Counterion distribution and charge-fluctuation interactions between like-charged fluid membranes

We revisit the problem of the electrostatic attraction between like-charged membranes. In particular, we solve for the spatial distribution of counterions and the effects of counterion-density fluctuations on the membrane interaction simultaneously. This allows for an explicit calculation of the interaction between the membranes for a wide range of the membrane separation D, without suppressing the spatial counterion distribution. Our approach suggests that multivalency is required for the adhesion of typical biomembranes, consistent with experimental and numerical data; the interaction is repulsive for monovalent cases and turns into an attraction when counterions become multivalent. When counterions are assumed to be localized to the membrane surface, however, the interaction is repulsive for divalent cases, even when the membranes are fully charged.