The smallest stalagmites: a hydrochemical lower bound on stalagmite radius

Stalagmites grow from the repeated impact of supersaturated water drops onto a cave floor. Existing theoretical descriptions typically model the water supply as a continuous thin film driven by a steady flux. Consequently, they neglect the discrete nature of individual drops and fail to predict a non-zero minimal stalagmite radius. Here, we demonstrate that the coupled hydrodynamics and precipitation kinetics of a single drop spreading as a thin viscous film on a stalagmite tip select a specific minimal radius. Using the similarity solution for an axisymmetric gravity current of fixed volume, coupled with precipitation kinetics, we derive an explicit expression for this lower bound in terms of drop volume, fluid properties and reaction rate. For typical cave parameters, the predicted radius is of the order of two centimetres, in quantitative agreement with the smallest stalagmites observed in the field. Our results provide a falsifiable constraint on stalagmite morphodynamics and offer a prototype for scale selection in reactive gravity currents generated by discrete sources.