Viscous Sheet Retraction
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Bush_Viscous Sheet.pdf
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Author(s)
Savva, Nikos
Bush, John W. M.
Date Issued
May 2009
Journal
Journal of Fluid Mechanics
Publisher
Cambridge University Press
Citation
NIKOS SAVVA and JOHN W. M. BUSH (2009). Viscous sheet retraction. Journal of Fluid Mechanics, 626 , pp 211-240
doi:10.1017/S0022112009005795
Version
Final published version
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1017/s0022112009005795
