FLUID FLOW IN NANOTUBES - Foundations of Nanotechnology: Pore Size in Carbon-Based Nano-Adsorbents - page 203

Q P . In the works of many scientists the parameter enhancement flow e is intro-
duced. It is defined as the ratio of the calculated volumetric flow rate of slippage
to Q P (calculated using the effective viscosity and the diameter of the CNT). If the
measured flux is modeled using the Eq. (4.3), the degree of enhancement takes
the form:

(4.4)

where, d = 2 R -diameter of CNT;

h - viscosity of water; L S ( d )- CNT slip length

depending on the diameter; ( )

h - the viscosity of water inside CNTs depending

on the diameter.
- If ( )

h finds to be equal to h , then the influence of the effect of slip on
e is significant,

h = h , then there will be no signifi-
cant difference compared to the Hagen-Poiseuille flow with no slip.
Table 4.1 shows the experimentally measured values of the enhancement wa-
ter flow. Enhancement flow factor and the length of the slip were calculated using
the equations given above.
Figure 4.2 depicts the change in viscosity of the water and the length of the
slip in diameter. As can be seen from the figure, the dependence of slip length to
the diameter of the nanotube is well described by the empirical relation.

- If

( ) ≥ . If

and ( )

L S d d

( )

L S d d

TABLE 4.1 Experimentally measured values of the enhancement water flow

Nanosystems Diameter (nm)

Enhancement, e

Slip length, , (nm)

L

S

carbonnanotubes 300-500 1 0

44 22-34 113-177

carbonnanotubes 7 10 4 -10 5 3900-6800

1.6 560-9600 140-1400