Simulation of interacting elastic sheets in shear flow

Abstract

In liquid-based material processing, hydrodynamic forces are known to produce severe bending deformations of two-dimensional (2D) materials such as graphene. The non-linear rotational and deformation dynamics of these atomically thin sheets is extremely sensitive to hydrodynamic particle-particle interactions. To investigate this problem, we developed a computational model of the flow dynamics of elastic sheets suspended in a linear shear flow, solving the full fluid-solid coupling problem in the two-dimensional, slender-body, Stokes flow regime. Both single and pairs of sheets in close proximity are analyzed. Despite the model being two-dimensional, the critical non-dimensional shear rate yielding single-particle buckling is comparable in order of magnitude to that reported for fully three-dimensional, disk-like sheets. For pairs of interacting sheets, hydrodynamic interactions lead either to parallel sliding or bending, depending on the value of an elasto-viscous number based on particle length. For sufficiently low bending rigidity or large shear rates, large deformations of initially stacked sheets lead to sheet reattachment after separation, unlike for the rigid case. A peeling-like dynamics where lubrication provides a viscous bonding force is observed for sheet pairs when one of the two sheets is more rigid than the other. Practical implications for graphene processing and exfoliation are discussed.