  In situations involving large potentials or surface charges, the Poisson
Boltzman(PB) equation has shortcomings because it neglects ion-ion interactions
and steric effects. This has been widely recognized by the electrochemistry
community, leading to the development of various alternative models resulting
in different sets "modified PB equations", which have had at least qualitative
success in predicting equilibrium ion distributions. On the other hand, the
literature is scarce in terms of descriptions of concentration dynamics in
these regimes. Here, adapting strategies developed to modify the PB equation,
we propose a simple modification of the widely used Poisson-Nernst-Planck (PNP)
equations for ionic transport, which at least qualitatively accounts for steric
effects. We analyze numerical solutions of these MPNP equations on the model
problem of the charging of a simple electrolyte cell, and compare the outcome
to that of the standard PNP equations. Finally, we repeat the asymptotic
analysis of Bazant, Thornton, and Ajdari(2004} for this new system of equations
to further document the interest and limits of validity of the simpler
equivalent electrical circuit models introduced in Part I for such problems.
