  Molten metallic nanoparticles have recently been used to construct graphene
nanostructures with crystallographic edges. The mechanism by which this
happens, however, remains unclear. Here, we present a simple model that
explains how a droplet can etch graphene. Two factors possibly contribute to
this process: a difference between the equilibrium wettability of graphene and
the substrate that supports it, or the large surface energy associated with the
graphene edge. We calculate the etching velocities due to either of these
factors and make testable predictions for evaluating the significance of each
in graphene etching. This model is general and can be applied to other
materials systems as well. As an example, we show how our model can be used to
extend a current theory of droplet motion on binary semiconductor surfaces.
