There's a new physicist in our office - a summer intern named Moriel. Over her first few days in the office, Moriel gave us each one of her unique business cards, unique because they include a built-in physics experiment. Impressive. Most impressive. So naturally, we had to try them out...
And voila! Here's a video of our boat race between a soap-powered business card and a card without any propellant.
As you can see, the business card with dish soap on the stern (the one on top) took off like a, well, jet while the plain paper one was still until it was pushed aside in the wake*. Why does this happen?
Liquids have surface tension. Think of the water in the tray in the video. Under the surface, the water's molecules pull on one another in every direction. But at the surface, there is air, not water, above, and the water molecules only pull down. This makes a sort of coating at the surface. It's helpful to imagine that the water is like stale pudding with a crusty top.
The dish soap, however, disrupts the water molecules' attractions to one another, relaxing the tension between the molecules and allowing them to spread out from one another. (This happens because the molecules of the soap - a surfactant - are attracted to the water on one side and to one another on the other side.) This is easy to see in the confetti blast video below. The confetti is carried along in the wake formed from the water-soap interaction.
In the case of the boat experiment, the rectangular notch at the back of the boat helps to steer all the water away from the back of the boat during the water-soap interaction, propelling the boat forward. The second soap-free boat is pushed aside by the wake of the soap-water interaction as it expands out and away from the soap-powered boat.
The dish soap surface tension trick also works with milk, as you can see in this video. The food coloring is less dense than the milk, so it stays on top, carried along for the ride just like the confetti.