  Most theoretical and simulation studies on charged particles suspensions are
at infinite dilution conditions. Hence these studies have been focused on the
electrolyte structure around an isolated central particle (or elctrode), where
phenomena as charge reversal, charge inversion and overcharging have been shown
to be relevant. However, experimental studiesat finite volume fraction exhibit
interesting phenomenology which imply very long-range correlations. Inthis
paper we apply an integral equation theory to a simple model for a charged
macroions suspension, at finite volume fraction, and find two new effects of
long-range overcharging and long-range charge reversal. These new effects are
different from the classical overcharging and charge reversal in that they
occur at finite macroion's volume fraction, far away from the central macroion,
are much more intense, and increase, not decrease, as a function of the
distance to the central particle, which is indicative of correlations at large
separations. We find our results to be qualitative consistent with existing
experimental results, and Monte Carlo simulations.
