Electrostatic correlations in colloidal suspensions: Density profiles and effective charges beyond the Poisson-Boltzmann theory

A theory is proposed which allows us to calculate the distribution of the multivalent counterions around a colloidal particle using the cell model. The results are compared with the Monte Carlo simulations and are found to be very accurate in the two asymptotic regimes, close to the colloidal particle and far from it. The theory allows to accurately calculate the osmotic pressure and the effective charge of colloidal particles with multivalent counterions.