  Understanding the force between charged surfaces immersed in an electrolyte
solution is a classic problem in soft matter and liquid-state theory. Recent
experiments showed that the force decays exponentially but the characteristic
decay length in a concentrated electrolyte is significantly larger than what
liquid-state theories predict based on analysing correlation functions in the
bulk electrolyte. Inspired by the classical Casimir effect, we consider an
alternative mechanism for force generation, namely the confinement of density
fluctuations in the electrolyte by the walls. We show analytically within the
random phase approximation, which assumes the ions to be point charges, that
this fluctuation-induced force is attractive and also decays exponentially,
albeit with a decay length that is half of the bulk correlation length. These
predictions change dramatically when excluded volume effects are accounted for
within the mean spherical approximation. At high ion concentrations the Casimir
force is found to be exponentially damped oscillatory as a function of the
distance between the confining surfaces. Our analysis does not resolve the
riddle of the anomalously long screening length observed in experiments, but
suggests that the Casimir force due to mode restriction in density fluctuations
could be an hitherto under-appreciated source of surface-surface interaction.
