Physicists have figured out how wrinkles erase themselves naturally — no Botox needed.
But Joan Rivers shouldn’t visit the laboratory just yet. These wrinkles appear not on skin, but on thin, floating sheets of polymers.
In a pair of papers published online July 14 in Physical Review Letters, scientists report how sharp folds can transition into smoother wrinkles, and how wrinkles themselves vanish toward the edges.
On a fundamental level, the research describes the mathematics behind everyday experiences of wrinkles, everywhere from the surface of pudding to a poorly made bed. “These are things you see everywhere, in beautiful and amazing deformation,” says materials scientist Douglas Holmes of Princeton University, coauthor of one of the studies. “It’s nice to be able to probe them.”
More practically, such insights could one day improve technologies that incorporate thin films, like flexible solar panels or tissues grown for biological applications.
In the first study, a team led by Jiangshui Huang of the University of Massachusetts Amherst tackled how wrinkles smooth themselves out toward the edge of an elastic sheet.
Imagine cramming a corrugated sheet edge-to-edge against a smooth one. One way the sheets can accommodate the incompatibility is for the corrugated one to develop a series of sharp, branching folds along its edge. But Huang saw something different when he floated a thin, wrinkly sheet of polystyrene on water and butted it up against a smooth one. Instead of a number of sharp folds, more and more tiny wrinkles appeared toward the edge, to smoothly accommodate the difference between the two sheets.
“It took us a little while to even visually recognize that we’d seen something a bit different,” says team member Narayanan Menon, a physicist at the University of Massachusetts Amherst. Similar elastic films, from shrink-wrap to skin to biomembranes, should exhibit the same sort of smooth cascade, he says.
In the second study, another team from the same university looked at how sharp folds transition into smooth wrinkles when a sheet is pinched in one spot and pulled up, like pulling a tissue out of a box.
To most people, wrinkles and folds look similar, but to physicists they are very different beasts. Folds concentrate strain along their length, while wrinkles distribute strain evenly. Holmes, who did the work while a graduate student at UMass Amherst, mapped out how one flowed into the other in his pinched sheet.
Very few researchers have looked before at how common this phenomenon might be. The new study “shows that the transition between wrinkles and folds is more universal than we expected,” says Enrique Cerda, a physicist at the University of Santiago in Chile who has studied similar features in other thin films.
Surprisingly, the folds also increased the stress in the rest of the sheet, instead of concentrating it along the folds, as usually happens. That may be because of the way the sheet was pinched, in its center. “The geometry can really alter how the rest of the material responds,” Holmes says.
Such studies could be important for understanding how organs grow in embryos, Holmes says, where wrinkling tissues dictate the start of, for instance, an eye.