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


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.


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

List of symbols


Constants determined by BC

A, B

Constants for inhomogeneous diffusion

Ai, Bi

Airy functions




Real constants


Bulk diffusion coefficient


Apparent diffusion coefficient


Diffusion functional


Apparent diffusion functional


Hypergeometric function


Magnitude of external driving force




Gibbs free energy


Gibbs free energy at equilibrium


Boundary value for concentration


Hermitian polyomial


Channel height


Diffusional flux


Gradient energy coefficient


Spring constant


Length of the computational domain in the x-direction


Length of the computational domain in the y-direction


Length of the computational domain in the z-direction


Diffusional mobility


Integer number, n = 0, 1, 2…




Boundary value for the non-classic flux term


Position of a wall atom on fcc lattice site


Position vector of atom i


Distance vector between ith and jth atom






LJ potential of atom i with atom j




Boundary condition for the normal flux


Normalized distances in the z-direction

Greek letters


Energy parameter in the LJ potential


Local chemical potential


Fluid density


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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