Environmental Engineering Reference
In-Depth Information
The effective viscosity of the liquid in a nanotube is defined as follows.
A conformity nanotubes filled with liquid, containing crystallites with the
same size tube filled with liquid, can be considered as a homogeneous medium
(i.e., without considering the crystallite structure), in which the same pressure
drop and flow rate of Poiseuille flow is realized. The viscosity of a homogeneous
fluid, whichensures the coincidence of these parameters, called the effective vis-
cosity of the flow in the nanotube.
While flowing in the narrow channels of width less than 2 nm, water behaves
like a viscous liquid. In the vertical direction, water behaves as a rigid body, and
in a horizontal direction it maintains its fluidity.
It is known that at large distances the van der Waals interaction has a magnetic
tendency and occurs between any molecules like polar as well as non-polar. At
small distances it is compensated by repulsion of electron shells. Van der Waals
interaction decreases rapidly with distance. Mutual convergence of the particles
under the influence magnetic forces continues until these forces are balanced with
the increasing forces of repulsion.
Knowing the deceleration of the flow
(Fig. 3.4)
of water
a
, the effective shear
stress between the wall of the pipe length
l
and water molecules can be calculated
by;
(3.3)
Here, the shear stress is a function of tube radius and flow velocity
v
, and
m
is mass
of water molecules. The average speed is related to volumetric flow
(
)
2
.
v
=
Q
/
π
R
Denoting
n
the density of water molecules number, we can calculate the
shear stress in the form of:
τ
=
n
0
mRa
/
2
(3.4)
r
=
R
Figure 3.5
shows the results of calculations concerning the influence of the size
of the tube
R
on the effective viscosity (squares) and shear stress
τ
(triangles),
when the flow rate is approximately 165 m/sec.
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