Lateral shaping and stability of a stretching viscous sheet |
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Authors: | B Scheid S Quiligotti B Tran and H A Stone |
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Institution: | (1) School of Engineering and Applied Sciences, Harvard University, 02138, Cambridge, MA, USA;(2) Saint-Gobain Recherche, 39 Quai Lucien Lefranc, B.P. 135, 93303 Aubervilliers Cedex, France |
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Abstract: | We investigate the changes of shape of a stretching viscous sheet by
controlling the forcing at the lateral edges, which we refer to as lateral shaping. We propose a one-dimensional model to
study the dynamics of the viscous sheet and systematically address
stability with respect to draw resonance. Two class of lateral forcing are considered: (i) for the case that the stress at
the edges is specified, we show that a pure outward normal stress Sn is usually unfavorable to the draw resonance instability as compared to the case of stress-free lateral boundaries. Alternatively,
a pure streamwise tangential stress St is stabilizing; (ii) for the case that the lateral velocity at the edges is specified, we show that the stability properties
are problem specific but can be rationalized based on the induced stress components (Sn,St). |
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Keywords: | PACS" target="_blank">PACS 47 15 gm Thin film flows 47 20 Gv Viscous and viscoelastic instabilities 47 85 M- Material processing flows industrial applications |
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