A quasi-continuum hydrodynamic model for slit shaped nanochannel flow.

We propose a quasi-continuum hydrodynamic model for isothermal transport of Lennard-Jones fluid confined in slit shaped nanochannels. In this work, we compute slip and viscous contributions independently and superimpose them to obtain the total velocity profile. Layering of fluid near the interface plays an important role in viscous contribution to the flow, by apparent viscosity change along the confining dimension. This relationship necessitates computing density profiles, which is done using the recently proposed empirical-potential based quasi-continuum theory [A. V. Raghunathan, J. H. Park, and N. R. Aluru, J. Chem. Phys. 127, 174701 (2007)]. Existing correlations for density dependent viscosity provided by Woodcock [AIChE J. 52, 438 (2006)] are used to compute viscosity profile in the nanopores. A Dirichlet type slip boundary condition based on a static Langevin friction model describing center-of-mass motion of fluid particles is used, the parameters of which are dependent on the fluctuations of total wall-fluid force from an equilibrium molecular dynamics simulation. Different types of corrugated surfaces are considered to study wall-fluid friction effects on boundary conditions. Proposed hydrodynamic model yields good agreement of velocity profiles obtained from non-equilibrium molecular dynamics simulations for gravity driven flow.