Microfluidics and Nanofluidics

, Volume 17, Issue 6, pp 1011–1023

A quasi-continuum multi-scale theory for self-diffusion and fluid ordering in nanochannel flows

Authors

  • Antonios E. Giannakopoulos
    • Department of Civil Engineering, School of EngineeringUniversity of Thessaly
  • Filippos Sofos
    • Department of Civil Engineering, School of EngineeringUniversity of Thessaly
    • Department of Civil Engineering, School of EngineeringUniversity of Thessaly
  • Antonios Liakopoulos
    • Department of Civil Engineering, School of EngineeringUniversity of Thessaly
Research Paper

DOI: 10.1007/s10404-014-1390-2

Cite this article as:
Giannakopoulos, A.E., Sofos, F., Karakasidis, T.E. et al. Microfluid Nanofluid (2014) 17: 1011. doi:10.1007/s10404-014-1390-2

Abstract

We present a quasi-continuum self-diffusion theory that can capture the ordering effects and the density variations that are predicted by non-equilibrium molecular dynamics (NEMD) in nanochannel flows. A number of properties that affect fluid ordering in NEMD simulations are extracted and compared with the quasi-continuum predictions. The proposed diffusion equation requires the classic diffusion coefficient D and a micro structural internal length g that relates directly to the shape of the molecular potential of the NEMD calculations. The quasi-continuum self-diffusion theory comes as an alternative to atomistic simulation, bridging the gap between continuum and atomistic behavior with classical hydrodynamic relations and reduces the computational burden as compared with fully atomistic simulations.

Keywords

Quasi-continuum theory Molecular dynamics Self-diffusion equation Nanochannel flows Fluid ordering Density profile oscillations

List of symbols

A 1–4

Constants determined by BC

A, B

Constants for inhomogeneous diffusion

A i , B i

Airy functions

c

Concentration

c 1–3

Real constants

D

Bulk diffusion coefficient

D ap

Apparent diffusion coefficient

F

Diffusion functional

F ap

Apparent diffusion functional

1 F 1

Hypergeometric function

F ext

Magnitude of external driving force

g

Wavelength

G

Gibbs free energy

G 0

Gibbs free energy at equilibrium

h

Boundary value for concentration

H

Hermitian polyomial

h ch

Channel height

J

Diffusional flux

K

Gradient energy coefficient

K *

Spring constant

L x

Length of the computational domain in the x-direction

L y

Length of the computational domain in the y-direction

L z

Length of the computational domain in the z-direction

M

Diffusional mobility

n

Integer number, n = 0, 1, 2…

p

Pressure

q

Boundary value for the non-classic flux term

r eq

Position of a wall atom on fcc lattice site

r i

Position vector of atom i

r ij

Distance vector between ith and jth atom

T

Temperature

S

Area

u(r ij )

LJ potential of atom i with atom j

V

Volume

w

Boundary condition for the normal flux

z *

Normalized distances in the z-direction

Greek letters

ε

Energy parameter in the LJ potential

μ

Local chemical potential

ρ

Fluid density

σ

Length parameter in the LJ potential

Copyright information

© Springer-Verlag Berlin Heidelberg 2014