Water entry of small disks, cones, or anything

TL;DR

This paper develops a unifying scaling law to predict water entry cavity behaviors across various impactors, including spheres, disks, cones, and liquid jets, based on impactor hydrodynamics rather than just geometry.

Contribution

It introduces a universal scaling framework using modified dimensionless numbers that accounts for different impactor types and their hydrodynamic properties.

Findings

Unified collapse regimes across impactor types

Good data collapse with the new scaling

Hydrodynamics govern cavity behavior more than geometry

Abstract

The water entry of solid and liquid bodies has been studied for over a century, and various researchers have classified the different behaviors that occur when the gas-filled cavity collapses. Although four main cavity collapse regimes have been described and classified for the water entry of small, dense, hydrophobic spheres, only some of these regimes have previously been seen for other impactors, and the scaling used for spheres is not universal across all impactor types. In this paper, we create a unifying scaling to predict cavity collapse regimes, pinch-off time, and pinch-off depth using modified definitions of the Bond, Weber, and Froude numbers for various impactor types. The scaling is based on the downward cavity velocity and an effective diameter, which considers the drag coefficient of the impactor. The impactors we tested include dense solid spheres, disks, and cones, as well as continuous liquid jets and droplet streams. Data for all of these impactor types and behaviors are plotted together with good collapse. Our results indicate that the hydrodynamic characteristics of the impactor, not simply its geometry, govern the global behavior of the cavity.