(242j) Dynamics of Elastic Thin Sheets in Stokes Flow: Wrinkling Dynamics in Uniaxial Extensional Flow and Simple Shear Flow

Two-dimensional materials, from inextensible graphene to stretchable polymeric films, are widely applied in many applications. Due to the small size, sheets are usually processed in a fluidic environment, where the dynamics are still poorly understood. We present a study of elastic sheets under two different scenarios: uniaxial extension and simple shear. Elastic sheets are modeled with a finite-element based continuum model that accounts for in-plane stretching and out-of-plane bending, and the fluid motion is computed by the method of regularized Stokeslets.

In uniaxial extensional flow, a soft disk-sheet undergoes a coil-stretch-like transition: when a critical flow strength (capillary number) is exceeded, the sheet snaps from a compact state to a fully stretched state. The discontinuity in length marks a bistable regime where both compact and highly stretched states exist. Flexible sheets, due to compressive stresses from the inward flow, may wrinkle. Though the bistability still occurs, it is strongly modified due to the hydrodynamic screening from wrinkled conformations. In addition, we can predict the nonlinear long-term dynamics for some parameter regimes with a simple linear stability analysis.

In shear flow, nearly inextensible sheets with nominally disk and rectangular rest shapes have been examined under different initial conditions. For a rectangular sheet slightly deviating from the flow-vorticity plane, we examine the transient flipping dynamics and obtain a buckling threshold for bending stiffness. Above the threshold, the sheet wrinkles due to compressive stresses and shows different buckling modes based on bending stiffness. When the sheet is initially inside the flow-gradient plane, the long-term dynamics are determined by bending stiffness. Under small perturbation, sufficiently flexible sheets quickly deform out of the shear plane and finally align with the flow-vorticity plane. Sheets with moderate stiffness end up with a quasi-periodic flapping orbit without managing to align with the flow-vorticity plane. Finally, stiff sheets stay inside the shear plane and undergo a 2D rolling motion.