  We study theoretically the osmotic pressure of a suspension of charged
objects (e.g., colloids, polyelectrolytes, clay platelets, etc.) dialyzed
against an electrolyte solution using the cell model and linear
Poisson-Boltzmann (PB) theory. From the volume derivative of the grand
potential functional of linear theory we obtain two novel expressions for the
osmotic pressure in terms of the potential- or ion-profiles, neither of which
coincides with the expression known from nonlinear PB theory, namely, the
density of microions at the cell boundary. We show that the range of validity
of linearization depends strongly on the linearization point and proof that
expansion about the selfconsistently determined average potential is optimal in
several respects. For instance, screening inside the suspension is
automatically described by the actual ionic strength, resulting in the correct
asymptotics at high colloid concentration. Together with the analytical
solution of the linear PB equation for cell models of arbitrary dimension and
electrolyte composition explicit and very general formulas for the osmotic
pressure ensue. A comparison with nonlinear PB theory is provided. Our analysis
also shows that whether or not linear theory predicts a phase separation
depends crucially on the precise definition of the pressure, showing that an
improper choice could predict an artificial phase separation in systems as
important as DNA in physiological salt solution.
