  We study the effective interaction mediated by strongly coupled Coulomb
fluids between dielectric surfaces carrying quenched, random monopolar charges
with equal mean and variance, both when the Coulomb fluid consists only of
mobile multivalent counterions and when it consists of an asymmetric ionic
mixture containing multivalent and monovalent (salt) ions in equilibrium with
an aqueous bulk reservoir. We analyze the consequences that follow from the
interplay between surface charge disorder, dielectric and salt image effects,
and the strong electrostatic coupling that results from multivalent counterions
on the distribution of these ions and the effective interaction pressure they
mediate between the surfaces. In a dielectrically homogeneous system, we show
that the multivalent counterions are attracted towards the surfaces with a
singular, disorder-induced potential that diverges logarithmically on approach
to the surfaces, creating a singular counterion density profile with an
algebraic divergence at the surfaces. This effect drives the system towards a
state of lower thermal "disorder", one that can be described by a renormalized
temperature, exhibiting thus a remarkable antifragility. The interaction
pressure acting on the surfaces displays in general a highly non-monotonic
behavior as a function of the inter-surface separation with a prominent regime
of attraction at small to intermediate separations. This attraction is caused
directly by the combined effects from charge disorder and strong coupling
electrostatics of multivalent counterions, which can be quite significant even
with a small degree of surface charge disorder relative to the mean surface
charge. The strong coupling, disorder-induced attraction is typically far more
stronger than the van der Waals interaction between the surfaces, especially
within a range of several nanometers for the inter-surface separation.
