RHEOLOGICAL PROPERTIES AND STRUCTURE OF THE LIQUID IN NANOTUBES - Foundations of Nanotechnology: Pore Size in Carbon-Based Nano-Adsorbents - page 193

FIGURE 3.5 Size effect of shearing stress (triangle) and viscosity (square).

According to classical mechanics of liquid flow at different pressure drops D

along the tube length l is given by Poiseuille formula;

4 D

π R p

Q P =

8 h l

, (3.5)

Therefore,

D pR

2

τ =

l

(3.6)

( )

= τh .
The change in the value of shear stress directly causes the dependence of the
effective viscosity of the fluid from the pipe size and flow rate. In this case the
effective viscosity of the transported fluid can be determined from Eqs. (3.5) and
(3.6) as

⋅ R / 4 v

and the effective viscosity of the fluid can be estimated as

= τ

⋅ R

h

(3.7)

4 v

It should be noted that the magnitude of the shear stress τis relatively small in the
range of pipe sizes considered. This indicates that the surface of carbon nanotubes
is very smooth and the water molecules can easily slide through it.