Prediction of sonochemical activity based on dimensionless analysis and multivariate linear regression

Acoustic cavitation is influenced by multiple variables, including ultrasound frequency, power, and reactor configuration, all of which exert interactive and nonlinear effects on the performance of sonochemical systems. Current research on parametric effects has predominantly focused on the general trends of individual parameters, with limited investigation into their combined and interdependent influences. In this study, the sonochemical activity was systematically measured using sonochemiluminescence (SCL) and potassium iodide (KI) dosimetry under over 110 distinct operating conditions. The experimental data were transformed into dimensionless form to examine multi-parameter coupling effects in ultrasonic processes. Through theoretical analysis and experimental validation, seven dimensionless numbers (Π1-Π7) were identified, elucidating the roles of bubble dynamics, cavitation environment, acoustic wave propagation, and thermal effects in sonochemical processes. A dimensionless multivariate regression model framework was then developed to predict sonochemical activity under varying operating conditions. The applicability and generalizability of the model were verified by comparing predictive results with published studies. The study is the first to systematically integrate dimensionless analysis with multivariate regression, enabling a comprehensive exploration of multi-parameter coupling effects on sonochemical activity and establishing a predictive mathematical modelling framework. This deepens the understanding of the dynamics of ultrasonic cavitation and lays the foundation for future applications in more complex fluid systems, non-aqueous media, and different types of ultrasound equipment. Therefore, this study represents an initial step toward advancing multi-parameter optimisation strategies in sonochemistry, offering a novel framework for systematically optimising sonochemical systems and guiding future experimental and industrial applications.