Capillary retraction of the edge of a stretched viscous sheet

Abstract

Surface tension causes the edge of a fluid sheet to retract. If the sheet is also stretched along its edge then the flow and the rate of retraction are modified. A universal similarity solution for the Stokes flow in a stretched edge shows that the scaled shape of the edge is independent of the stretching rate, and that it decays exponentially to its far-field thickness. This solution justifies the use of a stress boundary condition in long-wavelength models of stretched viscous sheets, and gives the detailed shape of the edge of such a sheet, resolving the position of the sheet edge to the order of the thickness.