Shape of ice stalagmites

Do ice stalagmites grow purely vertically? Our work shows that depending on the substrate temperature and the water flow rate, ice stalagmites can take a wide variety of shapes and forms. We determined a criterion that distinguish a purely vertical growth to a combined vertical and lateral growth dynamics. We also show that the main driving factor is the heat diffusion at the stalagmite's tip and that the combined knowledge of both the vertical and lateral growth allows us to determine the asymptotic aspect ratio of the ice stalagmites. Our predictions are compared and validated by experiments and can serve as a model experiment to study related physical phenomena.