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Fun with Flat Fluids |
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by Shawn Carlson |
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Rutgers's method is as ingenious as it is simple. He poises a reservoir of soap solution above two stretched monofilaments (single-strand string, such as 20- or 30-pound fishing line) and allows gravity to draw the solution over them. Once the filaments are thoroughly wet, he slowly separates them with four fine threads. A fast-flowing and extremely uniform soap film forms between the filaments. When he wets a small object, such as a toothpick, and pokes it into the flow, vortices form in the object's wake. The result is an awe-inspiring display of turbulent motion in two dimensions. I have now spent hours ruminating the complex interactions between patterns of vortices that I have created with toothpicks, hair combs and knife edges. A plastic two-liter soda bottle, hanging upside-down, makes an ideal reservoir for the soap [see inset diagram at above right]. In the bottom, cut a large hole (for refilling the solution) and two small holes (for stringing the monofilaments). The solution will drain out the bottle cap through a five-centimeter length of soft silicone tubing, which you can buy at an aquarium supply store. Drill a hole in the bottle cap with a diameter slightly greater than the inner diameter of the tube. Then cut the tip at a diagonal and thread the tube through the hole. This should create a watertight seal. If not, a dollop of aquarium cement will.
The bottle hangs from a short piece of monofilament, perhaps 30 centimeters long, strung through the small holes. A second piece of monofilament, four meters long, will guide the soap solution. Fold this piece in half, thread the two ends through the two small holes and pull them out through the tubing. At this point, you can screw the cap back on the bottle. To control the flow of solution through the tubing, attach an adjustable hose clamp, which you can find at any hardware store. To smooth out the flow as it moves onto the filament, Rutgers slides a disposable plastic pipette tip over the end of the tube, but you can also use the neck of a plastic eyedropper. You may have to trim the tip to keep the fluid flowing fast enough to maintain the film. We hung the apparatus from a beam in my workshop, but Rutgers recommends a wooden frame that can be easily set aside for later use. The monofilaments are kept taut by a large rubber band at the bottom [see illustration above]. Tie the two strands together, pass them through a small plastic funnel and tie them to the rubber band. A plastic tube from the funnel drains the solution into a container. Or you could just let it drip onto a large towel or into a pan. Last, take four thin threads about 50 centimeters long and attach a paper clip to one end of each. Tie the other ends to the monofilament. To create the film, bring the filaments together and open the hose clamp to wet them thoroughly. Then gently separate the filaments by pulling on the threads and secure the paper clips on hooks screwed into the wooden frame. This forms a film with a long straight section in which the film flows with a nearly constant speed. Opening the hose clamp increases the speed. The film will break often during your experiments, so just repeat this procedure to regenerate it. The ideal film-making mixture is a 1 to 2 percent solution made by combining one or two parts of clear liquid dishwashing soap with 100 parts water. In English units, a 1 percent solution results from one teaspoon of soap in one pint of water. Whatever you do, avoid those bubble-blowing fluids. Gravity limits a bubble's lifetime by draining fluid away from the top until the bubble ruptures. To slow this down, toy companies add glycerin to increase the solution's viscosity. But viscosity is the last thing you need if you're studying turbulence, because high viscosity damps out turbulent motion. The film flows between about 0.5 and 4 meters per second (1 to 9 mph)Ñfar too fast to study the millimeter-size vortices by eye. Moreover, the turbulence can be seen only under high-contrast lighting. You'll need a strobe light or video camera with a Òsports shutterÓ option, which limits exposure on each video frame to between 1/1,000 and 1/10,000 of a second. Most new camcorders have this feature. You can also take fantastic still photographs using a fast shutter and high-speed film. Rutgers recommends ASA 3200 black-and-white film (which provides the best contrast) and a shutter speed of 1/2,000 of a second or faster. The light source must be bright enough to compensate for the quick shutter, and the best way to create high contrast is to use monochromatic light. Rutgers uses a low-pressure sodium ÒsoxÓ lamp, which generates an intense band of yellow light with a wavelength of around 585 nanometers. Because essentially all the energy goes into a single wavelength, you don't need a high-wattage bulb. An 18-watt sox bulb is plenty bright and retails for about $40. Unfortunately, it requires a fixture with an electric ballast, which costs about $100. You can find such fixtures at most industrial-lighting specialty stores. To save money, check a local industrial liquidator or an on-line auction site such as eBay. com. You'll want a floodlight with a trunnion fixture that can be mounted to a tripod. If you're in the U.S., make sure the fixture is compatible with a 120-volt outlet.
As an alternative to a special lamp, Mike Rivera of the University of Pittsburgh suggests adding powdered milk to the soap solution. Place a black cloth behind the milk film and light the setup with any bright lamp. The milk film scatters more light where it is thicker, and this can provide enough contrast to show what's happening. I can show turbulence using this technique, but the results have not been as good as with sodium light. You may have better luck with a spoonful of white paint. Let me know what you find. Reflected energy reaches the camera from both the front and back surfaces of the soap film. These two light trains can interfere to create fringesÑwidely spaced dark and light bands whose separation varies inversely with the thickness of the film. Rutgers reports that he can often get a uniformly bright surface in his laboratory, which means that the variation in film thickness is less than 100 nanometers. But the best I've been able to manage is six fringes. Turbulent flows will contort the fringes, making flow patterns visible much like smoke in a wind tunnel. Try two simple experiments. A cylindrical obstruction, such as a toothpick, sheds pairs of oppositely rotating vortices. When two toothpicks are placed side by side, the leftmost vortex of the right toothpick interacts with the rightmost vortex of the left toothpick with a repulsive force. Can you decipher how the force between these objects changes with the separation between them? You can also experiment with shock waves. Just open the hose clamp until the flow speed is so fast that a bow shock, like the wake of a boat, appears around a toothpick. The shock wave moves toward the sides, but when it encounters fluid that is flowing too slowly, it reflects back to create a classic diamond shape. I've enjoyed examining the flow around knife blades and through the teeth of a hair comb. And I've delighted in repeating an experiment conducted by Jun Zhang of New York University. Tie one end of a silk thread to a toothpick and let the thread whip back and forth in the flow. The motion of the thread is strikingly similar to the tail action of a swimming fish. You'll find a great many more ideas at www.physics.ohio-state.edu/~maarten on Rutgers's Web site.
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Maarten
A. Rutgers makes soap films three stories tall. And not just for fun.
Some of today's most intractable physics conundrums involve turbulent
fluids. Physicists often look for ways to experiment with simpler, two-dimensional
systems to check their ideas before they tackle real-world, three-dimensional
problems. Rutgers, a professor at Ohio State University, has mastered
2-D fluids. So I was quite honored when he recently came to my home laboratory
to teach me his secrets for making a lab-size version. 
