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

Abstract

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.

Vibration analysis of nanotubes conveying fluid based on gradient elasticity theory

“…The stress gradient beam models, of course, have been utilized to analyze the vibration characteristics of fluid-conveying nanotubes before, by several investigators Chang, 2008, 2009;Kuang et al, 2010;Tounsi et al, 2009;Wang, 2009a,b;Xia and Wang, 2010). In this work, therefore, the other two combined strain/inertia gradient beam models will be discussed in detail.…”

“…Therefore, the utilization of higher order continuum theories containing internal material length scale parameters is inevitable. As a higher order continuum theory, the nonlocal elasticity theory was recently used to explore the size effect on the vibration properties of nanotubes conveying fluid by several researchers (Kuang et al, 2010;Chang, 2008, 2009;Tounsi et al, 2009;Wang, 2009a,b;Xia and Wang, 2010). Compared with the classical (local) continuum theory, the nonlocal elasticity theory assumes that the stress state at a given point is defined as a function of the strain states of all points in the body.…”