(398f) Coil-Stretch-like Transition and Wrinkling Dynamics of Elastic Sheets in Extensional Flows

Thin-structured materials, such as graphene or polymeric sheets, are often processed in fluidic environments that involve extensional flow field. We study the dynamics of elastic sheets in various extensional flows with a continuum model that accounts for in-plane deformation and out-of-plane bending. The fluid motion is computed using the method of regularized Stokeslets.

In planar and biaxial extension, all stable conformations of the sheet are flat – wrinkled sheets are only observed as initial transients. Sheet displaying strain-hardening shows a bistable regime where multiple stable conformations (compact and stretched) 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 surface and will vanish if the hydrodynamic interaction is screened.

In uniaxial extension, a sheet with sufficiently small bending rigidity will wrinkle due to the inward radial flow, which leads to compressive stresses. While the compact-stretched bistability described above can still occur, it is strongly modified if wrinkling occurs. A highly stretched planar state can become unstable, with respect to wrinkling, after which it may dramatically shrink in length because of hydrodynamic screening associated with wrinkling. We can predict the nonlinear long-term dynamics for some parameter regimes with a simple linear stability analysis.