title: Universality of tip singularity formation in freezing water drops.
abstract: A drop of water deposited on a cold plate freezes into an ice drop with a pointy tip. While this phenomenon clearly finds its origin in the expansion of water upon freezing, a quantitative description of the tip singularity has remained elusive. Here we demonstrate how the geometry of the freezing front, determined by heat transfer considerations, is crucial for the tip formation. We perform systematic measurements of the angles of the conical tip, and reveal the dynamics of the solidification front in a Hele-Shaw geometry. It is found that the cone angle is independent of substrate temperature and wetting angle, suggesting a universal, self-similar mechanism that does not depend on the rate of solidification. We propose a model for the freezing front and derive resulting tip angles analytically, in good agreement with the experiments.
authors.affiliation: Institute for Aerodynamics and Fluid Mechanics, Bundeswehr University Munich, 85577 Neubiberg, Germany.
authors.forename: A G
authors.initials: AG
authors.lastname: Marín
authors.affiliation: Physics of Fluids Group, Faculty of Science and Technology, Mesa+Institute, University of Twente, 7500 AE Enschede, The Netherlands.
authors.forename: O R
authors.initials: OR
authors.lastname: Enríquez
authors.affiliation: Laboratoire Matière et Systèmes Complexes UMR CNRS 7057, 10 rue Alice Domon et Léonie Duquet 75205 Paris Cedex 13, France.
authors.forename: P
authors.initials: P
authors.lastname: Brunet
authors.affiliation: Université Libre de Bruxelles, Laboratory TIPs, Fluid Physics Unit, CP 165/67, F. D. Roosevelt Ave. 50, 1050 Brussels, Belgium.
authors.forename: P
authors.initials: P
authors.lastname: Colinet
authors.affiliation: Physics of Fluids Group, Faculty of Science and Technology, Mesa+Institute, University of Twente, 7500 AE Enschede, The Netherlands and Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.
authors.forename: J H
authors.initials: JH
authors.lastname: Snoeijer