Microfluidics and Nanofluidics

, Volume 17, Issue 6, pp 1011–1023 | Cite as

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

  • Antonios E. Giannakopoulos
  • Filippos Sofos
  • Theodoros E. Karakasidis
  • Antonios Liakopoulos
Research Paper

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

A1–4

Constants determined by BC

A, B

Constants for inhomogeneous diffusion

Ai, Bi

Airy functions

c

Concentration

c1–3

Real constants

D

Bulk diffusion coefficient

Dap

Apparent diffusion coefficient

F

Diffusion functional

Fap

Apparent diffusion functional

1F1

Hypergeometric function

Fext

Magnitude of external driving force

g

Wavelength

G

Gibbs free energy

G0

Gibbs free energy at equilibrium

h

Boundary value for concentration

H

Hermitian polyomial

hch

Channel height

J

Diffusional flux

K

Gradient energy coefficient

K*

Spring constant

Lx

Length of the computational domain in the x-direction

Ly

Length of the computational domain in the y-direction

Lz

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

req

Position of a wall atom on fcc lattice site

ri

Position vector of atom i

rij

Distance vector between ith and jth atom

T

Temperature

S

Area

u(rij)

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

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Antonios E. Giannakopoulos
    • 1
  • Filippos Sofos
    • 1
  • Theodoros E. Karakasidis
    • 1
  • Antonios Liakopoulos
    • 1
  1. 1.Department of Civil Engineering, School of EngineeringUniversity of ThessalyPedion Areos, VolosGreece

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