Many a white shirt has met the disaster of a nearly-empty condiment bottle. One moment, you’re carefully squeezing out ketchup, and the next — sppplltlttt — you’re covered in red splatters. This messy phenomenon of gas displacing a liquid is widespread, showing up in condiments, some volcanic eruptions, and even the reinflation of a collapsed lung. Researchers have now constructed a mathematical model to fully capture and explain the process.
When you squeeze a container with both air and a liquid — like ketchup — in it, the air is easily compressed but the liquid is not. The extra pressure of the air creates a driving force that pushes the liquid out, despite its viscous resistance. Most of the time, these two forces are balanced, and the ketchup flows smoothly out of the container. But when the volume of ketchup is small compared to the air, squeezing can overpressurize the air, driving the ketchup out in an uncontrolled burst.
Luckily, the mathematics also suggest a solution to this problem: squeeze more slowly and double the size of the nozzle. You can also, they note, simply remove the top to avoid splatter. (Image credit: Rodnae Productions; research credit: C. Cuttle and C. MacMinn; via Ars Technica; submitted by Kam-Yung Soh)