A new strategy for modelling sonochemical reactors: Coupling of the non-linear Louisnard model with mass and heat transport equations with applications to cavitating viscous fluids

Abstract

In this work, novel numerical models were developed and validated to offer new strategies in modelling sonochemical reactors. More specifically, in our original approach the non-linear Louisnard model was coupled with heat and mass transport equations to predict gradients in temperature and species concentration in a sonicated reactor. Additionally, a new operating window was investigated by modelling mixtures of increasing viscosity on both micro- and macroscale sonochemical effects. On the microscale, the effects of increasing viscosity on bubble dynamics were determined by solving the Keller-Miksis equation. Various cavitation threshold definitions were evaluated. The bubble collapse temperature was determined for all investigated mixtures and the energy dissipation of a single bubble was calculated. On the macroscale, different acoustic attenuation models were compared accounting for either linear or non-linear equations. Specifically, viscous losses were implemented in the non-linear Louisnard model, and model predictions were validated against experimental data. The model was able to predict multiple zones of cavitation in the reactor, as observed experimentally, and to estimate the dissipated energy for the different mixtures. Moreover, it was demonstrated that the cavitation-based attenuation dominates the other dissipation phenomena even for the most viscous solutions. The Louisnard model was coupled with heat transport equations, and using this extended version of the model, the temperature profiles were predicted for mixtures of increasing viscosity during sonication. Using a regression formula available in literature, radical production was related to the acoustic pressure field. By including reactions and mass transport in the acoustic model, for the first time in modelling ultrasonic reactors, the full distribution of light in the reactor during sonochemiluminescence (SCL) experiments for water was quantified.