We consider a mixture of large spherical nanoparticles with the charge distributed over the surface and point-like ions embedded in an aqueous solution between two similarly-charged surfaces. The finite size of nanoparticles is included via a lattice gas entropy. The electrostatic energy takes into account exact charge distribution on the nanoparticles surface. For this system the Euler-Lagrange equations are derived and solved numerically. The results show a big impact of nanoparticle's size on the concentration profiles and characteristics of electric double layer. The theoretical model predicts an attractive interaction between like charged surfaces for large enough nanoparticles with large enough charge and the addition of point-like salt ions decreases the range of attraction.
