General analytical solution expressions for analyzing Langmuir-type kinetics of sonochemical degradation of nonvolatile organic contaminants in water

•Ultrasonic oxidation of nonvolatile contaminants in water was examined under different conditions.•Two solution expressions of the Langmuir-type model were used to predict degradation kinetics.•Degradation increased as initial concentration and frequency decreased and as intensity increased.•The two solution expressions provided an excellent description of the ultrasonic oxidation data. Detailed kinetic studies of the ultrasonic decomposition of contaminants in water are scarce. Most of the work has used a pseudo-first order kinetics law, which is unrealistic. The model based on a Langmuir-type mechanism has been shown to fit the sonolytic decomposition data well, especially by using the non-linear technique. To avoid unrealistic assumptions, general analytical solutions to a time-dependent non-linear Langmuir-type equation may be the appropriate method. In this work, the sonolytic oxidation of organic contaminants, i.e., naphthol blue black and furosemide, in water was analyzed using two general analytical solution expressions of the Langmuir-type kinetics model, which describe the pollutant concentration in water. The validity of the two general analytical solution expressions was tested under a diversity of operating conditions, such as initial substrate concentration and varying ultrasonication frequency and intensity. As the initial substrate concentration increased, the sonolytic oxidation kinetics decreased, while the initial ultrasonic decomposition rate increased and then plateaued. Consequently, a heterogeneous kinetics equation based on a Langmuir-type mechanism can be used to simulate the sono-decomposition process. The decomposition yield increased with increasing sonication intensity and decreasing frequency. The two analytical solution expressions seem to be in excellent agreement with the experimental results of the sonochemical decomposition of the nonvolatile organic contaminants tested for the different operating conditions examined. These expressions provide a valuable tool for the analysis and simulation of advanced sonochemical oxidation processes under various experimental conditions.