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dc.contributor.authorSrinivasan, Siddarth
dc.contributor.authorWei, Zhiyan
dc.contributor.authorMahadevan, Lakshminarayanan
dc.date.accessioned2019-09-11T22:21:22Z
dc.date.issued2017-07-27
dc.identifier.citationSrinivasan, Siddarth, Zhiyan Wei, and L. Mahadevan. 2017. Wrinkling Instability of an Inhomogeneously Stretched Viscous Sheet. Physical Review Fluids 2, no.7: 074103.en_US
dc.identifier.issn2469-990Xen_US
dc.identifier.urihttp://nrs.harvard.edu/urn-3:HUL.InstRepos:41343849*
dc.description.abstractMotivated by the redrawing of hot glass into thin sheets, we investigate the shape and stability of a thin viscous sheet that is inhomogeneously stretched in an imposed nonuniform temperature field. We first determine the associated base flow by solving the long-time-scale stretching flow of a flat sheet as a function of two dimensionless parameters: the normalized stretching velocity α and a dimensionless width of the heating zone β. This allows us to determine the conditions for the onset of an out-of-plane wrinkling instability stated in terms of an eigenvalue problem for a linear partial differential equation governing the displacement of the midsurface of the sheet. We show that the sheet can become unstable in two regions that are upstream and downstream of the heating zone where the minimum in-plane stress is negative. This yields the shape and growth rates of the most unstable buckling mode in both regions for various values of the stretching velocity and heating zone width. A transition from stationary to oscillatory unstable modes is found in the upstream region with increasing β, while the downstream region is always stationary. We show that the wrinkling instability can be entirely suppressed when the surface tension is large enough relative to the magnitude of the in-plane stress. Finally, we present an operating diagram that indicates regions of the parameter space that result in a required outlet sheet thickness upon stretching while simultaneously minimizing or suppressing the out-of-plane buckling, a result that is relevant for the glass redraw method used to create ultrathin glass sheets.en_US
dc.description.sponsorshipEngineering and Applied Sciencesen_US
dc.description.sponsorshipOrganismic and Evolutionary Biologyen_US
dc.description.sponsorshipPhysicsen_US
dc.language.isoen_USen_US
dc.publisherAmerican Physical Society (APS)en_US
dash.licenseLAA
dc.titleWrinkling Instability of an Inhomogeneously Stretched Viscous Sheeten_US
dc.typeJournal Articleen_US
dc.description.versionVersion of Recorden_US
dc.relation.journalPhysical Review Fluidsen_US
dash.depositing.authorMahadevan, Lakshminarayanan
dc.date.available2019-09-11T22:21:22Z
dash.workflow.commentsFAR2017en_US
dc.identifier.doi10.1103/physrevfluids.2.074103
dc.source.journalPhys. Rev. Fluids
dash.source.volume2;7
dash.contributor.affiliatedSrinivasan, Siddarth
dash.contributor.affiliatedMahadevan, Lakshminarayanan


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