A quasicontinuum multiscale theory for selfdiffusion and fluid ordering in nanochannel flows
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DOI: 10.1007/s1040401413902
 Cite this article as:
 Giannakopoulos, A.E., Sofos, F., Karakasidis, T.E. et al. Microfluid Nanofluid (2014) 17: 1011. doi:10.1007/s1040401413902
Abstract
We present a quasicontinuum selfdiffusion theory that can capture the ordering effects and the density variations that are predicted by nonequilibrium molecular dynamics (NEMD) in nanochannel flows. A number of properties that affect fluid ordering in NEMD simulations are extracted and compared with the quasicontinuum 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 quasicontinuum selfdiffusion 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
Quasicontinuum theory Molecular dynamics Selfdiffusion equation Nanochannel flows Fluid ordering Density profile oscillationsList 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 xdirection
 L _{ y }

Length of the computational domain in the ydirection
 L _{ z }

Length of the computational domain in the zdirection
 M

Diffusional mobility
 n

Integer number, n = 0, 1, 2…
 p

Pressure
 q

Boundary value for the nonclassic 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 zdirection
Greek letters
 ε

Energy parameter in the LJ potential
 μ

Local chemical potential
 ρ

Fluid density
 σ

Length parameter in the LJ potential