Fluids, Form, and Function: the Role of Fluid Dynamics in the Evolution of Stalactites, Icicles, and Aquatic Microorganisms

This dissertation is devoted to better understanding the role that fluids play in the selection of the shapes and functions of objects and creatures in nature. Toward that end, three specific examples are considered: stalactites, icicles, and species of colonial green algae known as Volvox. In the cases of stalactites and icicles, the object's growth is considered as a free-boundary problem. For stalactites, the coupling of thin-film fluid dynamics with calcium carbonate chemistry leads to a local, geometric growth law that is proportional to the thickness of the water layer covering the surface at any point. Application of this law to a uniformly translating shape allows a universal stalactite form to be derived; the comparison of this shape to images of actual stalactites supports the theory. In the case of icicles, the transport of the latent heat of fusion is coupled with the dynamics of both the thin-film of water encompassing the icicle and a thermally buoyant boundary layer in the immediately surrounding air. The uniformly translating shape solution is found to be parameter-free, and is, in fact, the same shape exhibited by stalactites. A comparison between this shape and icicle images validates the theory. The final example considers how advection of nutrients due to the stirring of water by the flagella of a Volvox colony leads to a metabolite uptake rate that is much greater than would occur by diffusion alone. Moreover, nutrient acquisition by pure diffusion would limit the size of Volvox species to a certain bottleneck radius at the point where diffusional uptake just meets metabolic demands, whereas advection increases the uptake in such a way as to avoid this problem entirely, thus enabling the evolution of the larger Volvox species.