  The forces between charged macromolecules, usually given in terms of osmotic
pressure, are highly affected by the intervening ionic solution. While in most
theoretical studies the solution is treated as a homogeneous structureless
dielectric medium, recent experimental studies concluded that, for a bathing
solution composed of two solvents (binary mixture), the osmotic pressure
between charged macromolecules is affected by the binary solvent composition.
By adding local solvent composition terms to the free energy, we obtain a
general expression for the osmotic pressure, in planar geometry and within the
mean-field framework. The added effect is due to the permeability inhomogeneity
and nonelectrostatic short-range interactions between the ions and solvents
(preferential solvation). This effect is mostly pronounced at small distances
and leads to a reduction in the osmotic pressure for macromolecular separations
of the order 1--2 nm. Furthermore, it leads to a depletion of one of the two
solvents from the charged macromolecules (modeled as planar interfaces).
Lastly, by comparing the theoretical results with experimental ones, an
explanation based on preferential solvation is offered for recent experiments
on the osmotic pressure of DNA solutions.
