A drop does not fall in a straight line: a rationale for the width of stalagmites

Drops loaded in calcium ions detach from stalactites and impact the underlying stalagmites, thereby allowing these latter to grow through calcite precipitation. Nevertheless, little is known about the influence of the drop free fall and splash dynamics on stalagmite shape and width. Through high-speed imaging of impacting drops on stalagmites from several caves, we observed that the impact point position of the drops is scattered, sometimes over several centimetres. We show that this dispersal has no external cause and must, therefore, be self-induced. Using a Langevin-like equation, we then propose a prediction of the impact point dispersal as a function of the falling height travelled by the drops. We finally show that measured stalagmite widths are correlated to the dispersal in the impact point position of the drop.