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We show that a nonlocal formulation of the Lifshitz theory of van der Waals interactions valid for continuous dielectric profiles can be used as a starting point to calculate self-consistent dielectric profiles. The general approach advocated here is very close to the formulation of electrostatic self-consistent charge density profiles obtained from the Poisson - Boltzmann theory. The calculated dielectric profiles obtained from minimization of the free energy containing a lattice gas entropy contribution on top of the Lifshitz interaction energy give quite surprising and interesting results. The ramifications of these results for the distribution of polarizable matter between two homogeneous dielectric slabs will be discussed in detail.

Self-consistent inhomogeneous dielectric response profiles from a nonlocal continuous Lifshitz formulation of van der Waals interactions