Faraday instability of non-Newtonian fluids under low-frequency vertical harmonic vibration

Resonance Acoustic Mixing® (RAM) technology applies an external low-frequency vertical harmonic vibration to convey and mix the non-Newtonian fluid across space. However, although this method is used for various applications, its mechanism is yet not well understood. In this paper, we investigate the Faraday instability of power-law non-Newtonian fluids in RAM utilizing theory and simulations. According to the Floquet analysis and the dimensionless Mathieu equation, the critical stable region besides the stable region and the unstable region is discovered. Based on the numerical solutions of the two-dimensional incompressible Euler equations for a prototype Faraday instability flow, the temporal evolution of the surface displacement and the mechanism of Faraday waves for two cases are explored physically. For the low forcing displacement, there are only stable and critical stable regions. The surface deformation increases linearly and then enters the steady-state in which the fluctuation frequency is twice the vertical harmonic vibration. For the large forcing displacement, there are only stable and unstable regions. Under the effect of the inertial force, both cases have a sudden variation after the brief stabilization period. Furthermore, a ligament structure is observed, which signals that the surface is destabilized. In addition, a band-like pressure minimum distribution below the interface is formed. The fluid flows from the bottom to the crest portion to balance the pressure difference, which raises the crest.