M ECHANISTIC A NALYSIS OF H YBRID S ONO –P HOTO –F ERRIOXALATE S YSTEM
4.3.4 Kinetics of decolorization
The degradation pathway of both ARB and MB dye has complex chemistry involving formation of numerous intermediates. Several earlier authors have dealt with this matter (for example: Thiam et al., 2015; Xia et al., 2014; Yu and Chuang, 2008; Houas et al., 2001;
Wang et al., 2014). The main chemical mechanism of degradation is hydroxylation / oxidation induced by OH and HO2 radicals formed by AOPs. Many of these intermediates are unstable and difficult to monitor using standard techniques like GC or HPLC. In view of this difficulty, we have assumed that overall kinetics of dye degradation follows pseudo 1st order kinetics with respect to dye concentration. As stated in the tables of experimental results, description of dye degradation / decolorization profile using pseudo 1st order kinetic model has yielded regression coefficients > 0.85, indicating excellent fit of this model to the decolorization process.
4.4 CAVITATION BUBBLE DYNAMICS MODEL
As noted earlier, ultrasound, and its secondary effect, cavitation give rise to physical and chemical effects that contribute to enhancement of the kinetics of the reaction system.
We have estimated the magnitudes of these effects using a mathematical model for cavitation bubble dynamics. Before description of this model, we would like to discuss the rational underlying the technique of variation in dissolved gas content and addition of alcohol in the medium employed in experiments.
In the present study, the three experimental techniques employed are: (1) degassing
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(or de-oxygenation) of the medium, (3) sparging of gas through the reaction mixture, and (2) addition of alcohols to reaction mixture. All of these techniques have implication on the cavitation phenomenon. For occurrence of cavitation phenomenon in liquid, nuclei are needed. These nuclei could be the gas pockets trapped in the crevices of solid boundaries in the medium or they could be tiny gas bubbles freely floating in the liquid. Degassing of the medium (by subjecting the medium to vacuum or heating of the medium) reduces both free and dissolved gas content of the medium, and increases the intensity of cavitation phenomena. In the context of present study, degassing of the medium also reduces the dissolved oxygen in the medium. As noted in section 2, chemical mechanisms of both sonolysis and photo–ferrioxalate system involve reactions with dissolved oxygen. Hence, variation in the dissolved oxygen content also affects the chemical mechanism dye decolorization / degradation. With sparging of gas through reaction mixture during treatment, additional nuclei get seeded in the medium, which increase the cavitation intensity. Sparging of gas also leaves the reaction mixture saturated with the gas – stripping away the dissolved oxygen in the medium. Depletion of dissolved oxygen in the medium affects the photo–
ferrioxalate pathway, in which the CO2 radical reacts with dissolved oxygen to yield O2
and HO2 radical species, which lead to formation of H2O2 and Fenton–reaction.
Alcohol molecules are efficient radical scavenger. In the present context, there are two sources of radicals in the reaction mixture, viz. sonolysis and photo–ferrioxalate pathway. Addition of alcohols in the system can scavenge radicals produced through both pathways. As far as sonolysis is concerned, addition of alcohol in the system can also affect production of radicals. Alcohol molecules can adversely affect generation as well as of utilization of •OH radicals, in the reaction mixture. As shown by Ashokkumar et al. (1997), alcohol molecules have tendency to adsorb onto the gas/ liquid interface of the bubble. These interfacially adsorbed molecules are able to evaporate into the bubble core during collapse.
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During the compression phase of radial bubble motion, as the size of the bubble (and hence the area of bubble interface) reduces at fast rate, lateral interaction between the adsorbed alcohols molecules causes expulsion of some molecules in the bulk solution, while some molecules get evaporated into the bubble core. This phenomenon causes “quenching” effect in the transient collapse of bubble that reduces the intensity of the temperature and pressure peak reached in the bubble. However, the physical effects induced by transient cavitation, i.e.
micro–turbulence and shock waves, remain unaffected. Addition of alcohols in the reaction mixture thus gives a means of discriminating between the relative influence of physical and chemical effects of cavitation on the reaction.
In the present study, the diffusion limited model for cavitation bubble dynamics has been used (Toegel et al., 2000). This model is based on hypothesis that solvent vapor entrapment in the bubble during transient collapse is diffusion–limited process. A brief description of this hypothesis is as follows: the expansion of the bubble in the rarefaction half cycle of ultrasound is accompanied by evaporation of the solvent at the bubble interface.
Vapor molecules diffuse towards the bubble core. In the subsequent compression phase, the vapor molecules diffuse towards the bubble interface and condense. However, in the final moments of bubble collapse, the velocity of the bubble wall (or bubble interface) becomes extremely fast, i.e. equal to or even greater than the velocity of sound in the medium. At this condition, the time scale of the bubble motion becomes smaller than the time scale of diffusion of vapor molecules. This essentially means that the vapor molecules do not have sufficient time to diffuse towards the bubble interface and undergo condensation. Thus, the solvent vapor gets entrapped in the bubble. Moreover, the vapor molecules that have diffused to the bubble interface also cannot completely stick to the surface to undergo phase change.
This phenomenon also causes non–equilibrium phase change in the bubble and entrapment of the vapor molecules. The compression of the bubble is extremely fast and adiabatic. The
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temperature and pressure inside the bubble reach extreme (5000 K and 500 bar) and the vapor entrapped in the bubble undergoes thermal dissociation at these conditions. A wide variety of species are formed out of dissociation, some of which are radical species. At the point of maximum compression (or minimum bubble radius) the bubble may get fragmented and the bubble contents are released into the bulk liquid. The radicals released from the bubble can induce reactions in the liquid medium.
The diffusion limited bubble dynamics model comprises of 4 equations that take into account essential physics and chemistry of bubble dynamics using boundary layer approximation (Storey and Szeri, 2000), viz. (1) Keller–Miksis equation for the radial motion of the bubble; (2) Equation for the diffusive flux of water vapor through bubble wall, (3) Equation for heat conduction through bubble wall; and (4) Overall energy balance treating the cavitation bubble as an open system. The essential equations (along with relevant boundary conditions) and thermodynamic data of this model are given in Tables 2.1A & 2.1B (in Chapter 2). Equations for diffusive flux and conductive heat transfer requires thermal conductivity and diffusion coefficient (i.e. transport parameters). These are determined at the bulk temperature of the liquid medium using Chapman–Enskog theory that employs Lennard–Jones 12–6 potential. Dimensional analysis has been used to estimate thermal and diffusive penetration depths. During the bubble expansion, the gas dissolved in the liquid can also diffuse inside the bubble. However, gas diffusion is a much slower process than cavitation bubble dynamics. Typically, the time scale for the diffusion of gases is of the order of milliseconds, while the time scale for the radial motion of bubble is of the order of microseconds. Thus, diffusion of gas across bubble interface for a period of few tens of acoustic cycles is negligible. The equations of diffusion–limited model of cavitation bubble dynamics can be solved simultaneously using Runge–Kutta adaptive step size method (Press et al., 1992).
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Some experimental categories (viz. categories 4A, B and C) of present study make use of sparge gas. For these categories, the cavitation bubble is considered to be made up of sparge gas. For other categories, an air bubble is considered as the cavitation bubble. The bubble collapse (or essentially the bubble fragmentation) is assumed to occur at the first compression after an initial expansion. The thermodynamic parameters for gases and wter were taken from Hirschfelder et al. (1954) Condon and Odishaw (1958) and Reid et al.
(1987). Other numerical values of different parameters used in the simulation of bubble dynamics equation are: ultrasound frequency (f) = 40 kHz; ultrasound pressure amplitude (PA) = 190 kPa (determined using calorimetric techniques); vapor pressure of liquid medium (water) = 2500 Pa (calculate using Antoine type correlation), density of water (L) = 1000 kg/m3, kinematic viscosity of water () = 10–6 Pa–s, surface tension of water () = 0.072 N/m, sonic velocity in water (c) = 1481 m/s. The equilibrium bubble radius (Ro) is difficult to measure experimentally and usual approach is to assume a representative value for the same.
Larger bubbles (size > 50 microns) have sufficient buoyancy to rise to surface of the liquid and escape. Therefore, we have considered bubble sufficiently small to undergo transient collapse at the conditions of frequency or ultrasound pressure amplitude present in the sonication bath used in this study. Typically, for the ultrasound frequencies in the range of 20–100 kHz, and (modest) ultrasound pressure amplitudes in the range of 1.5–2.5 bar, bubbles with initial radii < 10 m undergo transient motion (Mettin et al., 1997). Considering this, an equilibrium bubble size of Ro = 10 m has been assumed for simulations.