Wrinkling and multiplicity in the dynamics of deformable sheets in uniaxial extensional flow

The processing of thin-structured materials in a fluidic environment, from nearly inextensible but flexible graphene sheets to highly extensible polymer films, arises many applications. So far, little is known about the dynamics such thin freely suspended fluid. In this work, we study soft uniaxial extensional flow. Elastic are modeled with continuum model that accounts for in-plane deformation and out-of-plane bending, fluid motion computed using method regularized Stokeslets. We explore two types sheets: "stiff" strongly resist bending deformations always stay flat, "flexible" both out-of plane deformability can wrinkle. For stiff sheets, observe coil-stretch-like transition, similar what has been observed long-chain linear polymers under extension as well elastic planar extension: certain range capillary number (flow strength relative deformability), exhibit either compact or stretched conformation, depending on history. sufficiently small stiffness wrinkle form various conformations. Here, compact-stretched bistability still occurs, modified by wrinkling instability: highly-stretched state become unstable wrinkle, after which it may dramatically shrink length due hydrodynamic screening associated wrinkling. Therefore, renders shift regime. addition, predict understand nonlinear long-term some parameter regimes stability analysis flat steady states.