Faraday instability of a three-layer fluid system in a Hele-Shaw cell: Transition from zigzag mode to B-interface instability mode

We experimentally observe the Faraday instability transition of a three-layer fluid system from zigzag mode to B-interface instability mode in a Hele-Shaw cell by changing the excitation, the thickness of the liquid layer, and the fluid properties. Floquet analysis shows that the transitions strongly depend on the interfacial coupling in the system. For a more detailed explanation of the mode transition process, the relationship between the interface coupling and the amplitude ratio ζA/ζB of two interfaces is established. Considering the zero-order interface coupling effect, we identify that the mode transition can be promoted by increasing the wave number and thickness of the middle layer liquid. Furthermore, by including the effect of first-order interface coupling, it is evident that a decrease in vibration acceleration and an increase in viscosity can promote mode transition from the dispersion relation. However, the interface tends to stabilize as the viscosity is further increased.