Physical features of ultrasound-enhanced heterogeneous permanganate oxidation

Ultrasonics Sonochemistry 17 (2010) 123–131

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Physical features of ultrasound-enhanced heterogeneous permanganate oxidation Ramesh Kuppa, Vijayanand S. Moholkar * Department of Chemical Engineering, Indian Institute of Technology Guwahati, Guwahati – 781 039, Assam, India

a r t i c l e

i n f o

Article history: Received 17 February 2009 Received in revised form 29 March 2009 Accepted 15 May 2009 Available online 20 May 2009 Keywords: Cavitation Ultrasound Bubble Sonochemistry Permanganate oxidation Process intensification

a b s t r a c t This paper addresses the matter of mechanistic features of ultrasound-assisted permanganate oxidation of organic compounds in aqueous phase. This reaction system is essentially a liquid–liquid heterogeneous one, which is limited by the mass transfer characteristics. Previous research has established that ultrasound irradiation of reaction mixture enhances the kinetics and yield of permanganate oxidation. The principal physical effect of ultrasonic cavitation is formation of fine emulsion between immiscible phases that eliminates the mass transfer resistance, while principal chemical effect is production of radicals through transient collapse of cavitation bubbles, which accelerate the reaction. In this paper, we have tried to discriminate between these physical and chemical effects by coupling experiments with different conditions (which alter the nature of cavitation phenomena in the medium) to simulations of cavitation bubble dynamics. It is revealed that in absence of radical conserving agent, the enhancement effect is merely physical. Diffusion of radicals towards interface between phases, where the oxidation reaction occurs is the limiting factor in contribution of chemical effect of ultrasonic cavitation towards enhancement of oxidation. Enhancement of total radical production in the aqueous phase (by degassing of the medium) increases the overall oxidation yield, but only marginally. On the other hand, addition of a radical conserver such as FeSO47H2O results in marked enhancement in oxidation yield, as the conserver assists deeper penetration of radicals in the aqueous medium and diffusion towards interface. Ó 2009 Elsevier B.V. All rights reserved.

1. Introduction Potassium permanganate is a widely used oxidant. In the 1980s, KMnO4 treatment became popular as an odor control method in municipal sewage lines. It has also been widely used for destruction or detoxification of several organic pollutants appearing in industrial wastewater discharge. KMnO4 has been used to reduce TOC, COD and BOD values of wastewater. Industrially, oxidation of alkylarenes to aryl carboxylic acids is an important process [1,2]. In addition, several other functional groups in organic compounds and molecules present in industrial wastewater discharge are oxidized by KMnO4. Some examples of KMnO4 oxidation are: (1) oxidation of olefins to a-hydroxy ketone at pH 4–8 and ambient temperature; (2) oxidation of olefins to corresponding diols at pH > 9; (3) oxidation of primary alcohols (with two a-hydrogens) to aldehyde and carboxylic acid; (4) oxidation of secondary alcohol to ketone; (5) oxidation of t-carbamines to corresponding nitro compounds; and (6) oxidation of primary aromatic amines (containing a-hydrogens) to aldehydes [3]. Most of the permanganate oxidations are carried out in aqueous solutions. Different pathways for permanganate oxidation of organic compounds are: (1) electron abstraction, (2) hydrogen atom abstraction, (3) hydride ion * Corresponding author. Tel.: +91 361 258 2258; fax: +91 361 269 0762. E-mail address: [email protected] (V.S. Moholkar). 1350-4177/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.ultsonch.2009.05.011

abstraction and (4) direct donation of oxygen to organic substrate [3]. The pH of the medium determines whether oxidation will involve one, three or five electron exchange [4]. Under extremely alkaline conditions (pH > 12–13), oxidation involves only one electron transfer. Between pH 3.5–12, the permanganate ion undergoes 3-electron exchange, and under strongly acidic conditions (pH < 3.5, in addition to the presence of strong reducing agents), permanganate ion undergoes 5-electron exchange. Thus, under acidic conditions permanganate is most aggressive, which is the desired condition for destruction of pollutants. In a paper published by Gardner et al. [5] (in which authors have studied permanganate oxidation of alkylarenes such as toluene, ethylbenzene, diphenyl methane, xanthane and fluorine), it has been proven that hydrogen atom abstraction is the rate limiting step in overall permanganate oxidation reaction. In many cases, oxidative capability of KMnO4 is enhanced by mixing the solution with acids such as H2SO4. Despite this, the kinetics of the permanganate oxidation of organic molecules is limited by the mass transfer characteristics of the system. The organic and aqueous phases are immiscible and the reaction occurs only at the interface between the two phases. The agitation provided in the reaction system, which determines the dispersion of the phases and the interfacial area between them, becomes a crucial factor dominating the overall kinetics of the reaction. Phase transfer catalysts (such as PEG) have also been used as means of facilitating mass transfer between phases [6].

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More recently, ultrasound has been attempted as a tool for enhancing the kinetics of the permanganate oxidation of alkylarenes [6–9]. However, the exact mechanism of the enhancement effect is not known. The physical and chemical effects of ultrasound are attributed to phenomenon of cavitation, which is nucleation, growth and transient collapse of tiny bubbles driven by the ultrasound wave. Both of these effects could possibly contribute towards enhancement of the kinetics and yield of the reaction. However, in many situations, the influence of one of these effects is more dominant than the other. Therefore, discrimination between the physical and chemical effects of ultrasonic cavitation is an important step of investigation in sonochemical reactions. In this paper, we try to establish the mechanism of the ultrasound-assisted permanganate oxidation of alkylarenes, with identification of the individual contribution by the physical and chemical effects of the ultrasonic cavitation towards enhancement of reaction kinetics and yield, with toluene as the model alkylarene. The methodology adopted is coupling of experiments under different conditions (which vary the characteristics of the acoustics and cavitation phenomenon in the system) with simulation of radial motion of cavitation bubbles.

2. Physical and chemical effects of ultrasound and cavitation Passage of ultrasound through liquid medium gives rise to sinusoidal variation in the bulk pressure. This variation gives rise to the phenomenon of cavitation. Possible nuclei for occurrence of cavitation events are gas pockets trapped in the walls and crevices of the reactor wall, or they could be small bubbles already present in the medium. Cavitation bubbles grow from these nuclei during rarefaction half cycle of ultrasound, when the bulk pressure in the medium falls sufficiently below ambient or static pressure [10]. If the pressure amplitude of the ultrasound wave is sufficiently high (>1.2 bar), bubble undergoes rapid expansion (to more than two times its original size) in the rarefaction half cycle of ultrasound. This expansion is accompanied by large evaporation of water at the bubble interface. The water vapor molecules diffuse towards the core of the bubble. The ensuing compression phase is also dominated by inertial forces and the spherical convergence of fluid elements results in intense energy concentration at bubble collapse [11,12]. Thus, the bubble collapse is extremely violent and energetic, which results in generation of very high temperatures (5000 K) and pressures (500 bar) inside the bubble [13–15]. The vapor molecules entered into the cavitation bubble during expansion diffuse towards the bubble interface during the compression phase and condense at the interface. However, during the final moments of bubble collapse, the radial motion of the bubble becomes extremely fast and not all vapor molecules are able to diffuse towards and condense at the bubble wall. Moreover, during rapid motion of bubble wall at transient collapse, the phase change or condensation at the bubble interface becomes non-equilibrium. This means that not all vapor molecules that approach the bubble interface stick to it and undergo condensation. As a result, a fraction of the water vapor gets ‘‘entrapped” into the bubble and is subjected to the extreme temperatures and pressure conditions generated in the bubble at the transient collapse. The vapor molecules undergo dissociation in the bubble to generate radicals such as H, O, OH and HO2 , with OH being the dominant radical species [16–20]. Perceptibly, the rate of radical generation is dependent on the total number of water vapor molecules present in the bubble during collapse, the intensity of the collapse (i.e. the magnitude of the temperature and pressure reached in the bubble at the moment of collapse), and the number of bubbles in the medium. At the instance of maximum compression, the bubble may get fragmented with release of radicals into the bulk medium, where these

radicals induce and accelerate chemical reactions. This is the wellknown sonochemical effect. In the present context, the radicals generated from cavitation bubble can assist hydrogen atom abstraction (which the rate limiting step in the overall oxidation, as noted earlier) and provide additional [O] species (refer to reaction scheme for oxidation given in Section 3), which would enhance the oxidation yield. However, these radicals are quite unstable and do not diffuse to significant distances in the bulk liquid medium from the location of transient bubble collapse. The sonochemical reaction would therefore occur only if the radicals can interact with the reactant molecules. Thus, the probability of the radical–reactant interaction becomes an important factor in the overall yield of the sonochemical reaction. In case, the radicals are not able to interact with reactant molecules, they may simply recombine among themselves generating molecular species. This is loss of sonochemical potential. For high probability of reactant–radical interaction, the concentration of the reactant at the location of bubble collapse (or at the bubble interface) should be high. Another means of increasing probability of radical–reactant interaction is addition of a radical conserving agent to the medium. A radical conserver reacts with the radicals generated from bubble collapse or the molecular species such as H2O2 formed due to recombination of radicals to generate additional radical species. This phenomenon helps deeper penetration of radicals from the location of transient bubble collapse and raises the probability of radical–reactant interaction. The physical effects of ultrasound and cavitation are several folds. These effects are mainly responsible for generating strong convection in the bulk liquid medium through several mechanisms, as described below: 2.1. Microstreaming The propagation of ultrasound waves through the liquid medium creates small amplitude oscillatory motion of fluid elements around a mean position. This is phenomenon is called microstreaming [21]. The velocity of the microstreaming is given as v ¼ PA =qC where PA is the pressure amplitude of ultrasound wave, q is the density of the medium and C is the velocity of sound in the medium. For a typical pressure amplitude of 1.2 bar in water (with q = 1000 kg/m3 and C = 1500 m/s), v = 0.08 m/s. 2.2. Microturbulence Radial motion of cavitation bubble induces high velocity oscillatory motion of the fluid in its vicinity. This is called microturbulence [22,23]. This phenomenon is explained as follows: during the expansion phase of radial motion, the fluid is displaced away from the bubble center. During the collapse phase, the liquid is pulled towards the bubble as it fills in the vacuum created in liquid with size reduction of the bubble. The mean velocity of the microturbulence depends on the amplitude of the oscillation of the bubble. It should, however, be noted that phenomenon of microturbulence is restricted only in the region in close vicinity of the bubble. The velocity of the microturbulence diminishes very rapidly away from the bubble. 2.3. Acoustic waves (or shock waves) As mentioned above, during the compression phase of radial motion, the fluid elements in the vicinity of the bubble wall spherically converge towards bubble wall. For a gas bubble (containing non-condensable gas such as air), the adiabatic compression results in rapid rise of the pressure inside the bubble. At the point of minimum radius (or maximum compression), the bubble wall comes to a sudden halt and rebounces with high velocity. At this

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instance, the converging fluid elements are reflected back from the bubble interface [24]. This reflection creates a high-pressure shock wave that propagates through the medium [25–28]. 2.4. Microjets During radial motion driven by ultrasound wave, the cavitation bubble maintains spherical geometry as long as the motion of liquid in its vicinity is symmetric and uniform, and thus, there are no pressure gradients. If the bubble is located close to a phase boundary (either solid–liquid or gas–liquid or liquid–liquid), the motion of liquid in its vicinity is hindered, resulting in development of pressure gradients around it. This non-uniformity of pressure results in the loss of spherical geometry of the bubble. Numerous authors have investigated this phenomenon in past three decades with different approaches: either numerical and/or experimental [29–33]. During the asymmetric radial motion, the portion of the bubble exposed to higher pressure collapses faster than the rest of the bubble, which gives rise to formation of a high speed liquid jet. However, the direction of this jet depends on the characteristics of the solid boundary [30,31]. Rigid boundaries (e.g. metal surfaces) are characterized by the condition r  / ¼ 0, where u is velocity potential at the boundary, while free boundaries (or pressure release boundaries, e.g. gas–liquid interface) are characterized by the condition u = 0. For a rigid boundary, the microjet is directed towards the boundary, while for a free boundary, the microjet is directed away from the boundary. The velocity of these microjets has been estimated in the range of 120–150 m/s [32,33]. In case of rigid boundaries, these jets can cause severe damage at the point of impact and can erode the surface. For a homogeneous chemical reaction system, only the chemical effects of cavitation bubbles are relevant. However, for a liquid–liquid heterogeneous reaction system, both physical and chemical effects of cavitation influence kinetics and yield of the reaction. Intense microturbulence created by the cavitation bubbles disrupts the liquid–liquid interface and creates very fine emulsion between the phases. This greatly enhances the interfacial area and obviates need for additional agents for mass transfer enhancement such as phase transfer catalysts.

Fig. 1. Schematic of the experimental setup [Legends: 1 – ultrasound bath; 2 – transducer attached to the bottom of the bath; 3 – reaction mixture; 4 – stand for holding the reaction flask; 5 – time regulator; 6 – rubber bulb with air flow control valve and 7 – medium for ultrasound propagation].

ultrasound waves to the reaction mixture. For every experiment, the reaction flask was immersed to the same level so as to ensure uniformity of sonication of reaction mixture. The intensity of the ultrasound field in the bath shows significant spatial variation. Any change in the location of placement of the reaction flask in the bath in consecutive experiments can result in artifacts due to variation of intensity of the ultrasound field. In view of this, during all experiments the position of the reaction flask in the bath was carefully maintained constant with the help of a burette stand with clamp (see Fig. 1). In addition, an arrangement was also made to raise the static pressure in the reaction flask. The mouth of the flask was air-sealed using a rubber cork with a metal tube pierced centrally in the cork. A rubber bulb with an air flow control valve was attached to the outer end of the tube, which could be pressed to raise the static pressure inside. This arrangement could raise the absolute pressure inside the flask upto 1.5 bar, i.e. 500 kPa above atmospheric. 3.2. Chemicals

3. Experimental The overall reaction of permanganate oxidation of toluene is represented by following reaction scheme: 2 KMnO4

+

H2O

2 MnO2

CH3

+ 2 KOH +

3 [O]

COOH 3 [O]

3.1. Experimental setup Oxidation reactions were carried out in a 100 mL round bottom flask made of borosilicate glass. A schematic of the experimental set up is shown in Fig. 1. For sonication of the reaction mixture, an ultrasound bath (Make: Transonic, Model: T460) was used. This bath had a frequency of 35 kHz and power input (max) of 35 W, with transducers attached to the bottom of the bath. The total capacity of the bath was 1.5 L. During sonication, the bath was filled with water, which formed the medium for transmission of

The chemicals used in the experiments are: potassium permanganate (Ranbaxy, Grade: LR), toluene (Merck, Grade: synthesis) and chloroform (Merck, Grade: GR). All chemicals were used as received without any treatment or purification. Millipore water (Model: Elix 3) was used for preparing KMnO4 solution in all experiments. 3.3. Experimental procedure About 3.16 g (20 mmol) of KMnO4 was added to 50 mL of water and stirred for 24 h for complete mixing. To this solution, 1 mL (10 mmol) of toluene (the model alkylarene) was added, which results in a heterogeneous mixture due to immiscibility between aqueous KMnO4 solution and toluene. This heterogeneous mixture was subjected to sonication in ultrasonic bath. This reaction was conducted for 2 h, in periods of 30 min sonication followed by 5 min gap or silent period. The mean temperature of the reaction mixture during experiment was 25 °C. The water in the ultrasound bath was replaced every 1 h to avoid temperature rise (with less than ±2 °C variation) during the experiment. After 2 h of total sonication time (excluding silent periods), the precipitate formed out of this reaction mixture was filtered. The filtered product was washed with chloroform (3  10 mL) to remove unreacted alkylarene (toluene) present in the MnO2 precipitate. After washing, the precipitate was kept for drying in hot air oven for 24 h at

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100 °C. The dried product was cooled in desiccator and weighed for yield calculation. The experiments were done in different sets with variation of four parameters, viz. (1) saturation level (or dissolved gas content) of the medium; (2) addition of a radical conserving species (Fe2+ ions in the form of FeSO47H2O); (3) variation of the static pressure in the flask, and (4) amount of toluene added to the aqueous permanganate solution. With permutation–combination of the above experimental variables, the experiments were grouped as follows: (1) Saturated medium; static pressure = 1 bar; no additives. (2) Saturated medium; static pressure = 1 bar; FeSO47H2O addition (10 mmol). (3) Saturated medium; static pressure = 1.5 bar; no additives. (4) Unsaturated medium; static pressure = 1 bar; no additives. (5) Unsaturated medium; static pressure = 1 bar; FeSO47H2O addition (10 mmol). (6) Unsaturated medium; static pressure = 1.5 bar; no additives.

Experiments in these groups were carried out for two other volumes of toluene, viz. 2 and 3 mL, with amount of aqueous KMnO4 remaining the same, i.e. 50 mL. This introduced an additional variable for the experiments, i.e. organic to aqueous volume ratio (1:50, 2:50 and 3:50). Thus, including this variable, there were 18 sets of experiment. Each experiment was repeated twice in order to assess reproducibility of results. The rationale behind these permutations and combinations of experimental conditions will be discussed subsequently. The yield of the reaction was calculated on absolute basis using reaction stoichiometry as follows:

Yield ¼ Actual amount of toluene oxidized ¼

Weight of MnO2 obtained 2  Molecular weight of MnO2

3.4. Unsaturation (or degassing) of the medium Since the aqueous solution of KMnO4 was prepared using Millipore water, the ‘‘dissolved gas” is essentially air. Unsaturated medium refers to aqueous KMnO4 solution with reduced level of dissolved oxygen (DO). In order to reduce DO level in the medium,

50 mL of KMnO4 solution was degassed in a filtering flask by means of a vacuum pump (Riviera, Model: TID-25-S). Vacuum pressure of 650 mm of Hg was applied for 40 min with intermittent stirring. This procedure can reduce the DO content of the medium to 2 ppm. 4. The mathematical model The overall physical or chemical effect of the cavitation events in the bulk medium is a manifestation of ‘‘multibubble phenomena”, i.e. collective oscillations and collapse of bubble clouds comprising of millions of cavitation bubbles, with strong interaction among them. Cavitation bubble dynamics models appeared in literature so far do not address multi-bubble systems along with its other facets such as bubble–bubble coalescence and breakup, clustering and rectified diffusion. Another important parameter that governs the overall sonophysical or sonochemical effect is the population or number density of bubbles. A direct measurement of this parameter is not available, to the best of knowledge of the authors of this paper. However, previous authors have used an indirect method of measurement of iodine liberation through Weissler reaction for estimation of the number density of the bubbles [17]. The principal aim of this study is to establish the mechanism of the ultrasonic enhancement of the aqueous phase permanganate oxidation of toluene by discriminating between the physical and chemical effects of cavitation phenomena. No attempt has been made in this study to predict quantitatively the yield or kinetics of the oxidation reaction. For our analysis, we have chosen a mathematical model for a single cavitation bubble. This approach is justified in view of earlier research, which has proven that all characteristic features of the physical and chemical effects of cavitation bubbles can be explained by dynamic behavior of a single bubble [17,34–37]. Thus, although the single bubble analysis does not address the entire physics of the sonochemical system that would enable a quantitative prediction of yield or kinetics, it does provide a qualitative physical insight into the system behavior; and hence, it is sufficient to meet the objectives of the present study. Modeling of cavitation bubble dynamics with associated heat and mass transfer effects and production of various chemical species has been attempted by several authors [16–20,38–42]. Our previous papers [37,43] have presented a review of literature in this area. The most general treatment of the problem of water vapor transport in large amplitude nonlinear motion of the cavitation bubbles, which relaxed most of the assumptions made in earlier

Table 1A Model for the radial motion of cavitation bubble. Model component

Equations

1. Radial motion of the cavitation bubble



1

Initial values



2



dR=dt d R 3 dR=dt R 2þ 1 c 2 3c dt



dR dt

2

  1 dR=dt R dPi dR=dt 2r ðPi  Pt Þ þ   4m ¼ 1þ c R qL qL c dt qL R

N tot ðtÞkT 3 ½4pðR3 ðtÞ  h Þ=3 Pressure in bulk liquid medium: P t ¼ P 0  P A sinð2pftÞ    dNw ¼ 4pR2 D @C w   4pR2 Dw C wR  C w w @r r¼R dt ldiff rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  RDw ; R Diffusive penetration depth: ldiff ¼ min jdR=dtj p    dQ ¼ 4pR2 k@T   4pR2 k T 0  T @r r¼R dt lth rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  Rj ; R Thermal diffusion length: lth ¼ min jdR=dtj p

At t = 0, R = Ro, dR/dt = 0

Internal pressure in the bubble: P i ¼

2. Water vapor transport

3. Conductive heat transfer

4. Overall energy balance

C V;mix dT=dt ¼ dQ=dt  P i dV=dt þ ðhw  U w ÞdN w =dt P Mixture heat capacity: C V ;mix ¼ C V;i N i Molecular enthalpy of water: hw = 4kTo P hi =T Internal energy of water: U w ¼ N w kTð3 þ 3i¼1 Þ expðhi =TÞ  1 Heat capacity of other species (i = N2/O2/H2O): C V;i ¼ N i kðfi =2 þ

At t = 0,Nw = 0

At t = 0,Q = 0

At t = 0,T = T0

P ððhi =TÞ2 expðhi =TÞ=ðexpðhi =TÞ  1Þ2 ÞÞ

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R. Kuppa, V.S. Moholkar / Ultrasonics Sonochemistry 17 (2010) 123–131 Table 1B Thermodynamic properties of various species.* Species

Degrees of freedom (translational + rotational) (fi)

Lennard–Jones force constants

r (10 N2 O2 H2O

5 5 6

3.68 3.43 2.65

10

m)

Characteristic vibrational temperatures h (K)

e/k (K) 92 113 380

3350 2273 2295, 5255, 5400

Notations: R – radius of the bubble; dR/dt – bubble wall velocity; c – velocity of sound in bulk liquid medium; qL – density of the liquid; m – kinematic viscosity of liquid; r – surface tension of liquid; k – thermal conductivity of bubble contents; j – thermal diffusivity of bubble contents; h – characteristic vibrational temperature(s) of the species; Nw – number of water molecules in the bubble; t – time, Dw – diffusion coefficient of water vapor; Cw – concentration of water molecules in the bubble; CwR – concentration of water molecules at the bubble wall or gas–liquid interface; Q – heat conducted across bubble wall; T – temperature of the bubble contents; To – ambient (or bulk liquid medium) temperature; k – Boltzmann constant; fi – translational and rotational degrees of freedom; CV,i – heat capacity at constant volume; Ntot – total number of molecules (gas + vapor) in the bubble; h – van der Waal’s hard core radius; Po – ambient (bulk) pressure in liquid; PA – pressure amplitude of ultrasound wave; f – frequency of ultrasound wave. * Data taken from Ref. [46,50,52].

studies, was presented by Storey and Szeri [18]. The principal result of analysis of Storey and Szeri [18] was that water vapor transport in the cavitation bubble is a diffusion-limited process. Based on these conclusions, Toegel et al. [44] developed a simplified model using boundary layer approximation, which has been used in the present study. We have given essential equations and thermodynamic data of this model in Table 1. For greater details, we refer the readers to our earlier papers [37,43,45] as well as the original papers [44,46]. The model comprises of four simultaneous ordinary differential equations (ODEs) as follows:

(1.7 bar), as measured calorimetrically [37]. This amplitude is attenuated as the wave reaches the reaction mixture in the flask. The attenuation is caused due to viscous dissipation in the water filled in the bath, and also through the walls of the reaction flask. Bubbles present in the water filled in bath also contribute to attenuation by scattering the ultrasound wave [55]. Amplitude of the ultrasound wave inside the reaction flask was measured calorimetrically using saturated and unsaturated (or degassed) water. For unsaturated water, the amplitude was PA = 1.4 bar, while for saturated medium the amplitude was measured to be PA = 1.2 bar.

(1) Keller–Miksis equation for the radial motion of the bubble [47–49]. (2) Equation for the diffusive flux of water vapor across bubble wall. (3) Equation for heat conduction through bubble wall. (4) Overall energy balance treating the cavitation bubble as an open system.

4.1.3. Vapor pressure of water The vapor pressure of water was calculated at 25 °C using Antoine’s equations. As the temperature fluctuation in the reaction mixture was quite small (±2 °C), we have ignored it in the simulations, assuming bulk liquid medium at constant temperature.

The transport parameters for the heat and mass transfer (thermal conductivity and diffusion coefficient) are determined using Chapman–Enskog theory using Lennard–Jones 12-6 potential at the bulk temperature of the liquid medium [50–53]. Thermal and diffusive penetration depths are estimated using dimensional analysis. This model ignores the diffusion of gases across the bubble wall, as time scale for the diffusion of gases is much higher than time scale for the radial motion of bubble. 4.1. Numerical solution The set of simultaneous ODEs given in Table 1A can be solved using Runge–Kutta 4th–5th order adaptive step size method [54]. The cavitation bubble may collapse at the instance of maximum compression during radial motion. The word ‘‘collapse” essentially means fragmentation of the cavitation bubble. For conditions of maximum shape and flow instability, the cavitation bubble fragmentation can occur at the first compression after an initial expansion. In view of this, the condition for bubble collapse is taken to be first compression during radial motion [18]. Various parameters required for the numerical solution of the model have been estimated as follows: 4.1.1. Frequency The frequency of the ultrasound wave was taken as 35 kHz, which is the frequency of the ultrasound bath used in the experiments. 4.1.2. Acoustic pressure amplitude Acoustic pressure amplitude generated by the transducers attached to the bottom of the ultrasound bath is quite high

4.1.4. Initial (or equilibrium) radius and contents of the bubble Direct measurement of the initial size of cavitation bubbles is beyond the capabilities of instrumentation used in this study. Moreover, the equilibrium size of the bubble keeps on changing due to phenomena such as rectified diffusion, fragmentation of the bubble etc. The minimum radius of the cavitation nuclei, which could grow into bubbles for particular amplitude of acoustic wave, can be determined by the analysis given by Young [56]. For PA = 1.2 or 1.4 bar, this value is 2 lm. In an unsaturated medium, the bubble size is expected to be smaller than the saturated medium, as the bubble shrinks during radial motion due to dissolution of gas in the medium [57,58]. On the other hand, in a saturated medium, dissolved gas in the medium slowly diffuses into the bubble during radial motion, which leads to increase in the equilibrium bubble size during radial motion. In this study, both saturated and unsaturated media have been used. Therefore, we have chosen two representative values for the initial or equilibrium bubble radius: a value of 10 lm for the saturated medium, and a value of 5 lm for the unsaturated medium. Any other value chosen for this parameter would make only quantitative changes to the simulation results, with trends remaining essentially unchanged. The bubble is assumed to be comprised of gas alone initially (or at t = 0). The vapor content of the bubble at initial conditions is, thus, zero. 4.1.5. Generation of radicals during transient bubble collapse Equilibrium composition of the various species formed in the bubble with dissociation of entrapped water molecules (i.e. H2O, H2, O2, H ,  OH, O , H2O2, HO2 , O3) at the conditions of temperature and pressure at first the compression was calculated using software FACTSAGE, which uses the free-energy minimization algorithm proposed by Eriksson [59]. The equilibrium approach in the present study is justified by the fact that the rates of various

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reactions occurring in the bubble are extremely fast. This is due to two reasons: (1) extremely high specific rate constants of radical reactions, and (2) large concentrations of various species in the bubble at the point of maximum compression of the bubble. Our previous paper [43] shows that the rates of various reactions in the bubble are at least two orders of magnitude higher than the time scale of bubble motion. As a result, thermal equilibrium should prevail in the bubble at all times [60]. 5. Results and discussion As discussed in Section 2, the radial motion of cavitation bubble has both physical and chemical consequences, which could render favorable effect on a reaction system. In the context of the present study, the key chemical effect is production of free radicals that can assist hydrogen atom abstraction, while the key physical effect is formation of fine emulsion between toluene and water that increases the interfacial area. Both of these effects can raise the kinetics as well as yield of the toluene oxidation. The experimental conditions employed in this work can significantly alter the relative contribution of these effects. We give herewith a description of the influence of different experimental parameters on the physical and chemical effect of cavitation bubbles as preamble, on the basis of which the results of the simulations and experiments have been analyzed and correlated. 5.1. Addition of FeSO47H2O The radicals formed out of transient bubble collapse are extremely reactive, and thus, do not diffuse significantly away from the location of bubble collapse. The reaction zone of these radicals is, thus, restricted to a small area around the point of bubble collapse. If the reactant molecules are not present in this zone, the radicals may simply recombine, which is the loss of oxidation potential of the radicals. In the present context, the radicals have to diffuse to the interface between water and toluene, in order to assist/accelerate oxidation of toluene. Addition of Fe2+ can help revert this loss by regeneration of the radicals with simultaneous oxidation of Fe2+ to Fe3+. The reactions in this regard are [61]: 

OH þ  OH H2 O2

H2 O2 þ Fe

2þ

ð1Þ

3þ

! Fe





þ OH þ OH

ð2Þ

2+

ions are regenerated in the medium by following reactions:

3þ

þ H2 O2 ! Fe2þ þ HO2 þ Hþ

Fe

Fe

3þ

Fe

þ

HO2

! Fe

2þ

þ

þ O2 þ H

ð3Þ ð4Þ

Due to continuous regeneration, the average concentration of Fe2+ in the bulk medium stays very nearly constant. Due to these features, Fe2+ can provide effective utilization of radicals produced from cavitation bubbles for toluene oxidation. 5.1.1. Raising static pressure The intensity of cavitation events is directly proportional to the negative maxima of the bulk pressure reached (below ambient pressure) during propagation of ultrasound wave. If the ambient pressure is increased (with acoustic pressure amplitude remaining the same), the negative pressure reached in the bulk medium decreases. A consequence of this is that radial motion of the bubble transforms from high amplitude transient motion to a stable, small amplitude and oscillatory type. The temperature and pressure peaks reached in the bubble (at the moment of maximum compression) in such radial motion are quite small, and hence, the production of radicals reduces drastically. In addition, the intensity of the microturbulence created by the bubble also reduces. 5.1.2. Organic to aqueous volume ratio (or amount of toluene added to KMnO4 solution) The reaction zone for toluene oxidation is restricted to the interfacial area between the organic and aqueous phases. With the intensity of turbulence or mixing in the medium remaining the same, the interfacial area increases with volume fraction of the organic phase (or addition of toluene). The production of radicals by the cavitation bubbles is not uniform throughout the aqueous medium, but rather localized at the sites of transient bubble collapse. Thus, the probability of interaction between toluene molecules and the radicals becomes an important parameter governing the rate of reaction. The greater the quantities of toluene present in the reaction mixture, the higher the interfacial area and the greater the probability toluene–radical interaction leading to oxidation of toluene. Thus, variation in organic to aqueous volume ratio gives an important insight into the overall physics of the process. 5.2. Experimental results The experimental results of all eighteen sets of experiments (with permutation–combination of four experimental parameters as mentioned in Section 3) are given in Table 2. For each set, mean amount of toluene oxidized in three experimental runs along with standard deviation (indicated by sign ±) is given. Some peculiar trends in oxidation yields are as follows: (1) For all experimental sets, oxidation yields are higher for unsaturated medium than saturated medium.

Table 2 Results of permanganate oxidation of toluene under different experimental conditions. Toluene volume

Amount of toluene oxidized (mmol) 1 mL (10 mmol)

Condition of the reaction

Saturated solution at 1 bar static pressure

Pure reaction mixture Reaction mixture with FeSO47H2O addition

1.4 ± 0.05 2.56 ± 0.04

2 mL (20 mmol)

3 mL (30 mmol)

1.55 ± 0.06 2.62 ± 0.35

2.01 ± 0.24 2.28 ± 0.49

Saturated solution at 1.5 bar static pressure Pure reaction mixture

1.33 ± 0.09

1.84 ± 0.35

2.10 ± 0.01

Unsaturated solution at 1 bar static pressure Pure reaction mixture Reaction mixture with FeSO47H2O addition

1.89 ± 0.06 2.86 ± 0.13

1.89 ± 0.07 3.14 ± 0.11

2.59 ± 0.21 2.82 ± 0.77

Unsaturated solution at 1.5 bar static pressure Pure reaction mixture

2.06 ± 0.34

1.81 ± 0.21

2.13 ± 0.08

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(2) Yields in both saturated and unsaturated solution fall with raised static pressure in the medium. Nonetheless, for a particular volume of toluene added to the medium, the yields in unsaturated solutions are higher than the saturated solutions. (3) For both saturated and unsaturated medium (without any additive) at atmospheric static pressure, the oxidation yield increases with volume of toluene added to the solution or the organic to aqueous phase ratio. (4) Addition of FeSO47H2O to the medium boosts oxidation yields in both saturated as well as unsaturated media. Inter-

1

2 3 No. of Acoustic Cycles

4

5

No. of Water Molecules

10

6 .10

1

2 3 No. of Acoustic Cycles

4

1

2

3

1

4

5

Pressure (atm)

4000

4

5

0

1

2 3 No. of Acoustic Cycles

4

5

4

5

4

5

0.002

(E) 1

2 3 No. of Acoustic Cycles

4

5

(D)

0

1

2

3

No. of Acoustic Cycles

0.002

0

2 3 No. of Acoustic Cycles

50

0

1

3

(C)

100

(D)

0

2

750

0 0

0

1500

Oscillatory Velocity (m/s)

Pressure (atm)

5

No. of Acoustic Cycles

(C)

8000

Oscillatory Velocity (m/s)

4

(B)

No. of Acoustic Cycles

0.006

3

9

5

2000

0

2

3 .10

0

0

Temperature (K)

No. of Water Molecules

1

9

(B)

4000 Temperature (K)

0

No. of Acoustic Cycles

10

0

(A)

1.5

0

0

4 .10

0

Representative simulations of radial motion of a 5 lm air bubble are shown in Figs. 2 and 3. The summary of the simulation re-

Radius (R/Ro)

Radius (R/Ro)

(A)

3

2 .10

5.3. Simulation results

3

6

0

estingly, with addition of FeSO47H2O, the absolute yield becomes insensitive to the organic to aqueous phase ratio, i.e. almost similar yields are obtained for all three volumes of toluene (1, 2 and 3 mL) added to either saturated or unsaturated medium.

4

5

Fig. 2. Simulation of the radial motion of 5 lm air bubble in the permanganate solution at static pressure of 1 bar. Time variation of (A) normalized bubble radius (R/Ro); (B) number of water molecules in the bubble; (C) temperature in the bubble and (D) pressure inside the bubble.

0.001

(E)

0

0.001

0

1

2

3

No. of Acoustic Cycles Fig. 3. Simulation of the radial motion of 5 lm air bubble in the permanganate solution at 1.5 bar static pressure. Time variation of (A) normalized bubble radius (R/Ro); (B) number of water molecules in the bubble; (C) temperature in the bubble and (D) pressure inside the bubble.

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Table 3 Summary of the simulation results for air bubbles (ambient pressure: 1 bar). Species Parameters for simulations Unsaturated medium Ro = 5 lm

Saturated medium Ro = 10 lm

Conditions at first compression of the bubble Tmax = 3374 K Pmax = 4281 bar NN2 = 1.306E+010 NO2 = 3.471E+09 NWT = 1.320E+09 Vturb = 2.964 mm/s

Tmax = 1968 K Pmax = 488.3 bar NN2 = 9.289E+010 NO2 = 2.469E+010 NWT = 8.513E+09 Vturb = 6.626 mm/s

Net production of various radicals from transient collapse NOH 1.426E+08 1.696E+06 NH 3.897E+07 NO 8.498E+06 NHO2

3.841E+07 0 1.294E+06 2.175E+06

NOH – number of OH radicals present in the bubble at transient collapse; NH – number of H radicals present in the bubble at transient collapse; NO – number of O radicals present in the bubble at transient collapse; NHO2 – number of HO2 radicals present in the bubble at transient collapse; Vturb – velocity of microturbulence generated by cavitation bubble; Tmax – temperature peak reached in the bubble at transient collapse; Pmax – pressure peak reached in the bubble at transient collapse; NN2 – number of nitrogen molecules in the bubble; NO2 – number of oxygen molecules in the bubble; NWT – number of water vapor molecules entrapped in the bubble at the moment of collapse.

Table 4 Summary of the simulation results for air bubbles (ambient pressure: 1.5 bar). Species Parameters for simulations Unsaturated medium Ro = 5 lm

Saturated medium Ro = 10 lm

Conditions at first compression of the bubble Tmax = 1018 K Pmax = 60.03 bar NN2 = 1.814E+010 NO2 = 4.822E+09 NWT = 6.740E+08 Vturb = 0.698 mm/s

Tmax = 878.9 K Pmax = 34.19 bar NN2 = 1.336E+011 NO2 = 3.550E+010 NWT = 6.609E+09 Vturb = 2.79 mm/s

Net production of various radicals from transient collapse 7.65E+02 NOH NH 0 0 NO 0 NHO2

0 0 0 0

NOH – number of OH radicals present in the bubble at transient collapse; NH – number of H radicals present in the bubble at transient collapse; NO – number of O radicals present in the bubble at transient collapse; NHO2 – number of HO2 radicals present in the bubble at transient collapse; Vturb – velocity of microturbulence generated by cavitation bubble; Tmax – temperature peak reached in the bubble at transient collapse; Pmax – pressure peak reached in the bubble at transient collapse; NN2 – number of nitrogen molecules in the bubble; NO2 – number of oxygen molecules in the bubble; NWT – number of water vapor molecules entrapped in the bubble at the moment of collapse.

sults is given in Tables 3 and 4 for atmospheric and 1.5 bar static pressures respectively. We list below some peculiar trends in simulations results: (1) The intensity of the collapse (characterized by temperature and pressure peaks reached in the bubble at the moment of collapse) of a 5 lm bubble is much higher than 10 lm bubble. The equilibrium mole fraction of radicals in the species formed out of dissociation of water vapor varies directly with the temperature peak reached at the transient collapse. As a consequence, the extent of radical production is higher in an unsaturated medium.

(2) The intensity of the microturbulence, indicated by mean velocity of microturbulence (Vturb), generated by a 10 lm bubble is much higher than 5 lm bubble. (3) The intensity of collapse of both 5 and 10 lm bubbles reduces drastically with rise in static pressure. Nonetheless, the temperature peak reached at the collapse of 5 lm bubble is still moderately high (1018 K) and a small production of  OH radicals is seen. For 10 lm bubble, however, the production of radicals drops to zero with raised static pressure. (4) The intensity of microturbulence reduces by an order of magnitude for both 5 and 10 lm bubble with raised static pressure. 5.4. Correlation of experimental and simulation results Correlating the simulations and experimental results reveals some interesting aspects of the overall physics of permanganate oxidation of toluene. One can see that the physical and chemical effects of cavitation vary in opposite direction with saturation level of the medium: (1) the extent of radical production increases, and (2) the velocity of microturbulence responsible for formation of emulsion decreases. Let’s see how these two conflicting phenomena manifest their effect on the reaction system. (1) The extent of oxidation increases with increasing unsaturation of the medium. This is clearly attributed to higher production of radicals in the medium. (2) With increasing amount of toluene addition to the medium, the extent of oxidation increases. This effect is more marked for the saturated medium, where oxidation yield increases by 40% as the organic to aqueous phase ratio increases from 1:50 to 3:50. However, the oxidation yield is similar for 3:50 volume ratio for both saturated and unsaturated media. This is a clear manifestation of the conflicting phenomena mentioned above. For saturated medium, extent of radical production is low, but intensity of microturbulence is high. This results in formation of fine emulsion that gives maximum utilization of the radicals for oxidation. On the other hand, radical production in an unsaturated medium is higher, but intensity of microturbulence is low. This results in formation of a relatively coarse emulsion with lesser interfacial area. Thus, the probability of interaction between radicals and toluene molecules is relatively low, which limits the extent of utilization of radicals. As a consequence, the oxidation yield is moderate. (3) With addition of FeSO47H2O to both saturated and unsaturated media, the oxidation yield showed a marked rise. This is clearly attributed to the effective utilization of radicals due to conserving phenomena. It is interesting to note that the yield for 1, 2 and 3 mL toluene addition is almost same for the saturated medium. This means that radical conservation coupled with higher microturbulence in saturated medium gives maximum utilization of radicals, and thus, the yield is independent of the organic to aqueous phase ratio in the system. Explanation of almost same oxidation yield in unsaturated medium (within experimental error) with FeSO47H2O addition can also be given along similar lines. (4) At 1.5 bar static pressure, the intensity of cavitation phenomena reduces drastically. Thus, both radical and emulsion formation diminishes. The net outcome is marked fall in the yield. As stated earlier, the radical production of saturated medium (represented by 10 lm bubble) reduces to practically zero. For unsaturated medium, there exists a small production of radicals. This effect is manifested in somewhat higher yields for unsaturated medium than saturated medium for a particular organic to aqueous phase ratio.

R. Kuppa, V.S. Moholkar / Ultrasonics Sonochemistry 17 (2010) 123–131

6. Conclusion In this paper, we have attempted to discern the mechanistic features of the ultrasound-assisted aqueous phase permanganate oxidation of organic compounds using toluene as the model alkylarene. As toluene and aqueous solution of KMnO4 are immiscible, the reaction mixture is essentially a liquid–liquid heterogeneous system, which is limited by the mass transfer characteristics. The principal physical effect of ultrasonic cavitation is formation of fine emulsion between immiscible phases that eliminates the mass transfer resistance, while principal chemical effect is production of radicals through transient collapse of cavitation bubbles, which accelerate the reaction. We have tried to discriminate between these effects by coupling experiments with different conditions that alter the nature of acoustics and cavitation phenomena in the medium to the simulations of cavitation bubble dynamics. It is revealed that in absence of conservation of radicals (through a radical conserving agent such as Fe2+), the enhancement effect of ultrasonic cavitation is merely physical. Diffusion of radicals (formed from transient collapse of cavitation bubbles) towards interface between toluene and aqueous KMnO4 solution, where the oxidation reaction occurs, is the limiting factor in contribution of chemical effect of ultrasonic cavitation towards enhancement of oxidation yield. Enhancement of total radical production in the aqueous phase (by degassing of the medium) increases the overall oxidation yield, but only marginally. On the other hand, addition of a radical conserver such as FeSO47H2O results in marked enhancement of oxidation yield, as the conserver assists deeper penetration of radicals in the aqueous medium and diffusion towards interface. References [1] T. Kimura, M. Fujita, T. Ando, Chem. Lett. 8 (1988) 1387. [2] A.R. Hajipour, S.E. Mallakpour, G. Imanzadeh, Chem. Lett. 2 (1999) 99. [3] J. Walton, P. Labine, A. Reidies, The chemistry of permanganate in degradative oxidations, in: W.W. Eckenfelder, A.R. Bowers, J.A. Roth (Eds.), Chemical Oxidation, Technomic Publishing Co. Inc., Basel, 1997, pp. 205–219. [4] K. Pisarczyk, Manganese compounds, in: Kirk Othmer (Ed.), Encyclopedia of Chemical Technology, vol. 15, John Wiley and Sons, New York, 1991, pp. 501– 532. [5] K.A. Gardner, L.L. Kuehnert, J.M. Mayer, Inorg. Chem. 36 (1997) 2069. [6] R. Neumann, Y. Sasson, J. Chem. Soc. Chem. Commun. (1986) 616. [7] S.R. Soudagar, S.D. Samant, Ultrason. Sonochem. 2 (1995) S15. [8] G.V. Ambulgekar, S.D. Samant, A.B. Pandit, Ultrason. Sonochem. 12 (2005) 85. [9] G.V. Ambulgekar, S.D. Samant, A.B. Pandit, Ultrason. Sonochem. 11 (2004) 191. [10] A.A. Atchley, A. Prosperetti, J. Acoust. Soc. Am. 86 (1989) 1065. [11] H.G. Flynn, J. Acoust. Soc. Am. 57 (1975) 1379. [12] H.G. Flynn, J. Acoust. Soc. Am. 58 (1975) 1160.

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