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Wall Functions for Incorporation of Atomistic Physics into Continuum Modeling of Electrokinetic Flow

R.H. Nilson and S.K. Griffiths
Sandia National Laboratories, US

microfluidics, nanofluidics, DFT, micro-chemlab, nanochannel

The atomistic physics of fluid/solid interfacial layers may substantially influence liquid flow and ion transport, particularly in nanoscale channels. Previous studies addressing non-continuum fluid mechanics have been largely based on Molecular Dynamics (MD) simulations that often require long computing times and are not readily integrated into traditional continuum models needed to address complex multiscale systems of engineering interest. To address these concerns, we utilize Density Functional Theory (DFT) to compute continuous time-mean profiles of fluid density and ion concentrations in nanoscale channels. These results are then used to evaluate fluid viscosities and electrical driving forces appearing in the continuum Navier-Stokes equations. Electroosmotic speeds determined in this hybrid atomistic/continuum manner are typically two to three times smaller than classical continuum estimates, in keeping with previous MD simulations of nanoscale flows. In addition, it is demonstrated that “wall functions” derived from a single DFT calculation for a channel of moderate width can be applied to all other channel widths with very little loss of accuracy. The primary inputs to the DFT model and the associated wall functions are the Lennard-Jones parameters and charge numbers of the fluid and solid species, just as in MD simulations.

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