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

1. Configuring the experiment for vertical impacts

1. 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 negligible⁹. Greater entry speeds than those described here will require greater tank depth. The visual scale used to determine drop heights and calibration of tracking software is discussed in section 7.
2. Place an additional meter ruler under the water, which can act to magnify dimensions. This visual scale is used for calibrating tracking software for underwater measurements.
3. Construct a hinged platform (‘release mechanism’) that suspends spheres above the fluid and rotates downward, to achieve tangential acceleration greater than gravity at the impactor location when released, as seen in Figure 1a. Rapid rotation is achieved by connecting the hinged platform to the center of the supporting component using elastic bands. The result is an unsupported and non-rotating impactor.
   NOTE: The platform is easily fabricated with 3D printer.
4. For impact trials, place thumb to base of hinged platform and rotate it 90° to a horizontal position for placement of spheres above the fluid.
   NOTE: Retraction is triggered when thumb is released from base of the platform.
5. Affix the release mechanism to a retort stand, such that the device can be adjusted to various heights.
6. Place the retort stand next to the tank such that the release mechanism is within the same depth plane as the visual scale. Add a weight to the base of the retort stand as needed to prevent toppling.
7. Adjust the release mechanism to the maximum desired experimental drop height. This is necessary for optimal splash visualization as discussed in section 6 and ensures the splash characteristics of interest are always within the viewing frame of the camera.
8. Attach a multi-LED light to an articulating arm such that the light is mounted above the camera, looking down onto the splash zone. Ambient light alone is insufficient to illuminate the scene at the high frame rates needed to extract splash kinematics.
   NOTE: One can never have too much light.
9. Place a black screen at the back of the water tank to aid splash and cavity visualization as seen in Figure 2.
10. Place a glass-protecting shock absorber, such as a closed-cell sponge, at the bottom of water tank and affix with weights to prevent resurfacing.
    NOTE: The height of the fluid in the tank should be such that the sphere does not interact with shock absorber prior to air cavity pinch off¹⁰.

2. Controlling dimensionless parameters

1. Conduct experiments with smooth spheres of various masses and diameters. For this, polyoxymethylene (e.g., Delrin) coin-making balls work particularly well and have no mold part line. Measure masses and diameters with an analytical balance and Vernier caliper respectively.
2. Conduct experiments over a range of heights H to generate impact velocities where m/s² is the acceleration due to gravity. Measure height with the visual scale within the camera frame.
   NOTE: Use the Auto-Tracking feature in the video analysis tool as discussed in section 7 to measure impact velocities.
3. Conduct experiments with fluid mixtures of water and suitable surfactants (e.g., glycerin or soap) to modify surface tension. Measure surface tension with a surface tensiometer.
4. Calculate Reynolds numbers and Weber numbers , where ρ is the density of the fluid, D is the sphere diameter, μ is the dynamic viscosity of the fluid and σ the surface tension of the fluid.

3. Maintaining sanitary experimental conditions

1. Conduct experiments while wearing industrial nitrile gloves and retrieve spheres from water tank with a sanitized scoop.
   CAUTION: Skin naturally produces oils which can affect the wettability of impactors and taint fluid conditions.
2. Clean the spheres with 99% isopropyl alcohol and allow to dry for 1 min in between trials to preclude the influence of impurities.
3. If using fabrics that break apart during impact, replace the water in the tank after every trial if scraps cannot be manually collected.
4. At the end of experiment, empty the tank and leave it to dry.
5. Before an experiment, clean the tank with water to remove any impurities.

4. Layering the surface with penetrable fabrics

1. Separate the fabric into square or round plies in preparation for impact trials. Use a Vernier caliper to obtain compressed thickness of the fabric.
   NOTE: Fabric thickness will change when wet.
2. Gently rest the dry fabric atop the surface of the liquid pool. Ensure that the plies do not begin descent before impactor release and replace fabrics immediately after collision.
3. Use a sanitized scoop to position the fabric below the hinged platform before releasing spheres.
4. (Optional) Conduct the following tests using a fabric sample for material characterization.
   1. Perform tensile testing using a tensile tester to determine the elastic modulus of the sample.
   2. Use a digital microscope to obtain a microscopic view of the fabric and determine fiber length using an imaging tool.

5. Preparing chemically hydrophobic spheres

1. Spray the hydrophobic base coat approximately 15–30 cm from the sphere surface. Avoid soaking the surface. Let it dry for 1‒2 min before adding additional coatings. Apply two more base coats. Allow it to dry for 30 min before applying the top coat.
   NOTE: The number of additional surface may vary based on recommendations from the product manufacturer.
2. Spray the hydrophobic top coat approximately 15–30 cm from the surface. Avoid soaking the surface. Let it dry for 1–2 min before adding additional coatings. Apply two or three more coatings of top coat. Allow to dry for 30 min for light use and 12 h for full use.
   NOTE: The number of additional surface coats may vary based on recommendations from the product manufacturer.
3. After approximately 20 trials, the hydrophobic coating becomes compromised due to excessive handling. Remove coating with 99% isopropyl and repeat steps 5.1 and 5.2.

6. Synchronizing cameras for splash visualization

1. Place a high-speed camera with a suitable lens perpendicular to the impact axis and in-line with the surface of the fluid.
   NOTE: A 55 mm prime lens provides a good starting point.
2. Where fabrics are to be used, add an additional high-speed camera to the experiment to provide a top-down view of the impacts, as seen in Figure 1b.
3. Synchronize multiple cameras to a computer using the following steps.
   1. Connect both output terminals of the horizontal camera to both input terminals of the additional camera using BNC cables.
   2. Connect the trigger switch to the horizontal camera only.
   3. Plug Ethernet cables from both cameras into an off-network router connected to the computer.
      NOTE: In the absence of a router, connect Ethernet cables of cameras to separate computers.
4. In the video acquisition software, configure the cameras with the following settings. Set frame rate to a minimum of 1,000 fps, set screen resolution to the desired resolution. Set the shutter speed to 1 per frame second and set trigger mode to end.
5. From maximum release height, conduct a series of test trials to ensure that the Worthington jets are within the video frame.
6. Adjust the camera position and focus accordingly until the desired visualization quality is achieved.
7. After recording, extract kinematic and geometric measurements from videos using a suitable video analysis tool. Use Tracker, an open source analysis tool or any software of comparative capability.

7. Digitizing impact kinematics with tracker software

1. Select calibration stick from the Tracker toolbox and match it to the visual scale (Figure 2a), making the stick as long as possible.
2. Click calibration stick and set the scaling value to the length of the visual scale spanned by the stick. That is, if the calibration stick spans 1 cm on visual scale, set scaling value to 1.
   NOTE: This ensures measurements taken from software are in the order of centimeters.
3. Toggle video playback by clicking start and stop and set video to the desired frame.
4. Select measuring stick from the Tracker toolbox and extract splash crown height k, cavity width b, cavity depth l, and Worthington jet height h, as seen in Figure 2b,c.
   NOTE: The measuring stick is adjustable at both ends and can be used simultaneously with other toolbox selections.
5. Select protractor from the Tracker toolbox and measure the separation angle q of fluid with respect to the impactor, as seen in Figure 2b. The protractor is adjustable at both ends and can be used simultaneously with other toolbox selections.
6. Select the Auto-Tracking feature in the software to record temporal position and velocity data. When tracking is interrupted due to lack of clarity in the video, use manual tracking until clarity is obtained and auto-tracking is resumed.