Graphene nanoplatelets attain a stable orientation in a shear flow: an investigation on the role of Brownian fluctuations

We study theoretically the rotational dynamics of a rigid graphene nanoplatelet suspended in a simple shear flow. We have recently shown that in the infinite Peclet number limit a rigid platelet presenting the interfacial hydrodynamic slip properties of graphene does not follow the periodic rotations predicted by Jeffery’s theory, but rather aligns itself at a small inclination angle $\alpha_c$ with respect to the flow. This unexpected result is due to the low tangential friction at the graphene-solvent surface (the slip lengths for many 2D materials/solvent combinations can amount to several tens of nanometers). By analyzing the Fokker-Plank equation for the orientational distribution function for decreasing Peclet numbers, we show that the platelet fluctuates about $\alpha_c$ until a slip length dependent critical Peclet number is reached. Below this value, Brownian forces are large enough to produce full rotations, bringing the particle outside of a “hydrodynamic potential well”. In the stable region, 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.