CHAPTER 9: Mathematical Modelling and Simulations for Using Nanotubes and Graphene for Ultrafiltration and Molecular and Charge Transport

This chapter demonstrates how applied mathematics intertwines with nanoscience and nanotechnology in order to provide insights for using nanotubes and graphene for molecular and charge transport, which is crucial to reveal mechanisms for ultrafiltration and high performance lithium-ion batteries. Four topics will be covered, including single-file transport of water in carbon nanotubes, Newtonian flow through large radii carbon nanotubes, molecular flow inside graphene and lithium-ion transport between double-layered graphene sheets. Special interest will be paid to the governing equations for these problems, and, in particular, how applied mathematics could be used to address multi-body interactions among molecules and ions for the proposed systems. Solution techniques, including numerical simulations, will be provided and the results discussed. This chapter shows how mathematical techniques could provide deductive and rapid means to tackle problems arising from molecular and charge transport in nanotechnology, and demonstrates that mathematics can present alternative views in comparison with the prevailing methodologies of using experimental investigations and purely computational simulations.