How do small two-dimensional sheets behave in fluids? Despite the prevalence of soft matter systems comprising 2-D materials (e.g., graphene, transition metal dichalcogenides and 2-D polymers), there is still little known at a fundamental level regarding the dynamical behavior of 2-D materials dispersed in fluids and their effects on bulk material properties. We perform numerical simulations of athermal and thermal semiflexible sheets with hydrodynamic interactions in shear flow. In the athermal case, sheets initially oriented in the flow-gradient plane exhibit buckling instabilities of different mode numbers that vary with bending stiffness and can be understood with a quasi-static model of elasticity. For different initial orientations, chaotic tumbling trajectories are observed. In the thermal case, as a function of the ratio of bending rigidity to shear energy (a dimensionless quantity we denote as "S") and the ratio of bending rigidity to thermal energy, we observe behavior ranging from stochastic flipping to chaotic tumbling. The effects of these dynamical conformations on rheological properties such as viscosity and normal stress differences are quantified.
