  We investigate the effect of monopolar charge disorder on the classical
fluctuation-induced interactions between randomly charged net-neutral
dielectric slabs and discuss various generalizations of recent results (A. Naji
et al., Phys. Rev. Lett. 104, 060601 (2010)) to highly inhomogeneous dielectric
systems with and without statistical disorder correlations. We shall focus on
the specific case of two generally dissimilar plane-parallel slabs, which
interact across vacuum or an arbitrary intervening dielectric medium. Monopolar
charge disorder is considered to be present on the bounding surfaces and/or in
the bulk of the slabs, may be in general quenched or annealed and may possess a
finite lateral correlation length reflecting possible `patchiness' of the
random charge distribution. In the case of quenched disorder, the bulk disorder
is shown to give rise to an additive long-range contribution to the total
force, which decays as the inverse distance between the slabs and may be
attractive or repulsive depending on the dielectric constants of the slabs. We
show that in the case of two dissimilar slabs the net effect due to the
interplay between the disorder-induced and the pure van der Waals interactions
can lead to a variety of unusual non-monotonic interaction profiles between the
dielectric slabs. In particular, when the intervening medium has a larger
dielectric constant than the two slabs, we find that the net interaction can
become repulsive and exhibit a potential barrier, while the underlying van der
Waals force is attractive. On the contrary, when the intervening medium has a
dielectric constant in between that of the two slabs, the net interaction can
become attractive and exhibit a free energy minimum, while the pure van der
Waals force is repulsive. Therefore, the charge disorder, if present, can
drastically alter the effective interaction between net-neutral objects.
