  We apply the scattering approach to the Casimir interaction between two
dielectric half-spaces separated by an electrolyte solution. We take the
nonlocal electromagnetic response of the intervening medium into account, which
results from the presence of movable ions in solution. In addition to the usual
transverse modes, we consider longitudinal channels and their coupling by
reflection at the surface of the local dielectric. The Casimir interaction
energy is calculated from the matrix describing a round-trip of coupled
transverse and longitudinal waves between the interacting surfaces. The
nonzero-frequency contributions are approximately unaffected by the presence of
ions. We find, at zero frequency, a contribution from longitudinal channels,
which is screened over a distance of the order of the Debye length, alongside
an unscreened term arising from transverse-magnetic modes. The latter defines
the long-distance asymptotic limit for the interaction.
