  The classical Gibbs-Donnan equilibrium describes excess osmotic pressure
associated with confined colloidal charges embedded in an electrolyte solution.
In this work, we extend this approach to describe the influence of multivalent
ion binding on the equilibrium force acting on a charged rod translocating
between two compartments, thereby mimicking ionic effects on force balance
during in vitro DNA ejection from bacteriophage. The subtle interplay between
Gibbs-Donnan equilibrium and adsorption equilibrium leads to a non-monotonic
variation of the ejection force as multivalent salt concentration is increased,
in qualitative agreement with experimental observations.
