FLUID FLOW IN NANOTUBES - Foundations of Nanotechnology: Pore Size in Carbon-Based Nano-Adsorbents - page 209

The Fig. 4.8 shows the velocity profiles for Poiseuille flow without slip ( L s =
0) and with slippage L s = 2 R . The flow rate is normalized to the speed correspond-
ing to the flow without slip. Thick vertical lines indicate the location of the pipe
wall. The thick vertical lines indicate the location of the tube wall.
Velocity of the liquid on a solid surface can also be quantified by the coef-
ficient of slip L c . The coefficient of slippage is a difference between the radial
positio ns in whi ch the velocity profile would be zero. Slip coefficient is equal to
R

2

L = R + 2 RL = 5

.
For linear velocity profiles (e.g., Couette flow), the length of the slip and slip
rate are equal. These values are different for the Poiseuille flow.
Figure 4.9 shows dependence of the volumetric flow rate Q from the pressure
gradient

C S

∂ / in long nanotubes with diameters between 1.66 nm and 6.93 nm.
Pressure gradient Q is proportional to

p ∂ z

∂ / . As in the Poiseuille flow, volumet-
ric flow rate increases monotonically with the diameter of CNT at a fixed pressure
gradient. Magnitudes of calculations error for all the dependencies are similar to
the error for the CNT diameter 4.44 nm (marked in the Fig. 4.9).

p ∂ z

FIGURE 4.9 Volumetric flow rate in CNTs versus pressure gradient.