Energy Distribution during Resonant Acoustic Mixing.

Resonant acoustic mixing (RAM) systems utilize vertical oscillations at resonance frequencies to mix fluids and powders efficiently. Understanding the thermodynamic and energy transfer mechanisms underlying RAM processes is critical for optimizing mixing applications, but they are poorly understood. This study investigates the multiscale energy redistribution in RAM systems, focusing on the interplay between surface energy and turbulent kinetic energy. A first- and second-law thermodynamic analysis is employed to model energy contributions from work, heat transfer, surface instabilities, and kinetic energy dissipation. The proposed model couples the surface deformation to the scale of subsurface rotational flow, where activated Faraday instability surface modes control how input work affects the bulk fluid kinetic energy distribution. Experimental measurements of fluid surface curvature under nominal accelerations of 5, 15, and 20 g reveal a significant increase in the rate of smaller radii, corresponding to active surface modes. Specific kinetic energy was calculated using fluid surface element position data and revealed an approximately 70% increase for decaying features over growing features. These findings demonstrate the multiscale redistribution of energy from larger- to smaller-scale rotational flow and its coupling to the surface modes before culminating in viscous dissipation. The implications of this coupling on the mixing process are discussed. This work provides a foundation for optimizing RAM systems and advancing their application across a range of industrial processes.