Buoyancy and Drag on Immersed Bodies

1. Fabrication of gas injection test section (see schematic and photograph, Fig. 2)

1. Drill a hole in the bottom of a tall, flat walled plastic container. Install a through-wall bulkhead fitting through this hole. Install a reducing fitting to a ~3.2 mm tube compression connection in the bulkhead fitting outlet. This will be the bubble/droplet injection port.
2. Insert a short length (~1 cm) of 3.2 mm diameter soft rubber cord in the compression connection, and tighten the fitting nut. Using a sewing pin, puncture a thin hole through the rubber cord. This will be the valve for injecting bubbles/droplets into the fluid container.
3. Fill the container with glycerin to a level of ~25 cm. Pour the glycerin slowly as a film down the container sidewall to help reduce bubble entrainment in the container. Wait for ~2 hours to allow larger bubbles to rise out of the container.
4. Mount a video camera on a tripod facing the container, with the upper portion of the liquid in view. Mount a bright light on the other side of the container, facing the camera (backlighting). Insert a diffuser sheet between the light and container to ensure even illumination.

2. Performing experiments

1. Insert a ruler or flat object of known size into the glycerin container, above the injection port, facing the camera. Record a brief video of the object. This will serve a scale to to map from bubble size in px and rise velocity in px s^-1 to m and m s^-1, respectively.
2. Using a syringe with a thin needle (e.g., 20 gauge). Inject gas bubbles of varying sizes through the rubber valve into the liquid. Use the camera to record videos of the bubbles rising through the liquid.
3. Mix oil-based food coloring with soybean vegetable oil (or other low-viscosity vegetable oil). Using the syringe, inject colored oil droplets of varying sizes into the glycerin container. Record videos of the droplets rising.

3. Analysis

1. Using software such as VLC media player, export image snapshots from the video of the ruler (Step 2.1). In an image editing software measure the pixel distance across a known length of the device. The length scaling factor can then be determined as , where L_m is the physical length of the object in meters and L_px is the object length in pixels in the image.
2. For each bubble or droplet rise velocity video, extract image snapshots from when the bubbles/droplets enter and exit the camera view window. Measure the bubble/droplet (horizontal) diameters in an image editing software (D_px). Measure the average rise velocities (U_px) as the difference in bubble/droplet nose positions divided by elapsed video times between initial and final image snapshots. Convert these pixel values to physical values as: D = sD_px and U = sU_px.
3. Evaluate bubble and droplet Reynolds numbers () and drag coefficients (Eqn. 2). Plot these values and compare with theoretical results from Eqn. 3. Fluid properties at room temperature (22°C) are:
   • Glycerin: ρ_f = 1300 kg m^-3, µ_f = 3.7 kg m^-1 s^-1
   • Air: ρ_b = 1.19 kg m^-3
   • Soybean oil: ρ_b = 920 kg m^-3

Figure 2: (a) Schematic and (b) photograph of experimental facility.