A Continuum Model of the Van der Waals Interface for Determining the Critical Diameter of Nanopumps and its Application to Analysis of the Vibration and Stability of Nanopump Systems

Carbon nanotubes make ideal nanopumps for the transport of fluid. To analyze the vibration and stability of nanopump systems with inner fluid effectively, it is necessary to incorporate nanoscale effects into continuum-based simulations. This paper first proposes a continuum model for the van der Waals (vdW) interface between a single-wall carbon nanotube (SWCNT) and incompressible inner fluid to determine the critical tube diameter above which continuum fluid mechanics may be reasonably applied to that inner fluid. Then, with overall consideration of the scale effects, including the nonlocal effects of the carbon nanotube, the surface tension of the inner fluid and the vdW interface, an improved Euler beam/plug fluid model is developed to investigate the vibration and stability of the nanopump system. The two models are both validated by comparing with molecular dynamic simulations. The results show that the critical diameter for water flow is about 1.8 nm. Nanopump stability is noticeably enhanced by the surface tension of the inner fluid for a high slenderness ratio. Both coaxial vibration frequency and stability decline as the system temperature is increased. Moreover, the proposed models predict that the transverse vibration of the inner fluid inside a nearly rigid SWCNT occurs due to the existence of the vdW interface gap and the negligible bending rigidity of the fluid.