  We demonstrate theoretically the possibility of spinodal de-wetting in
heterostructures made of light--atom liquids (hydrogen, helium, and nitrogen)
deposited on suspended graphene. Extending our theory of film growth on
two-dimensional materials to include analysis of surface instabilities via the
hydrodynamic Cahn--Hilliard-type equation, we characterize in detail the
resulting spinodal de-wetting patterns. Both linear stability analysis and
advanced computational treatment of the surface hydrodynamics show micron-sized
(generally material and atom dependent) patterns of "dry" regions. The physical
reason for the development of such instabilities on graphene can be traced back
to the inherently weak van der Waals interactions between atomically thin
materials and atoms in the liquid. Similar phenomena occur in doped graphene
and other two-dimensional materials, such as monolayer dichalcogenides. Thus
two-dimensional materials represent a universal theoretical and technological
platform for studies of spinodal de-wetting.
