Universal solution for the retracting edge of a stretched viscous sheet

Surface tension acting alone causes the edge of a fluid sheet to retract and thicken. However, whether at the edge of the hole in a bursting bubble or at the edge of a falling ribbon of molten glass, such retracting edges are often simultaneously being stretched parallel to the edge, thus modifying the flow, the rate of retraction and even thinning the edge. Remarkably, a universal similarity solution for Stokes flow in a stretched edge shows that the scaled shape is actually independent of the stretching rate, and decays rapidly to the far-field thickness. This solution justifies the use of an integrated normal-stress boundary condition in long-wavelength models of viscous sheets, and gives the detailed shape of the edge, resolving its position to the order of the sheet thickness.