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Nanoscale Poiseuille flow and effects of modified Lennard–Jones potential function

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Abstract

Numerical simulation of Poiseuille flow of liquid Argon in a nanochannel using the non-equilibrium molecular dynamics simulation (NEMD) is performed. The nanochannel is a three-dimensional rectangular prism geometry where the concerned numbers of Argon atoms are 2,700, 2,550 and 2,400 at 102, 108 and 120 K. Poiseuille flow is simulated by embedding the fluid particles in a uniform force field. An external driving force, ranging from 1 to 11 PN (Pico Newton), is applied along the flow direction to inlet fluid particles during the simulation. To obtain a more uniform temperature distribution across the channel, local thermostating near the wall are used. Also, the effect of other mixing rules (Lorenthz–Berthelot and Waldman–Kugler rules) on the interface structure are examined by comparing the density profiles near the liquid/solid interfaces for wall temperatures 108 and 133 K for an external force of 7 PN. Using Kong and Waldman–Kugler rules, the molecules near the solid walls were more randomly distributed compared to Lorenthz–Berthelot rule. These mean that the attraction between solid–fluid atoms was weakened by using Kong rule and Waldman–Kugler rule rather than the Lorenthz–Berthelot rule. Also, results show that the mean axial velocity has symmetrical distribution near the channel centerline and an increase in external driving force can increase maximum and average velocity values of fluid. Furthermore, the slip length and slip velocity are functions of the driving forces and they show an arising trend with an increase in inlet driving force and no slip boundary condition is satisfied at very low external force (<1 PN).

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Abbreviations

\( \overrightarrow {F}_{\text{ext}} \) :

External force (N)

H n (z i ):

Function for adding particles

k B :

Boltzmann Constant (J K−1)

L s :

Slip length (m)

L x :

Box length along x direction (m)

L y :

Box length along y direction (m)

L z :

Box length along z direction (m)

m :

Mass of molecule (kg)

N(z):

Number of particles at height z (non-dimensional)

N atm :

Number of atoms (non-dimensional)

N bin :

Number of rectangular slabs (non-dimensional)

N sample :

Number of sampling (non-dimensional)

r :

Position vector (m)

r c :

Cutoff radius (m)

r ij :

Inter-particle separation (m)

T :

Temperature (K)

T wall :

Wall temperature

v :

Velocity vector (m s−1)

z :

Height (m)

\( \overrightarrow {\nabla } \) :

Dell gradient

Δz :

Thickness of rectangular slab (m)

σ :

Length parameter for Argon (m)

σ s :

Length parameter for platinum (m)

ψ 3 :

Uniformly distributed number in (0, 1)

ψ1, ψ2:

Gaussian-distributed random numbers with zero mean and unit variance

ρ :

Density (kg m−3)

ε :

Energy parameter (J)

ɛ s :

Energy parameter for platinum (J)

ϕ :

Potential function (J)

ϕ w :

Wall potential function (J)

δt :

Time step (s)

c:

Cutoff

i :

ith

s:

Solid

x :

x direction

y :

y direction

z :

z direction

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Authors and Affiliations

  1. Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran

    D. Toghraie Semiromi & A. R. Azimian

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  1. D. Toghraie Semiromi
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  2. A. R. Azimian
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Correspondence to D. Toghraie Semiromi.

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Toghraie Semiromi, D., Azimian, A.R. Nanoscale Poiseuille flow and effects of modified Lennard–Jones potential function. Heat Mass Transfer 46, 791–801 (2010). https://doi.org/10.1007/s00231-010-0624-4

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  • DOI: https://doi.org/10.1007/s00231-010-0624-4

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