The van der Waals interaction of microparticles with a substrate characterized by a nonlocal response

The van der Waals energy of the system constituted by a microparticle and a solid surface characterized by a nonlocal response is calculated taking into account an influence of another microparticle. A saturation of the dispersion interaction at short distances from the surface both for the spectral density of energy and for the total energy is shown. The known McLachlan expression for the pair and triple energies in the case of local media directly follows from the obtained general expression.