Modeling of ultrasonic degradation of non-volatile organic compounds by Langmuir-type kinetics

Sonochemical degradation of phenol (Ph), 4-isopropylphenol (4-IPP) and Rhodamine B (RhB) in aqueous solutions was investigated for a large range of initial concentrations in order to analyze the reaction kinetics. The initial rates of substrate degradation and H₂O₂ formation as a function of initial concentrations were determined. The obtained results show that the degradation rate increases with increasing initial substrate concentration up to a plateau and that the sonolytic destruction occurs mainly through reactions with hydroxyl radicals in the interfacial region of cavitation bubbles. The rate of H₂O₂ formation decreases with increasing substrate concentration and reaches a minimum, followed by almost constant production rate for higher substrate concentrations. Sonolytic degradation data were analyzed by the models of Okitsu et al. [K. Okitsu, K. Iwasaki, Y. Yobiko, H. Bandow, R. Nishimura, Y. Maeda, Sonochemical degradation of azo dyes in aqueous solution: a new heterogeneous kinetics model taking into account the local concentration OH radicals and azo dyes, Ultrason. Sonochem. 12 (2005) 255–262.] and Seprone et al. [N. Serpone, R. Terzian, H. Hidaka, E. Pelizzetti, Ultrasonic induced dehalogenation and oxidation of 2-, 3-, and 4-chlorophenol in air-equilibrated aqueous media. Similarities with irradiated semiconductor particulates, J. Phys. Chem. 98 (1994) 2634–2640.] developed on the basis of a Langmuir-type mechanism. The five linearized forms of the Okitsu et al.’s equation as well as the non-linear curve fitting analysis method were discussed. Results show that it is not appropriate to use the coefficient of determination of the linear regression method for comparing the best-fitting. Among the five linear expressions of the Okitsu et al.’s kinetic model, form-2 expression very well represent the degradation data for Ph and 4-IPP. Non-linear curve fitting analysis method was found to be the more appropriate method to determine the model parameters. An excellent representation of the experimental results of sonolytic destruction of RhB was obtained using the Serpone et al.’s model. The Serpone et al.’s model gives a worse fit for the sonolytic degradation data of Ph and 4-IPP. These results indicate that Ph and 4-IPP undergo degradation predominantly at the bubble/solution interface, whereas RhB undergoes degradation at both bubble/solution interface and in the bulk solution.     

Effects of ultrasound frequency and acoustic amplitude on the size of sonochemically active bubbles – Theoretical study

Numerical simulation of chemical reactions inside an isolated spherical bubble of oxygen has been performed for various ambient bubble radii at different frequencies and acoustic amplitudes to study the effects of these two parameters on the range of ambient radius for an active bubble in sonochemical reactions. The employed model combines the dynamic of bubble collapse with the chemical kinetics of single cavitation bubble. Results from this model were compared with some experimental results presented in the literature and good apparent trends between them were observed. The numerical calculations of this study showed that there always exists an optimal ambient bubble radius at which the production of oxidizing species at the end of the bubble collapse attained their upper limit. It was shown that the range of ambient radius for an active bubble increased with increasing acoustic amplitude and decreased with increasing ultrasound frequency. The optimal ambient radius decreased with increasing frequency. Analysis of curves showing optimal ambient radius versus acoustic amplitude for different ultrasonic frequencies indicated that for 200 and 300 kHz, the optimal ambient radius increased linearly with increasing acoustic amplitude up to 3 atm. However, slight minima of optimal radius were observed for the curves obtained at 500 and 1000 kHz.     

Energy analysis during acoustic bubble oscillations: Relationship between bubble energy and sonochemical parameters

In this work, energy analysis of an oscillating isolated spherical bubble in water irradiated by an ultrasonic wave has been theoretically studied for various conditions of acoustic amplitude, ultrasound frequency, static pressure and liquid temperature in order to explain the effects of these key parameters on both sonochemistry and sonoluminescence. The Keller–Miksis equation for the temporal variation of the bubble radius in compressible and viscous medium has been employed as a dynamics model. The numerical calculations showed that the rate of energy accumulation, dE/dt, increased linearly with increasing acoustic amplitude in the range of 1.5–3.0 atm and decreased sharply with increasing frequency in the range 200–1000 kHz. There exists an optimal static pressure at which the power w is highest. This optimum shifts toward a higher value as the acoustic amplitude increases. The energy of the bubble slightly increases with the increase in liquid temperature from 10 to 60 °C. The results of this study should be a helpful means to explain a variety of experimental observations conducted in the field of sonochemistry and sonoluminescence concerning the effects of operational parameters.     

Analysis of a Class of Frictional Contact Problems for the Bingham Fluid

We consider a mathematical model which describes the stationary flow of a Bingham fluid with friction. The frictional contact is modeled by a general velocity dependent dissipation functional. We derive a weak formulation of the model which consists in a variational inequality for the velocity field. We establish the existence and uniqueness of the weak solution as well as its continuous dependence with respect to the contact condition. Finally, we describe a number of concrete friction conditions which may be set in this general framework and for which our results apply.     

Some Difficulties in Applying Interactive Compromise Programming Illustrated by a Recent Method and a Case Study

The paper presents some of the difficulties in applying interactive, and interactive compromise, programming methods to real-life problems. These include the problem of dominated solutions when multiple optimal solutions exist to single objective function optimization, cycling, and the depiction of the analyst as a silent spectator in the decision making process. By taking as an example a recently proposed interactive compromise programming method, these difficulties are illustrated and necessary modifications are proposed to overcome these difficulties. These are further elucidated by a case study.     

Enhanced sonolytic mineralization of basic red 29 in water by integrated ultrasound/Fe2+/TiO2 treatment

Research on Chemical Intermediates - Advanced oxidation processes (AOPs), based on hydroxyl radical (·OH) induced oxidation, have been widely investigated to develop novel and green...