  Recent advance in nanotechnology has led to rapid advances in nanofluidics,
which has been established as a reliable means for a wide variety of
applications, including molecular separation, detection, crystallization and
biosynthesis. Although atomic and molecular level consideration is a key
ingredient in experimental design and fabrication of nanfluidic systems, atomic
and molecular modeling of nanofluidics is rare and most simulations at
nanoscale are restricted to one- or two-dimensions in the literature, to our
best knowledge. The present work introduces atomic scale design and
three-dimensional (3D) simulation of ionic diffusive nanofluidic systems. We
propose a variational multiscale framework to represent the nanochannel in
discrete atomic and/or molecular detail while describe the ionic solution by
continuum. Apart from the major electrostatic and entropic effects, the
non-electrostatic interactions between the channel and solution, and among
solvent molecules are accounted in our modeling. We derive generalized
Poisson-Nernst-Planck (PNP) equations for nanofluidic systems. Mathematical
algorithms, such as Dirichlet to Neumann mapping and the matched interface and
boundary (MIB) methods are developed to rigorously solve the aforementioned
equations to the second-order accuracy in 3D realistic settings. Three ionic
diffusive nanofluidic systems, including a negatively charged nanochannel, a
bipolar nanochannel and a double-well nanochannel are designed to investigate
the impact of atomic charges to channel current, density distribution and
electrostatic potential. Numerical findings, such as gating, ion depletion and
inversion, are in good agreements with those from experimental measurements and
numerical simulations in the literature.
