Innovative coupled fluid–structure interaction model for carbon
nano-tubes conveying fluid by considering the size effects of nano-flow
and nano-structure
Mehran Mirramezani, Hamid Reza Mirdamadi ⇑, Mostafa Ghayour
Department of Mechanical Engineering, Isfahan University of Technology, 84156-83111 Isfahan, Iran
a r t i c l e i n f o
Article history:
Received 20 February 2013
Received in revised form 8 April 2013
Accepted 16 April 2013
Available online 18 May 2013
Keywords:
Fluid–structure interaction (FSI)
Divergence instability
Critical flow velocity
Knudsen number
Viscosity parameter
Size-dependent continuum theory
a b s t r a c t
In this article, we reappraise the well-known equation of motion for a pipe conveying viscous fluid. We
utilize prominent principles of fluid mechanics such as Navier–Stokes’ equation as well as several benchmark
references in the field of fluid–structure interaction (FSI) to reveal that the viscosity of the fluid flow
should not appear explicitly in the equation of motion of pipe conveying fluid. Based on this result, we
could develop an innovative model for one dimensional coupled vibrations of carbon nano-tubes (CNTs)
conveying fluid using slip velocity of the fluid flow on the CNT walls as well as utilizing size-dependent
continuum theories to consider the size effects of nano-flow and nano-structure. Therefore, this innovative
coupled FSI equation suggests that CNTs conveying nano-flow remain stable for higher velocities. In
the other words, the critical average velocity of the fluid flow at which the divergence instability occurs,
should be greater in comparison with the critical velocity predicted by the models used plug flow and
classical continuum theories.
 2013 Elsevier B.V. All rights reserved.
1. Introduction
Carbon nano-tubes (CNTs) are becoming the most promising
material for nano-electronics, nano-devices and nano-composites
because of their enormous application such as nano-pipettes, actuators,
reactors, fluid filtration devices, biomimetic selective transport
of ions, targeted drug delivery devices, scanning molecule
microscopy, and scanning ion conductance microscopy [1–4]. In
this regard, a remarkable number of studies have been accomplished
to disclose the vibrational behavior of such nano-structures
conveying fluid. Tuzun et al. [5], Amabili et al. [6], Yoon et al. [7],
Natsuki et al. [8], Wang et al. [9], Xia et al. [10] and Wang and Qiao
[11] made important contributions in this practical area. In this research,
we would undertake a reevaluation for computational
modeling of carbon nano-tubes conveying viscous fluid with some
fresh insights as well as we try to develop an innovative one
dimensional (1D) coupled fluid–structure interaction (FSI) equation
by considering slip condition on the nano-tube wall. Khosravian
and Rafii Tabar [12] studied the flow of viscous fluid through a
carbon nano-tube and established a new equation of motion of
pipe conveying fluid by considering the viscosity effect. They found
that a nano-tube conveying a viscous fluid was more stable against
vibration-induced buckling than a nano-tube conveying a non-viscous
fluid. Wang and Ni [13] reappraised the computational modeling
of carbon nano-tube conveying viscous fluid represented by
Khosravian and Rafii Tabar [12] and then corrected the FSI equation
and disclosed that the effect of viscosity of fluid flow on the
vibration and instability of CNTs could be ignored. Lee and Chang
[14] analyzed the influences of nonlocal effect, viscosity effect, aspect
ratio, and elastic medium constant on the fundamental frequency
of a single-walled carbon nano-tube (SWCNT) conveying
viscous fluid embedded in an elastic medium. They revealed that
the frequency increased as the values of the viscosity parameter increased.
Soltani et al. [15] developed a transverse vibrational model
for a viscous fluid-conveying SWCNT embedded in biological soft
tissue. Their investigation determined that the structural instability
and the associated critical flow velocity could be affected by
the viscosity of the fluid and the nonlocal parameter. Khoddami
et al. [16] studied electro-thermo nonlinear vibration and instability
of embedded double-walled Boron Nitride nano-tubes
(DWBNNTs) conveying viscous fluid based on nonlocal piezoelasticity
theory. They reported that increasing the small scale parameter
decreased the real and imaginary parts of frequency and
critical fluid velocity. Furthermore, they concluded that the effect
of fluid viscosity on the vibration and instability of DWBNNTs
might be ignored. In many recent studies various size-dependent
continuum theories have been developed for vibration and stability
analysis of CNTs conveying fluid. Lee and Chang [17], Zhen
0927-0256/$ – see front matter  2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.commatsci.2013.04.047
⇑ Corresponding author. Tel.: +98 311 391 5248; fax: +98 311 391 2628.
E-mail addresses: m.mirramezani@me.iut.ac.ir (M. Mirramezani), hrmirdamadi@
cc.iut.ac.ir (H.R. Mirdamadi), ghayour@cc.iut.ac.ir (M. Ghayour).
Computational Materials Science

77 (2013) 161–171
Contents lists available at SciVerse ScienceDirect
Computational Materials Science
journal homepage: www.elsevier.com/locate/commatsci
and Fang [18], Jannesari et al. [19] included the effect of small-size
into equations of motion by using nonlocal elasticity in their studies
and showed that increasing nonlocal parameter had the effect
of a decrease in the critical velocity of fluid. Ke and Wang [20]
investigated vibration and instability of fluid-conveying doublewalled
carbon nano-tubes based on modified couple stress theory.
They showed that the imaginary component of the frequency and
the critical flow velocity of the CNTs increased with an increase in
length scale parameter. Wang [21] developed a theoretical analysis
of wave propagation of fluid-conveying single-walled carbon nanotubes
based on strain gradient elasticity theory. He showed that
the use of gradient elasticity theory had a dramatic effect on dispersion
relation. Wang [22] utilized nonlocal elasticity theory integrated
with surface elasticity theory to analyze dynamic response
of nano-tubes conveying fluid. He revealed that fundamental frequency
and critical flow velocity predicted by his new model was
generally higher than that predicted by the Euler–Bernoulli beam
model without surface effects. Some recent studies developed to
consider the small size effects of nano-flow as well as slip boundary
condition on nano-tube wall.

تعداد صفحه : 11

تکه هایی از متن ترجمه فارسی به عنوان نمونه :

مدل ساختار مایع تعاملی برای نانو لوله های کربنی با در نظرگرفتن اثر اندازه نانو جریان و نانو ساختار

چکیده:

در این مقاله معادله حرکت لوله های انتقال سیال بررسی شده است. ما با بهره گرفتن از اصول مکانیک سیالات مانند مدل استوکس و همچنین چندین معیار در زمینه تعامل ساختار مایع(FSI) استفاده کرده ایم و نشان می دهد که ویسکوزیته جریان سیال باید در معادله حرکت سیال صدق کند. براساس این نتیجه ما می توانیم یک مدل ابتکاری برای ارتعاشات نانولوله های کربنی (CNT) ها را با بهره گرفتن از سرعت لغزش جریان سیال بر دیواره های CNT ارائه نموده و همچنین از نظریه زنجیره اثر اندازه نانوجریان و نانو ساختار را بررسی کردیم. بنابراین ابتکار در معادله FSI نشان می دهد که نانو لوله برای انتقال نانوجریان برای سرعت های بالاتر پایدارتر است. به عبارت دیگر به طور متوسط سرعت برای جریان سیال که در آن بی ثباتی اتفاق می افتد باید در مقایسه با سرعت بحرانی پیش بینی شده توسط مدل های مورد استفاده مانند پلاگین و نظریه های زنجیره کلاسیک کارساز باشد.

کلیدواژه ها: تعامل ساختار مایع(FSI) ، بی ثباتی واگرایی،سرعت جریان بحرانی،عدد نودسن،پارامتر ویسکوزیته،تئوری نظریه زنجیره وابسته به حجم.

1-مقدمه:

نانو لوله های کربنی در حال تبدیل شدن به مواد نانو الکتریک،نانودستگاه ها و نانوکامپوزیت ها برای استفاده در نانوپیپت ها،دیسک ها،راکتورها و دستگاه های فیلتراسیون