Modelling flow and rheology of Graphene

We study theoretically the rotational dynamics and rheology of dilute suspensions of rigid graphene in a simple shear flow. In the infinite Péclet number limit, a rigid platelet with the interfacial hydrodynamic slip properties of graphene does not follow the periodic rotations predicted by Jeffery’s theory, but aligns itself at a small inclination angle α_c with respect to the flow. This unexpected result is due to the hydrodynamic slip reducing the tangential friction at the graphene-solvent surface. By analyzing the Fokker-Plank equation for the orientational distribution function for decreasing Péclet numbers, we show that the platelet fluctuates about α_c until a slip length dependent critical Péclet number is reached. Below this value, Brownian forces are large enough to induce full rotations. We compare the rheology of the suspension to Molecular Dynamics simulations of graphene-like platelets and show that slip can dramatically change the macroscopic behaviour of the suspension. For example, at large Péclet number, the effective viscosity of a dilute suspension of graphene platelets is predicted to drop by at least a factor of 2 for typical slip length values.