  We consider the limit of vanishing Debye length for ionic diffusion in
fluids, described by the Nernst-Planck-Navier-Stokes system. In the
asymptotically stable cases of blocking (vanishing normal flux) and uniform
selective (special Dirichlet) boundary conditions for the ionic concentrations,
we prove that the ionic charge density $\rho$ converges in time to zero in the
interior of the domain, in the limit of vanishing Debye length ($\epsilon\to
0$). For the unstable regime of Dirichlet boundary conditions for the ionic
concentrations, we prove bounds that are uniform in time and $\epsilon$. We
also consider electroneutral boundary conditions, for which we prove that
electroneutrality $\rho\to 0$ is achieved at any fixed $\epsilon> 0$,
exponentially fast in time in $L^p$, for all $1\le p<\infty$. The results hold
for two oppositely charged ionic species with arbitrary ionic diffusivities, in
bounded domains with smooth boundaries.
