Introduction: Fluid Interface Visualizer

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About: Account to share rapid-prototyped scientific devices used in the Harris Lab at Brown Engineering. Our hope is that our posts will serve as accessible launching points for your future applications and designs.…

The concept behind this demonstration device is based off of the idea presented in the article "Measuring the two-dimensional structure of a wavy water surface optically: A surface gradient detector" by Zhang and Cox, Experiments in Fluids, 1994.

A simple schematic of the working principle is provided above, adapted from the original publication. When the setup is viewed from directly above, the water slope is mapped to a particular color on the target pattern below via the physics of optical refraction.

The goal here is to reproduce the striking qualitative effect with a low-cost setup, although the technique can be used for quantitative measurements of the shape of a fluid interface with a more refined experimental setup and post-processing software.

Supplies

  1. Two (2) Plastic Solo Cups, 16 oz. (We used Hefty Party Cups).
  2. Plastic Petri Dish Base, 90 mm diameter. Link.
  3. Three (3) Credit Card Sized Magnifying Lenses. Link.
  4. X-acto knife.
  5. Cell phone or tablet.
  6. Electrical tape (optional).

Step 1: Stack Lenses

Stack three lenses, making sure they are all in the same orientation. Note that each lens has a "rough" and a "smooth" side: make sure they are all facing in the same direction within the stack. Ultimately the rough side will face downwards towards the color target pattern. (Optionally) tape the edges of the stack-up as shown.

Step 2: Cut Lens Slot

Mark a horizontal line 75 mm from the base of the cup. For the Hefty solo cup used here, this corresponded to the highest ridge of the parallel grip lines. Using the X-acto knife, carefully cut a slit about 2.5" (6.4 cm) long. Make the same cut on the opposite side of the cup.

Step 3: Insert Lens

Gently insert the lens stack in one of slots, pushing it through gently and guiding it through the corresponding slot on the opposite side of the cup. Adjust the lens so that it approximately centered in the middle of the cup when viewed from above.

Step 4: Cut Bottom

Cut a hole in the bottom of the cup, approximately 1.5" (3.8 cm) in diameter. For the Hefty brand cup, we used the existing ridge as a guide. (Optionally) tape the cut edges with electrical tape.

Step 5: Adjust Cup

Before proceeding, adjust the sides of the cup if necessary so that the view from above is unobstructed.

Step 6: Install Petri Dish

Insert petri dish in the top of the cup. You may need to twist and push it gently to install it securely. It should provide a snug fit that holds itself in place. Verify that the dish is secure, flat, and level before proceeding.

Step 7: Prepare Eyepiece

The second cup will be used as an eyepiece for live viewing and/or setting the working distance for a camera. This cup also serves the role of blocking ambient light and reflections. For this step you need to cut a circle out of the base exactly as before, and tape the edges, if desired. Also make two small relief cuts (approximately 0.25" or 6 mm) on opposite sides of the rim of the cup as shown.

Step 8: Target Setup

Download the sample target pattern on your phone or tablet. Turn up to full brightness.

Step 9: Alignment

Stack the assembly as shown on the target. While viewing by eye with your eye at the level of the eyepiece (top cup), move the position of the optical assembly and/or target until it is centered. You should see mostly white (corresponding to the center of the target) if aligned properly.

Step 10: Sample Experiment 1: Sessile Droplet

Now you can begin to experiment with the technique. An easy first experiment is to deposit small droplets on the Petri dish and view the effect from above with the eyepiece. Explore how the size of the color pattern changes the observed effect in the droplet, or how your viewing orientation changes the effect.

Step 11: Sample Experiment 2: Cheerios Effect

Now fill the Petri dish halfway with water. Put two Cheerios on the surface of the fluid. The small deformations they create at the surface (known as their meniscus) should become visible. You will observe that the Cheerios tend to attract each other, which is a result of surface tension pulling them together. Try with other cereal or small floating objects.

Step 12: Sample Experiment 3: Capillary Waves

Again fill the Petri dish halfway with water. Shake the table by bumping it repeatably (or carefully using a piece of equipment such as a drill, blender, or massage gun). The waves on the surface of the water should become visible. Play with other color patterns.

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Step 13: Be Creative!

While the circular rainbow target pattern provided here is a good place to start, there is no need to stick to that pattern. Any non-uniform color background will work, leading to exciting and unexpected results.

Step 14: Bonus Technique: Shadowgraph

The setup can be readily adapted to another visualization technique known as shadowgraphy. In this case, the magnifying lens serves to collimate a point source of light (i.e. align the light rays to be parallel), which then passes through the fluid interface. The wavy air-water interface acts as a lens, focusing light in certain areas while defocusing in others.

For this setup, some additional materials are needed:

  1. One additional Solo Cup, 16 oz.
  2. One additional Petri Dish, or the lid from the original dish.
  3. Translucent Screen Material, approximately 4" x 4" (10 cm x 10 cm). (Vellum or tracing paper works well).

Step 15: Remove One Lens

Remove one lens from the original stack-up of three. Reinsert the two remaining lenses. Tape if desired.

Step 16: Prepare Screen Holder

Cut the additional cup all the way around, approximately 45 mm below the rim. For the Hefty brand cup, we used the same ridge as a guide. Cut two small relief cuts (approximately 0.25" or 6 mm) on opposite sides of the rim as before. (Optionally) tape the cut edges with electrical tape.

Step 17: Assembly

Place the screen holder on top of the original optical setup with the two lenses. On top of the screen holder, place the extra petri dish (or lid) upside down, and then the translucent screen material on top of that, as shown. If the screen material is not flat, cut it to the shape of the petri dish and tape it down along the edges.

Step 18: Illumination

Fill the petri dish halfway, and carefully place the entire assembly on a localized "point" light source. For this step, we used the flashlight LED from an iPad tablet.

Step 19: Alignment

Move the optical assembly so the bright patch is centered on the projection screen, as shown. For taking photos, it can be helpful to make some small marks on the screen for focusing the camera.

Step 20: Make Some Waves

As in Sample Experiment 3, make some waves by bumping or forcing the table. You should see bright and dark patterns appearing on the screen. Depending on the wavelength and amplitude of the waves, you may need to move the screen nearer or farther away from the water to see the focusing effect most clearly.

For the visualization shown here we used a massage gun pressed on the table nearby to provide a constant frequency periodic forcing. At low amplitude the waves appeared as rings (circularly symmetric), whereas at high amplitude they destabilized into a star-like pattern.

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