Form of spinning liquids in diverse geometries

TL;DR

This paper investigates how liquids behave in various rotating containers, revealing how surface topology changes with speed and geometry, including a unique instability in conical vessels causing liquid expulsion.

Contribution

It provides experimental insights into the surface topologies of spinning liquids across diverse geometries and identifies a critical speed leading to spontaneous liquid expulsion in cones.

Findings

Surface topology transitions from sphere to torus with increased rotation speed.

In conical vessels, liquid always remains at the apex regardless of spin speed.

A critical angular speed causes liquid to be expelled from the cone, breaking symmetry.

Abstract

A series of experiments for steady state rotation of water in vessels of various geometries is presented. The experiments focus on the geometrical characteristics of the rotating liquids and the change in their surface topology, from that akin to a sphere to that of a torus (i.e., from genus 0 to 1), for sufficiently large angular speeds. Cylindrical, planar rectangular, cubic, spherical, and conical containers are considered. The cone is an exception as some liquid always remains in its apex, no matter how fast the spin. It is shown also that for any amount of liquid within, there exists a critical angular speed above which the liquid can no longer be confined and is therefore expelled from the cone spontaneously breaking the symmetry. This instability is investigated experimentally.