The Casimir effect, a macroscopic manifestation of quantum phenomena, arises from zero-point energy and thermal fluctuations. When two objects are brought into close proximity, the Casimir effect manifests as a repulsive force, while at greater separations, it transitions to an attractive force. There exists a specific distance at which the Casimir force vanishes, referred to as the stable Casimir equilibrium. Stable Casimir equilibria arise from the curve minima of the Casimir energy, which can create spatial trapping. The manipulation of stable Casimir equilibria offers promising applications in areas such as tunable optical resonators and self-assembly. This paper presents a scheme for achieving tunable Casimir equilibria in a dual-liquid system. The system comprises a multilayered stratified structure with a gold substrate. Above the gold substrate, a stratified liquid system is formed due to the immiscibility between organic solutions and water. The lower-density solution is on top, while the higher-density one lies beneath. Our results suggest that a stable Casimir equilibrium for a suspended gold nanoplate can be realized, when the suspended gold nanoplate is immersed in organic solutions of toluene or benzene. Moreover, the height of the suspended gold nanoplate, determined by the stable Casimir equilibrium, can be precisely tuned by varying the thickness of the water layer. The effects of finite temperature and ionic concentration on the Casimir equilibria are also analyzed in this work. The results suggest that the separation heights of Casimir equilibria decrease with increasing the temperature. Interestingly, the ionic concentration in water significantly affects the Casimir pressure when the Debye screening length is comparable or smaller than the separation, allowing for a wide range of modulations on Casimir equilibria. This work opens a new avenue for tuning Casimir equilibria, with significant applications for "quantum trapping" of micro-nano particles.
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