Environmental Engineering Reference
In-Depth Information
As one can see, there is conformance with the Darcy law, the average flow
rate for each CNT increases with increasing pressure gradient. For a fixed value
of
p /D , however, the average flow rate does not increase monotonically with
increasing diameter of the CNTs, as follows from Poiseuille equation. Instead,
when at the same pressure gradient, decrease of the average speed in a CNT with
the radius of 0.83 nm to a CNT with the radius of 1.10 nm, similar to the CNTs
1.10 and 1.25 nm, then increases from a CNT with the radius of 1.25 nm to a CNT
of 1.66 nm.
The non-linearity between v and
L
P /D are the result of inertia losses (i.e.,
insignificant losses) in the two boundaries of the CNT. Inertial losses depend on
the speed and are caused by a sudden expansion, abbreviations, and other obstruc-
tions in the flow.
Molecular modeling of many researchers shows that the Eq. (4.1) (Poiseuille
parabola) describes the velocity profile of liquid in a nanotube when the diameter
of a flow is 5-10 times more than the diameter of the molecule (≈0.17 nm for
water).
In Fig. 4.8, the effect of slip on the velocity profile at the boundary of radius R
of the pipe and fluid is shown. When L s = 0 the fluid velocity at the wall vanishes,
and the maximum speed (on the tube axis) exceeds flow speed twice.
L
FIGURE 4.8
No-slip Poiseuille flow and slip Poiseuille flow through a tube.
 
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