Fluid Interface Visualizer

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.

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).

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.

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.

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.

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.

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

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.

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.

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

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.

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.

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.

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.

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.