Universality of Tip Singularity Formation in Freezing Water Drops

TL;DR

This paper investigates the universal formation of pointed tips in freezing water drops, revealing that the tip geometry is governed by heat transfer and solidification front dynamics, independent of external conditions.

Contribution

It introduces a model linking the freezing front geometry to tip formation, demonstrating universality and self-similarity in the process.

Findings

Tip angles are independent of substrate temperature.

The solidification front dynamics determine tip geometry.

The proposed model accurately predicts observed tip angles.

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 observations.