Universal and non-universal hole closure in a liquid layer

We study how a thin layer of viscous fluid on a solid substrate flows inward to fill an initially dry circular region, under the action either of surface tension on the free surface or of stresses in a thin elastic sheet covering the fluid. We solve the lubrication equations numerically in various scenarios, including the closure of a hole in an infinite film, the release of an annular volume of fluid, and the prying apart of two elastic discs. For surface tension (or an elastic membrane), as the hole shrinks the closing speed diverges rapidly and a universal solution is obtained that does not depend on the initial or far-field conditions and is described by approximate power laws with slowly varying exponents depending on the length scale of the contact-line regularization. For elastic bending, the closing speed diverges only logarithmically, and the closure behaviour is non-universal as it depends on the initial and/or far-field boundary conditions. We elucidate the main physical balances with an asymptotic analysis involving a multitude of nested boundary layers.