Wrinkling, multiplicity and hydrodynamic screening in the dynamics of elastic sheets in extensional flow

Thin-structured materials, from flexible graphene sheets to highly extensible polymer films, are often processed in a fluidic environment. We study the dynamics of elastic sheets in the canonical extensional flows with a continuum model that includes in-plane deformation and out-of-plane bending, and the fluid motion is computed by the method of regularized Stokeslets. In planar and biaxial extensional flow, all stable conformations stay flat. Sheets modeled by a strain-hardening model exhibit a discontinuity in stretched length within a small increase in flow strength, which marks a bistable regime where multiple stable steady states exist. The bistability is analogous to coil-stretch hysteresis in linear polymers in solution: it arises from the hydrodynamic interaction between different parts of the sheet. In uniaxial extensional flow, we explore stiff sheets that strongly resist bending deformation and flexible sheets that can wrinkle. For stiff sheets, a similar compact-stretched transition has been observed. For flexible sheets, the wrinkling strongly modifies the bistability by rendering a shift of bistable regime to higher flow strength regime. We also apply a linear stability analysis to predict and understand the nonlinear long-term dynamics for some parameter regimes.