  In this paper we theoretically demonstrate the tunability of the Casimir
force both in sign and magnitude between parallel plates coated with dispersive
materials. We show that this force, existing between uncharged plates, can be
tuned by carefully choosing the value of the plasma frequency (i.e., the
epsilon-near-zero frequency) of the coating in the neighborhood of the
resonance frequency of the cavity. The coating layer enables a continuous
variation of the force between four limiting values when a coating is placed on
each plate. We explore the consequences of such variation when pairs of
electric and magnetic conductors (i.e. low and high impedance surfaces) are
used as substrates on either side, showing that this continuous variation
results in changes in the sign of the force, leading to both stable and
unstable conditions, which could find interesting potential applications in
nanomechanics including nanoparticle tweezing.
