A generalized dimensionless rule linking ultrasound cavitation and separation processes across multiple scales developed by experimental and simulation investigations.

The scale-up physics of ultrasound-enhanced separation is highly non-linear and remains insufficiently studied, limiting its industrial applications. To address this, the underlying mechanisms of ultrasound-enhanced extraction and adsorption were investigated using a 20 kHz probe with a diameter of 4 cm, and analyzed through interdisciplinary approaches, yielding novel insights. First, extraction and adsorption have distinct mass transfer resistances. For micron-level materials, the primary mass transfer resistance during extraction is concentrated at the solid-liquid interface, whereas the main resistance during adsorption is located inside the adsorbent. The disruption induced by ultrasound cavitation, instead of the direct effect of ultrasound cavitation, dynamically alters separation mass transfer mechanisms. Additionally, the solvent type used in separation influences the observable bubble density within the ultrasound cavitation cloud. The increased bubble number may not correspond to cavitation bubbles, as non-cavitation bubbles do not contribute to cavitation energy. Finally, a dimensionless rule has been formulated and validated to link separation with ultrasound cavitation across different scales. This rule introduces a polynomial relationship to quantify changes in separation yield (ΔC×Vm) using two dimensionless terms (lgACP×t×Lm and (rL). ACP×t×Lm represents ultrasonic separation factor incorporating the energy of single cavitation energy, cavitation bubble density and separation scale. rL characterizes the disruptive effects of ultrasound. As the first dimensionless rule to bridge ultrasound cavitation dynamics with mass transfer in separation processes, this work lays the foundation for scaling up these processes with greater precision and industrial applicability.