Contact singularity between curved dielectric surfaces

The induced polarization charges density on two dielectric surfaces in proximity appear to diverge as separation decrease. This diverging charge density cannot be resolved by the conventional numerical methods or series expansions because the surface charges demand ever-increasing spatial resolution that becomes intractable in the near-contact regime. We analyze the asymptotic behavior of this contact singularity by adopting the 'lubrication' approximation, and demonstrate explicitly the singular dependence on the gap distance and the curvature of two approaching surfaces. The result agrees with the known logarithmic singularity for conducting surfaces and, for dielectric surfaces, provides a means for isolating the singularity and calculating the cohesive energy for ensembles of dielectric particles in close contact.