Mathematics of laundry unveiled.

Physical Science

Have you ever wondered why laundry hung on a clothesline dries from the top down? This question so piqued the curiosity of Erik B. Hansen, a mathematican at the Technical University of Denmark in Lyngby, that he applied the rigor of mathematical modeling to the problem. Hansen reports on the secret life of laundry in the October issue of SIAM JOURNAL ON APPLIED MATHEMATICS.

"In almost everything you do, from shaving in the morning to putting your pajamas on at night, you'll find some interesting mathematics, and drying laundry is no exception," comments John Ockendon of the Mathematical Institute at the University of Oxford in England.

The most obvious explanation for top-down drying - that gravity draws the water down and out of the fabric until it is completely dry - is incorrect, says Hansen. Gravity is involved, but it plays a secondary role.

Hansen explains that water resides in discrete pores within damp cloth. Capillary forces act on these isolated islands of water, counterbalancing the tug of gravity. Therefore, gravity cannot pull water out of cloth in a continuous sheet.

Then what does cause clothes to dry from the top down? Hansen came up with an explanation for this phenomenon and used it to build his mathematical model of drying laundry.

In the model, vertical air movement causes top-down drying. To dry, hanging laundry must be cooler than the surrounding air. The air right next to the garment is also cooler, and therefore heavier, than the air around it. Gravity pulls this cooler air down across the surface of the cloth. The air current soaks up evaporated water, becoming more saturated as it sinks. Since the air flow can carry away less water vapor at the bottom than at the top, the garment dries from the top down.

But does real laundry behave as Hansen's model says it should? To find out, he used the model to predict the rate at which a garment should dry under certain conditions. Then he hung up a wet T-shirt and recorded what he observed. At first, the shirt dried more or less as predicted. As time passed, however, it began to dry more slowly. This came as no surprise to Hansen, because he had deliberately idealized some of the processes at work on the drying fabric. Despite these mixed results, Hansen claims success in reaching his general goal of better understanding the physics of drying laundry.

This kind of applied mathematical study aids the general health of the field, says Ockendon, because "mathematics gets very sterile unless it has input from the real world, and [the] drying of laundry is a perfectly good example of how you get exciting new mathematics that you would never get if you just sat at your desk."