Complex Dynamics of Inextensible Elastic Sheets in Shear Flow

Two-dimensional materials like graphene and polymeric films, due to their superior mechanical properties, are widely applied in many applications, where the dynamics in flow are still poorly understood. We present a numerical study of thin polymer films to investigate dynamics under simple shear. Elastic sheets are modeled with out-of-plane bending and negligible in-plane stretching, and the fluid motion is computed by the regularized Stokeslets. The presence of a free surface can be incorporated through use of an image system. We consider sheets with circular or rectangular rest shapes, freely suspended in shear flow. We observed both shapes undergo a quasi-periodic flapping motion, with part of the edges, when facing the compressive axis, flapping up and down alternatively. When close to the free surface, the rectangle only flaps away from surface and the disk forms a stable taco shape while rotating, like a 3D tank-treading motion. The bias in flapping direction here is caused by the broken symmetry introduced by the surface. The sheets slowly drift away from the free surface due to force dipole of the image system. During drifting, the bias in flapping gradually vanishes. The simulation results agree with experimental observations from the group of Lorenzo Botto.