Impacts of Free-falling Spheres on a Deep Liquid Pool with Altered Fluid and Impactor Surface Conditions

Summary

This protocol demonstrates the basic experimental configuration for water entry experiments with free-falling spheres. Methods for the alteration of liquid surface with penetrable fabrics, the preparation of chemically non-wetting spheres, and steps for splash visualization and data extraction are discussed.

Abstract

Vertical impacts of spheres on clean water have been the subject of numerous water entry investigations characterizing cavity formation, splash crown ascension and Worthington jet stability. Here, we establish experimental protocols for examining splash dynamics when smooth free-falling spheres of varying wettability, mass, and diameter impact the free surface of a deep liquid pool modified by thin penetrable fabrics and liquid surfactants. Water entry investigations provide accessible, easily assembled and executed experiments for studying complex fluid mechanics. We present herein a tunable protocol for characterizing splash height, flow separation metrics, and impactor kinematics, and representative results which might be acquired if reproducing our approach. The methods are applicable when characteristic splash dimensions remain below approximately 0.5 m. However, this protocol may be adapted for greater impactor release heights and impact velocities, which augurs well for translating results to naval and industry applications.

Introduction

The characterization of splash dynamics arising from vertical impacts of solid objects on a deep liquid pool¹ is applicable to military, naval and industrial applications such as ballistic missile water entry and sea surface landing^2,3,4,5. The first studies of water entry were conducted well more than a century ago^6,7. Here, we establish clear in-depth protocols and best practices for achieving consistent results for water entry investigations. To aid valid experimental design, a method is presented for the maintenance of sanitary conditions, alteration of interfacial conditions, control of dimensionless parameters, chemical modification of impactor surface, and visualization of splash kinematics.

Vertical impacts of free-falling hydrophilic spheres on the quiescent fluid show no sign of air-entrapment at low velocities⁸. We find that the placement of thin penetrable fabrics atop the fluid surface causes cavity formation due to forced flow separation¹. A meager amount of fabric on the surface amplifies splashing across a range of moderate Weber numbers while sufficient layering attenuates splashing as spheres overcome drag at fluid entry¹. In this article, we explain protocols suitable for establishing the effects of material strength on the water entry of hydrophilic spheres.

Cavity forming splashes from hydrophobic impactors show the ascension of a well-developed splash crown, followed by the protrusion of the primary jet high above the surface when compared to their water-liking counterparts⁸. Here, we present an approach for achieving water repellency through chemically modifying the surface of hydrophilic spheres.

With the advent of high-speed cameras, splash visualization and characterization have become more attainable. Even so, established standards in the field call for the use of a single camera orthogonal to the primary axis of travel. We show that the use of an additional high-speed camera for overhead views is necessary to adjudge spheres strike the intended location.

Protocol

1. Configuring the experiment for vertical impacts Fill a transparent water tank of dimensions approximately 60 cm x 30 cm x 36 cm (length x weight x depth) with 32 L of water and mount a meter ruler (‘visual scale’) vertically inside the container such that the base sits atop the fluid, as seen in Figure 1a. NOTE: Depth and width of the tank must be greater than 20 times the diameter of the largest spheres used in the experiment to ensure wall effects are negl…

Representative Results

This established protocols allow for the observance of the Worthington jets arising from vertical impacts over a range of Weber numbers as seen in Figure 2c. These results are published in Watson et al.1, which can be referenced for the exact experimental conditions used to produce the data presented herein. We focus on the narrow elongated film of fluid protruding abo…

Discussion

This protocol describes the experimental design and best practices for investigations of free-falling spheres onto a deep liquid pool. We begin by highlighting steps necessary for configuring the experiment for vertical impacts. It is important to create an ideal splash environment with the use of a sufficiently large splash zone such that wall effects are negligible⁹, and a suitable visual scale for extracting kinematics^12,13,<…

Materials

3D Printer	FlashForge	Creator Pro	Dual Extrusion
Alcohol	Swan	M314	99% Isopropyl
BNC Cables	Thorlabs	2249-C-24
Caliper	Anytime Tools	203185	Dial
Camera	Photron	Mini AX-100	16GB Ram
Computer	Dell	Windows 7 Pro
Fabric	Georgia Pacific	19378	Toilet Paper
Fabric	Kleenex	10036000478478	Tissue
Laser Cutter	Glowforge	Basic
Lights	GS Vitec	LT-V9-15	Multi-LED
Microscope	Keyence	VHX-900F	Digital
Retort Stand	VWR	VWRF08530.083
Router	ASUS	RT-N12	Off Network
Ruler	Westcott	10432	Meter Ruler
Software	Open-Source	Tracker	Video Analysis
Software	Photron	Fastcam Viewer	Video Recording
Sphere	Amazon	8DELSET	Delrin
Spray	Rust-Oleum	274232	Water Repelling
Surfactant	Dawn	37000973782	Liquid Soap
Surfactant	USP Kosher	5 Gallons	Glycerin
Tensile Tester	MTS	Model 42
Trigger Switch	Custom Made
Water Tank	Mr. Aqua	MA-730	Non-Tempered Glass