The dynamics of viscous sheets

We present the results of a combined theoretical and numerical investigation of the rim-driven retraction of flat fluid sheets in both planar and circular geometries. Particular attention is given to the influence of the fluid viscosity on the evolution of the sheet and its bounding rim. In both geometries, after a transient that depends on the sheet viscosity and geometry, the film edge eventually attains the Taylor– Culick speed predicted on the basis of inviscid theory. The emergence of this result in the viscous limit is rationalized by consideration of both momentum and energy arguments. We first consider the planar geometry and deduce new analytical expressions forthe speed of the film edge at the onset of rupture and the evolution of the maximum film thickness for viscous films. In order to consider the expansion of a circular hole, we develop an appropriate lubrication model that predicts the form of the early stage dynamics of film rupture. Simulations of a broad range of flow parameters confirm the importance of geometry on the dynamics, verifying the exponential hole growth reported in early experimental studies.

See paper:   Savva & Bush, JFM (2009).

The expansion of a hole in a soap film following puncture by a needle. The hole expands at high speed in response to surface tension.