A team of mathematicians has devised the most precise recipe yet for blowing perfect bubbles, and it's not just for fun and frolics. Achieving a better understanding of the dynamics at work could lead to more efficient industrial production of commercial sprays and foams, like shaving cream or Reddi-Wip—pretty much anything that has drops or bubbles in it.

Bubbles have long been serious science. Back in the 1800s, Belgian physicist Joseph Plateau outlined four basic laws of surface tension that determine the structure of soapy films. Surface tension is why bubbles are round; that shape has the least surface area for a given volume, so it requires the least energy to maintain. (As gravity pulls the liquid downward in a process known as coarsening, the shape starts to look more like a soccer ball rather than a perfect sphere.) American botanist Edwin Matzke used to build foams by hand in his lab in the 1940s, bubble by bubble, the better to examine their structure.

More recently, Irish mathematicians used computer modeling in 1994 to determine the best geometric shape bubbles can take for most efficient packing, while other scientists have used acoustic levitation—powerful sound waves—to suspend bubbles in mid-air. In 2006, Harvard University scientists figured out that adding tiny colloidal particles to the mix created a kind of coating or armor, producing much more stable bubbles that could be reshaped and molded at will. It's even possible to build rudimentary microfluidic bubble-based logic devices to transport therapeutic drugs or chemical reagents.

In search of the perfect bubble

Just two years ago, French physicists worked out a theoretical model for the exact mechanism for how soap bubbles form when jets of air hit a soapy film. They tested their model by hanging weighted fishing line from a three-foot contraption. Then they carefully dripped a soapy solution (a bit of Dawn dish soap in plain tap water) onto the top of the wires so the wires stuck together as it dribbled down. Gently pulling the wires apart again created a thin soap film. Then they zapped the film with jets of gas to see which speeds of blowing air produced bubbles, filming it all with a high-speed camera.

"We can now say exactly what wind speed is needed to push out the film and cause it to form a bubble."

The results: bubbles only formed above a certain speed, which in turn depends on the width of the jet of air. If the jet is wide, there will be a lower threshold for forming bubbles, and those bubbles will be larger than the bubbles produced by narrower jets with their higher speed thresholds. The former is often the case when we blow bubbles through a little plastic wand: the jet forms at our lips, and is usually wider than the soapy film suspended within the wand.

In a new paper in Physical Review Letters, mathematicians at New York University's Applied Math Lab have fine-tuned the recipe for the perfect bubble even further based on similar experiments with soapy thin films. "We can now say exactly what wind speed is needed to push out the film and cause it to form a bubble, and how this speed depends on parameters like the size of the wand," said co-author Leif Ristroph. The answer: you want a circular wand with a 1.5-inch perimeter, and you should gently blow at a consistent 6.9 cm/s. Blow at higher speeds and the bubble will burst. Use a smaller or larger wand, and the same thing will happen, or the bubbles will be smaller, or perhaps not form at all.

Ristroph and his colleagues also found that you can make bubbles either by blowing with a strong, steady wind on a soap film, or applying a gentle quick puff of wind on a soap film that then keeps growing even as you slow the flow of air. The latter is how most kids blow bubbles, while the first method is the one favored by street performers in city parks, or in science demonstrations. "They simply walk, sufficiently fast, with a soapy loop of rope, which provides the relative wind needed to stretch out the film," said Ristroph.

DOI: Physical Review Letters, 2018. 10.1103/PhysRevLett.121.094501 (About DOIs).