  Continuum simulation is employed to study ion transport and fluid flow
through a nanopore in a solid-state membrane under an applied potential drop.
Results show the existence of concentration polarization layers on the surfaces
of the membrane. The nonuniformity of the ionic distribution gives rise to an
electric pressure that drives vortical motion in the fluid. There is also a net
hydrodynamic flow through the nanopore due to an asymmetry induced by the
membrane surface charge. The qualitative behavior is similar to that observed
in a previous study using molecular dynamic simulations. The current--voltage
characteristics show some nonlinear features but are not greatly affected by
the hydrodynamic flow in the parameter regime studied. In the limit of thin
Debye layers, the electric resistance of the system can be characterized using
an equivalent circuit with lumped parameters. Generation of vorticity can be
understood qualitatively from elementary considerations of the Maxwell
stresses. However, the flow strength is a strongly nonlinear function of the
applied field. Combination of electrophoretic and hydrodynamic effects can lead
to ion selectivity in terms of valences and this could have some practical
applications in separations.
