  We consider two charged semipermeable membranes, which bound bulk electrolyte
solutions and are separated by a thin film of salt-free liquid. Small
counter-ions permeate into the gap, which leads to a steric charge separation
in the system. To quantify the problem, we define an effective surface charge
density of imaginary impermeable surface, which mimics an actual semipermeable
membrane and greatly simplify analysis. The effective charge depends on
separation, generally differ from the real one, and could even be of the
opposite sign. From the exact and asymptotic solutions of the nonlinear
Poisson-Boltzmann equation, we obtain the distribution of the potential and of
counter-ions in the system. We then derive explicit formulae for the disjoining
pressure in the gap and electro-osmotic velocity, and show that both are
controlled by the effective surface charge.
