Vacuum fluctuations are a fundamental and irremovable property of a quantized
electromagnetic field. These fluctuations are the cause of the Casimir effect
-- mutual attraction of two electrically neutral metallic plates in vacuum in
the absence of any other interactions. For most geometries and materials,
Casimir effect is strictly attractive, leading to the only stable equilibrium
configuration with merged plates. Recent observation showed, however, that this
unavoidable vacuum-induced attraction can be mitigated by the presence of
electrostatic repulsion produced by the formation of double electric layers,
and a stable equilibrium between two charged metallic plates in a solution of
an organic salt can be reached. Here, we study theoretically in details
equilibrium configurations and their dynamical behavior in the system of two
parallel metallic films coupled by the Casimir and electrostatic interactions.
We analyze the effect of various parameters of the system -- such as the salt
concentartion and temperature -- on the equilibrium cavity thicknesses, inspect
resonant properties of the resulting an-harmonic optomechanical system near
equilibrium, and examine its stochastic dynamics under the influence of thermal
fluctuations of the environment