The discovery of carbon nanostructures, such as graphene and carbon nanotubes, has led to the creation of many novel nano-devices. In this paper, we consider an environmental application of carbon nanostructures for filtering and adsorbing polycyclic aromatic hydrocarbons (PAHs) which are environmental pollutants. We mathematically investigate the adsorption of PAHs onto a graphene sheet and determine the underlying mechanisms of suction of PAHs into a carbon nanotube. We adopt a continuum approach together with the semi-empirical Lennard-Jones potential to determine van der Waals interaction forces and energies. Results obtained here for certain PAHs are well in agreement with existing experimental and theoretical results. We comment that the use of elementary mechanical principles and classical applied mathematical modelling techniques in this paper enables the formulation of explicit analytical criteria and ideal model behaviour for problems in nanotechnology for which previously only experiments and molecular dynamics simulations were available. Further the method presented here is less computationally intensive compared with conventional methods, such as ab initio calculations and density functional theory, making it an ideal approach for modelling molecules with large numbers of atoms, such as PAHs, carbon nanostructures and biomolecules.