcite. Their growth is commonly related to drip rate, water chemistry and cave environmental conditions.

This study asks a different question:

Could the physics of the falling drop itself influence stalagmite shape and width?

Tracking droplets from the cave ceiling to the stalagmite

582 high-speed movies · 3caves · 65 stalagmites

An instability of falling droplets

As a droplet falls through the air, its interaction with the surrounding air can generate small lateral deviations from a vertical trajectory. As a droplet accelerates, vortices develop in the air wake behind it. The wake becomes asymmetric and generates fluctuating aerodynamic lift forces. These forces continuously deflect the droplet in random horizontal directions during its fall. These deviations are amplified during the fall, producing a dispersion of impact positions.

The drop behaves like a tiny object performing a random walk through the air.

The higher the drop falls, the wider the dispersion

The dispersion of impact positions increases almost linearly with falling height.

A Langevin-like model based on the aerodynamic forces acting on the falling droplet reproduces the observed dispersion without a fitting parameter.

From falling droplets to stalagmite width

The width of a stalagmite is partly controlled by the physics of the droplets that build it.

Falling height → aerodynamic instability → impact-point dispersion → stalagmite width

My contribution

I contributed to the original idea, research design, field investigation and interpretation of the karst observations underlying this study.

Publication