FLUID FLOW IN NANOTUBES - Foundations of Nanotechnology: Pore Size in Carbon-Based Nano-Adsorbents - page 216

4

− − −

τ −τ − 4 A 2 l

Rp

τ

− − −

0 ef 0 ef 0 ef

τ =τ − , τ =

n − 1 n − 1

(4.17)

0 ef 0 ef 0 ef

n n − 1

3
0

D

−

4 τ− 4

ef

n − 1

The first component in Eq. (4.12) represents the contribution to the fluid flow due
to the slippage, and it becomes clear that the slippage significantly enhances the
flow rate in the nanotube, when

h >»D .
This result is consistent with experimental and theoretical results of Kalra et
al. [34], Majumder et al. [41], Skoulidas et al. [66], Hummer et al. [28], and Holt
et al. [25], which show that water flow in nanochannels can be much higher than
under the same conditions, but for the liquid continuum.
In the absence of slippage

2

l v pR

0

the Eq. (4.16) has a trivial solution 0 e t= .

e 1

0

4.3 THE RESULTS OF THE CALCULATIONS

Let's determine the dependence of the effective critical inner shear stress 0ef = τ
on the radius of the nanotubes, by taking necessary values for calculations

e from the work of Thomas John and McGaughey Alan [73]. The results
of calculations at D p/l = 2.1×10 14 Pa/m are in the tablebelow:

Q / Q

P

TABLE 4.2 Results of the Calculations

τ (Па)

0ef = 0

R , м

e Q / Q

P

0.83×10 -9 498,498 350

1.11×10 -9 577,500 200

1.385×10 -9 632,599 114

1.665×10 -9 699,300 84

1.94×10 -9 782,208 68

2.22×10 -9 855,477 57

2.495×10 -9 932,631 50

Calculations show that the value of effective internal shear stress depends on

the size of the nanotube. Figure 4.14 shows the dependence on the nanotube

τ

0ef = 0

radius, and Fig. 4.15 shows the structure of the flow.