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.
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.
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 landing2,3,4,5. The first studies of water entry were conducted well more than a century ago6,7. 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.
1. Configuring the experiment for vertical impacts
2. Controlling dimensionless parameters
3. Maintaining sanitary experimental conditions
4. Layering the surface with penetrable fabrics
5. Preparing chemically hydrophobic spheres
6. Synchronizing cameras for splash visualization
7. Digitizing impact kinematics with tracker software
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 above the free liquid surface. In Figure 3 we show a meager amount of fabric amplifies splashing while sufficient layering attenuates splash back. Results are non-dimensionalized using the sphere diameter D as seen in Figure 3b.
We show the relation between non-dimensionalized cavity properties such as cavity depth , splash crown height , cavity width and Weber number de Figure 4a–d. Results are captured with a single frontal high-speed camera in a well-lit environment. A representative camera view is seen in Figure 2b. Across the range of experimental de Figure 4, dimensions of cavities created by a sphere impacting a single layer of fabric show little variation.
We consider the trajectory of spheres after impact with the interfacial surface and track temporal position data until cavity pinch off occurs as seen in Figure 5a. We then smooth the data with a Savitzky-Golay filter11 to remove the effects of experimental noise prior to numerical differentiation. The resulting velocity curves in Figure 5b are again smoothed prior to numerical differentiation for obtaining necessary for force analysis.
Figure 1. Schematic of the experimental setup. (a) High-speed cameras capture frontal and overhead views with diffuse lighting positioned above the frontal camera. The trigger switch is optional, given the availability of manual controls in video recording software on the computer. (b) Photo sequence of hydrophilic sphere impact on a thin penetrable fabric atop the fluid, filmed using the overhead camera. A black dot is used to ensure no rotation present during free fall. Please click here to view a larger version of this figure.
Figure 2. Splash visualization for hydrophobic sphere impact on an unaltered surface. The photo sequence shows (a) water entry, (b) splash crown ascension and air-entrapment, (c) Worthington jet formation and, (d) jet breakup for a representative splash. Sphere has impact velocity of m/s. A meter stick is used to calibrate measurements within the video analysis tool, used to measure splash crown height , cavity width , cavity depth separation angle and Worthington jet height . Please click here to view a larger version of this figure.
Figure 3. Splash heights across Weber number (). (a) Worthington jet height vs. , with vs. shown in (b). Number preceding "Ply" denotes the layers of fabric. Please click here to view a larger version of this figure.
Figure 4. Variation of cavity dimensions across Weber numbers. Relation between and the (a) separation angle , (b) cavity depth , (c) splash crown height , and (d) cavity width . Properties are non-dimensionalized in terms of sphere diameter, . Error bars denote standard deviation for the average of five trials at each point. Figure is modified from Watson et al.1. Please click here to view a larger version of this figure.
Figure 5. Representative kinematics of sphere during underwater descent. Temporal tracks of (a) vertical position and (b) velocity for impacting spheres with 0- to 4- layers of fabric atop the water. Trajectories are non-dimensionalized in terms of the sphere diameter, and impact velocity respectively. Please click here to view a larger version of this figure.
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 kinematics12,13,14,15,16,17,18,19,20,21. While shock absorbers can be improvised from excess lab materials, they must be sanitized before the experiment with water and a suitable dirt removing agent. Failure to clean the shock absorber and the tank can lead to the introduction of impurities during an experiment and alter splash characteristics. In the literature, there exists a lack of detail regarding maintenance of experimental cleanliness and as such, this article presents guidelines for obtaining consistent results from water entry trials.
The techniques described above are subject to tuning as seen in previous studies. The spring-actuated release mechanism employed by the authors can be substituted with electromagnets15 when using ferrous spheres. The ease of use of the method is improved when high-speed cameras are set to automatically trigger after spheres fall through photocells12 or infrared triggers22,23, but these add complexity. Impactor surface treatments to control wettability can also be done by using more rigorous approaches as seen in Duez et al.8. For example, spheres grafted with octyltriethoxysilane, rinsed with isopropyl and heated in an oven at 90 °C achieve super-hydrophobicity8. The protocol can be further tuned for improved cavity visualization by replacing the black screen (shown in Figure 1a) with backlighting, which makes cavity features more pronounced3.
Care should be taken when considering temporal kinematics for theoretical investigations. Temporal position tracks present less distortion than for velocity tracks but require smoothing prior to numerical differentiation1,3,15. The Savitzky-Golay filter performs a polynomial regression on a range of equally spaced values to determine the smoothed value for each point and can more faithfully maintain a track's salient features11. For tracking sphere position, a second-degree polynomial within the Savitzky-Golay filter preserves the track's salient features while removing experimental noise. Finally, researchers have choice of the moving average span of the filter, which should be as small as possible while still achieving the desired level of smoothing.
The established protocol is not restricted to the list of materials presented here and can be undertaken on a larger scale to generate greater impact velocities and increased range of dimensionless parameters which augurs well for translating results to naval and industry applications.
The authors have nothing to disclose.
The authors would like to acknowledge the College of Engineering and Computer Sciences (CECS) at the University of Central Florida for funding this project, Joshua Bom and Chris Souchik for splash imagery and Nicholas Smith for valuable feedback.
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 |