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.

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We present a micromechanical analysis of flow-induced peeling of a layered 2D material suspended in a liquid, for the first time accounting for realistic hydrodynamic loads. In our model, fluid forces trigger a fracture of the inter-layer interface by lifting a flexible “flap” of nanomaterial from the surface of a suspended microparticle. We show that the so far ignored dependence of the hydrodynamic load on the wedge angle produces a transition in the curve relating the critical fluid shear rate for peeling to the non-dimensional adhesion energy. For intermediate values of the non-dimensional adhesion energy, the critical shear rate saturates, yielding critical shear rate values that are drastically smaller than those predicted by a constant load assumption. Our results highlight the importance of accounting for realistic hydrodynamic loads in fracture mechanics models of liquid-phase exfoliation.@en