  The non-linear Poisson-Boltzmann equation for a circular, uniformly charged
platelet, confined together with co- and counter-ions to a cylindrical cell, is
solved semi-analytically by transforming it into an integral equation and
solving the latter iteratively. This method proves efficient, robust, and can
be readily generalized to other problems based on cell models, treated within
non-linear Poisson-like theory. The solution to the PB equation is computed
over a wide range of physical conditions, and the resulting osmotic equation of
state is shown to be in fair agreement with recent experimental data for
Laponite clay suspensions, in the concentrated gel phase.
