Graphene nanoplatelets attain a stable orientation in a shear flow

Our group is interested in the hydrodynamics of graphene. The study of a rigid graphene nanoplatelet in a simple shear flow offers the opportunity to revisit basic assumptions regarding the rotational motion of plate-like particles. Current theories assume a nanoplatelet suspended in a simple shear flow should rotate continuously following a Jeffery's orbit. We show by combining Molecular Dynamics for a graphene-water system, Boundary Integral simulations, and theory, that a rigid nanoplatelet with normal in the plane of the shear flow does not follow Jeffery's orbit, but rather aligns itself at a small inclination angle with respect to the flow direction. This unexpected result is due to the slip velocity at the graphene-water surface and to molecular edge effects.

We develop a theory that suggests stable orientation occurs when the thickness 2b of the nanoplatelet is of the same order of the slip length λ; the stable inclination angle α_c depends on the aspect ratio b/a of the platelet according to α_c$\propto$(b/a)^1/2 for λ/a» 1. The stable orientation criterion is satisfied in many practical situations, suggesting that graphene could be held aligned indefinitely in controlled flows.