Distribution based design framework for ultrasonic process intensification using effective acoustic intensity

Abstract

Abstract Ultrasonic processes are widely applied for dispersion and structural transformation of layered materials. In such processes, performance is often evaluated based on total input energy. However, because the acoustic pressure field in a liquid medium is inherently spatially non-uniform and cavitation is a threshold-driven local phenomenon, the input power does not directly represent the spatial acoustic environment within the reactor. In this study, a distribution-aware framework is proposed to characterize ultrasonic process intensification beyond conventional power-based evaluation. Time-harmonicaxisymmetric (r–z) acoustic pressure fields were numerically obtained and reduced to statistical field descriptors, including the volume-averaged mean-square pressure and the effective acoustic intensity, I eff . These descriptors were quantitatively correlated with experimentally obtained dispersion kinetics of α-zirconium phosphate (α-ZrP) suspensions. For Jeffamine-intercalated systems, the effective dispersion rate constant increased monotonically with I eff , demonstrating a clear correlation between the FEM-derived acoustic-field descriptor and the experimentally observed dispersion kinetics. In contrast, TBAH-intercalated systems exhibited a weaker dependence on I eff , with a tendency toward saturation at higher intensities. Importantly, within the investigated conditions, the resulting particle morphology—nanosheet exfoliation versus fragmentation—was less sensitive to I eff and remained qualitatively dependent on the intercalating agent. These results support a distinction between field-dependent dispersion kinetics and material-dependent morphology within the investigated conditions. The proposed framework provides a quantitative basis for distribution-aware analysis of ultrasonic processes beyond conventional power-based evaluation.