Nanoscale fluid-structure interaction: Flow resistance and energy transfer between water and carbon nanotubes

Chao Chen, Ming Ma, Kai Jin, Jefferson Zhe Liu, Luming Shen, Quanshui Zheng, and Zhiping Xu

Phys. Rev. E 84, 046314 – Published 18 October 2011

Abstract

We investigate here water flow passing a single-walled carbon nanotube (CNT), through analysis based on combined atomistic and continuum mechanics simulations. The relation between drag coefficient $C_{D}$ and Reynolds number Re is obtained for a wide range of flow speed $u$ from 5 to 600 m/s. The results suggest that Stokes law for creep flow works well for small Reynolds numbers up to 0.1 ( $u$ ≈ 100 m/s), and indicates a linear dependence between drag force and flow velocity. Significant deviation is observed at elevated Re values, which is discussed by considering the interfacial slippage, reduction of viscosity due to friction-induced local heating, and flow-induced structural vibration. We find that interfacial slippage has a limited contribution to the reduction of the resistance, and excitations of low-frequency vibration modes in the carbon nanotube play an important role in energy transfer between water and carbon nanotubes, especially at high flow speeds where drastic enhancement of the carbon nanotube vibration is observed. The results reported here reveal nanoscale fluid-structure interacting mechanisms, and lay the ground for rational design of nanofluidics and nanoelectromechanical devices operating in a fluidic environment.

Received 2 August 2011

DOI:https://doi.org/10.1103/PhysRevE.84.046314

Authors & Affiliations

Chao Chen^1,2,3, Ming Ma^1,2,3, Kai Jin¹, Jefferson Zhe Liu⁴, Luming Shen³, Quanshui Zheng^1,2, and Zhiping Xu^1,2,*

¹Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
²Center for Nano and Micro Mechanics, Tsinghua University, Beijing 100084, China
³School of Civil Engineering, University of Sydney, Sydney, NSW 2006, Australia
⁴Department of Mechanical and Aerospace Engineering, Monash University, Clayton, Victoria 3800, Australia

^*Corresponding author: xuzp@tsinghua.edu.cn

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Issue

Vol. 84, Iss. 4 — October 2011

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Images

Figure 1
Flow resistance of water passing a (5, 5) carbon nanotube. (a) Results from molecular dynamics (MD) simulations (points with error bars for both velocity and force values) are compared with numerical results from Navier-Stokes equations (lines). In the computational fluid dynamics (CFD) simulations, we tune the slip length in the notion of the Navier boundary condition to account for the slip boundary conditions. The increasing of slip length results in downshift of log $_{10}$ $C_{D}$ –log $_{10}$ Re curve. The CFD results fit well to a scaling function of $C_{D} = C {Re}^{- 1}$ in the entire range of Re values, while MD results deviate when the flow velocity exceeds Re $=$ 0.1 (SPCE) or Re $=$ 0.3 (TIP3P). (b) Dependence of drag force of the carbon nanotube on the flow velocity. The legends for forces are the same as in (a).Reuse & Permissions
Figure 2
(a) Density and (b) temperature distribution across the $x$ - $y$ plane (nanotube cross section). Local flow velocity field is plotted using arrowed lines. (c) Local flow velocity along the $x$ direction and temperature as recorded along the dashed line in (a).Reuse & Permissions
Figure 3
The effect of interfacial slippage on flow resistance. When the slip length $l_{s}$ is smaller than or comparable to the size of carbon nanotube $D$ , drag force $F_{D}$ decreases significantly. However, when $l_{s}$ increases further, drag force converges to a constant, and the overall reduction of $F_{D}$ is limited by 14%. $F_{D}$ with a nonslip boundary, i.e., $l_{s}$ $=$ 0, is used as reference.Reuse & Permissions
Figure 4
Thermal effect on the viscosity calculated using SPCE model. Results from water flow around both flexible and rigid nanotubes are plotted and fitted by an exponential function. The relative viscosity is compared with corresponding viscosity at 300 K for flexible and rigid CNTs, respectively.Reuse & Permissions
Figure 5
Vibrational modes excited by fluid flow, obtained as eigenvectors from principal component analysis, for both (a) SPCE and (b) TIP3P water models. The analysis indicates that as flow velocity increases, more and more modes with higher frequencies are excited. Specifically, when it exceeds 100 m/s, a significantly enhanced occupation of bending and breathing modes is observed, suggesting significant mechanical energy imported from water flow.Reuse & Permissions
Figure 6
(a) Steady-state flow speed of water with different carbon-oxygen interactions but the same driving force. Here σ is kept as a constant as 0.319 nm, and ε is changed from 1.9495 to 6.498 meV, corresponding to contact angles from 30° to 140° (Table ). (b) The radial distribution function (RDF) of water molecules around the carbon nanotube for different ε values.Reuse & Permissions

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