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Scaling Navier-Stokes equation in nanotubes
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Image of FIG. 1.
FIG. 1.

Density profiles for different values of γ = 60, 75, 90) inside four nanotubes of different radius: (a) = 2 nm, (b) = 5 nm, (c) = 10 nm, (d) = 100 nm. Whatever the radius of the tube is, we note that the main part of the density variation near the wall accounts for a thickness of 1 nm and that, outside this thin layer, the liquid density is strongly constant.

Image of FIG. 2.
FIG. 2.

Density profiles inside a nanotube of radius 10.4 nm issued from molecular dynamics simulation (continuous line) and from the continuum model (dashed line). The dotted line which extends the density profile issued from MD simulation is associated with the gap of density due to the lack of water molecules beside the wall.

Image of FIG. 3.
FIG. 3.

Velocity profiles in nanotubes of different radius: (a) = 2 nm, (b) = 5 nm, (c) = 10 nm, (d) = 100 nm. The plots simply show the inner and outer regions up to and including a distinct point of separation of the two analytic representations. The region near the wall is represented in a grey area.

Image of FIG. 4.
FIG. 4.

Velocity profiles near the axis of the tube for four different nanotubes.


Generic image for table
Table I.

Gibbs adsorption at the wall predicted by the continuum model for different values of the parameter γ.

Generic image for table
Table II.

Numerical values of the coefficients in Eqs. (17)–(19) .

Generic image for table
Table III.

Numerical values of the slip velocity following the radius value of the nanotube.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Scaling Navier-Stokes equation in nanotubes