Casimir force for electrolytes

The Casimir force between a pair of parallell plates filled with ionic particles is considered. We use a statistical mechanical approach and consider the classical high temperature limit. In this limit the ideal metal result with no transverse electric (TE) zero frequency mode is recovered. This result has also been obtained by Jancovici and \v{S}amaj earlier. Our derivation differs mainly from the latter in the way the Casimir force is evaluated from the correlation function. By our approach the result is easily extended to electrolytes more generally. Also we show that when the plates are at contact the Casimir force is in accordance with the bulk pressure as follows from the virial theorem of classical statistical mechanics.