Viscous Sheet Retraction Citation

Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. 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 considered by Brenner & Gueyffier (Phys. Fluids, vol. 11, 1999, p. 737) and deduce new analytical expressions for the 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. We demonstrate the sensitivity of the initial retraction speed on the film profile, and so suggest that the anomalous rate of retraction reported in these experiments may be attributed in part to geometric details of the puncture process. 1. Introduction Sheet retraction arises in a wide range of physical settings, ranging from fuel injectors to foams in the food industry to biological membranes (for an overview see de Gennes, Brochart-Wyart & Quéré 2003). The disintegration of fluid sheets is of primary importance in the context of fluid fragmentation or atomization (Lefebvre 1989; Bayvel & Orzechowski 1993; Villermaux 2007). Commonly, such atomization processes involve a cascade from fluid volumes to sheets to filaments to droplets, a route that depends critically on the dynamics and stability of fluid sheets and their bounding rims. Depending on the application at hand, film rupture can be either desirable, as in spray formation (e.g. Pomeau & Villermaux 2006), or undesirable, as in curtain coating …