RHEOLOGICAL PROPERTIES AND STRUCTURE OF THE LIQUID IN NANOTUBES - Foundations of Nanotechnology: Pore Size in Carbon-Based Nano-Adsorbents - page 187

3.1 SLIPPAGE OF THE FLUID PARTICLES NEAR THE WALL
According to the Navier boundary condition, the velocity slip is proportional to
fluid velocity gradient at the wall:

v |  L dv / dy |

(3.1)

y  0 S y  0

Here and in Fig. 3.1, L s represents the “slip length” and has a dimension of length.
Because of the slippage, the average velocity in the channel pdf v increases.
In a rectangular channel (of width >> height h and viscosity of the fluid h ) due
to an applied pressure gradient of dp/dex :

   

h

2

dp 6 L

   v   1 

S

 



(3.2)

pdf

12 dx h

ç

 

FIGURE 3.1

Three cases of slip flow (with slip length b ).

The results of molecular dynamics simulation for nanosystems with liquid,
show that a large slippage lengths (of the order of microns) should occur in the
carbon nanotubes of nanometer diameter and, consequently, can increase the flow
rate by three orders of (

L S ). Thus, the flow with slippage is becoming
more and more important for hydrodynamic systems of small size.
The results of molecular dynamics simulation of unsteady flow of mixtures
of water-water vapor, water and nitrogen in a carbon nanotube are reported pre-
viously. Based on these studies, a flow of water through carbon nanotubes with
different diameters at temperature of 300°K was considered.
Carbon nanotubes have been considered “zigzag” with chiral vectors (20, 20),
(30, 30) and (40, 40), corresponding to pipe diameters or 2712, 4068 and 5424
nm, respectively.

6 / h > 1000