Effect of Ultrasound on Adsorption and Desorption Processes

During the collapse, energy is set free, inducing extreme thermodynamic conditions of several thousand kelvin and a few hundred bar in the vicinity of...
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Ind. Eng. Chem. Res. 2003, 42, 5635-5646

5635

Effect of Ultrasound on Adsorption and Desorption Processes Marc Breitbach,*,† Dieter Bathen,‡ and Henner Schmidt-Traub* Department of Chemical Engineering, University of Dortmund, Dortmund, Germany

The following paper is aimed at finding the effects of ultrasound on adsorption/desorption processes. Experiments concerning the ultrasonic power input indicate that particles absorb ultrasonic energy effectively if they are in resonance with the ultrasound. The ultrasonic energy is dissipated into heat. Hence, desorption processes are promoted. Desorption experiments at different frequencies show that neither particle oscillations nor cavitation effects are responsible for ultrasonically enhanced desorption processes for an adsorption system with surface diffusion as the rate-limiting step. Measured ultrasonic power distributions show that the ultrasonic field inside the adsorber is very inhomogeneous. With the temperature distribution inside the adsorber, the courses of concentration of ultrasonically enhanced desorption experiments can be explained by a hot-water desorption model. Thus, simulations substantiate the experimental results that thermal effects are responsible for ultrasonically enhanced desorption with the applied adsorption system. 1. Introduction The desorption step has a great impact on the process design and the efficiency of adsorption processes. In industrial processes, different desorption methods exist for adsorber resins loaded in the liquid phase. These involve the use of desorption chemicals, therefore implying a difficult secondary separation step of the desorbed molecules and the extractant, which leads to high investment and running costs.1,2 As a consequence thereof, industry seeks alternative desorption methods, one of which is desorption by ultrasound and water: (i) Ba¨ssler et al. show the feasibility of ultrasonic desorption of a polymeric resin at two different frequencies (24 and 850 kHz).3-5 The enhancement of desorption by ultrasound is explained by the phenomenon of acoustic cavitation. By applying ultrasound in subsequent desorption steps, they show the long-term stability of the resins. (ii) The research group of Prof. Yang finds an acceleration of desorption processes by ultrasound of activated carbon and adsorber resins loaded with phenol.6,7 They conclude that cavitation and acoustic streaming enhance desorption processes by acceleration of the intra- as well as interparticle mass transport. (iii) Yu et al. examine the desorption of colorants from adsorber polymers.8 The desorption rate is increased by acoustic vortex microstreaming. (iv) Feng and Aldrich enhance the elution of adsorbed ions on polymeric resins by ultrasound.9 (v) Qin et al. examine the desorption of different organic adsorbates on various adsorber resins by ultrasound and hot-water desorption.10 They find higher desorption rates by ultrasonication due to a thermal as well as an ultrasonic “spot energy effect”. * To whom correspondence should be addressed. Tel.: ++49/ (0)231/755-2338. Fax: ++49/(0)231/755-2341. E-mail: schmtr@ ct.uni-dortmund.de. † Present address: Shell & DEA Oil GmbH, Elbe Mineralo¨lwerke, BP-2 CE, Postfach 90 02 34, D-21042 Hamburg, Germany. ‡ Present address: Degussa AG, VT-F, Rodenbacher Chaussee 4, D-63457 Hanau, Germany.

The effect of ultrasound on adsorption and desorption processes is not clarified yet. Undisputedly, ultrasound accelerates mass transport phenomena, whereas it is not fully understood how. On the other hand, phenomenological results of the effect of ultrasound on adsorption equilibrium are contradictory: (i) Chmutov and Alekseev find a higher adsorption capacity of activated carbon for fatty acids when applying ultrasound.11 They conclude that the molecules are pushed into micropores by sound waves, hence reaching more adsorption sites. Experiments of Qin et al. also show higher equilibrium loading of acetic acids on weak basic ion exchangers when applying ultrasound.12 (ii) Schu¨ller and Yang did not find an ultrasonic effect on adsorption isotherms of a polymeric resin loaded with phenol.7 (iii) For a similar system, Li et al. measured adsorption isotherms shifted toward lower loading when sonicated.13 Breitbach and Bathen got similar results for fructose adsorbed onto a microporous resin.14 This paper is aimed at finding the effects of ultrasound on adsorption and desorption processes in a fixed bed by varying ultrasonic (frequency, power, etc.) as well as process parameters (flow rate, temperature, etc.). Conclusions will be drawn by experimental and simulative studies if the enhancement of desorption processes is due to ultrasonic or cavitational effects on the local adsorption equilibrium and/or the adsorption kinetics. 2. Theoretical Section 2.1. Modeling of Fixed-Bed Adsorption/Desorption. The ultrasound-induced fixed-bed desorption process is modeled with a temperature-dependent homogeneous diffusion model15 with an inhomogeneous energy input and subsequent local temperature profile due to ultrasonication. Temperature gradients inside the particles due to high heat capacities of the adsorbent material16 and differences between solid and fluid temperatures can be neglected (simulation studies have shown a difference of a maximum of 0.12 K). Therefore, one overall heat balance for the liquid-filled fixed bed is sufficient to

10.1021/ie030333f CCC: $25.00 © 2003 American Chemical Society Published on Web 10/03/2003

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model the energy flow through the adsorber. Also, temperature effects due to the heat of adsorption/ desorption can be neglected in liquid adsorption systems.16 The heat-transfer processes are convection, dispersion, heat loss to the adsorber wall, and a heat source due to ultrasonication:

∂TF ∂TF ) -u0FFlcpFl + ∂t ∂z ∂2 TF ∂FFl - TF[L + (1 - L)P]cpFl λDL 2 ∂t ∂z 4pdiff(z) 4hi (TF - TW) + (1) D πD2

the mass balance inside the particles

[

2

λW ∂ TW hi ∂TW D )+ (T - TW) ∂t FWcpW ∂z2 FWcpW Ds + s2 Fl ha D (T - Te) (2) FWcpW Ds + s2 W The mass balance for the fluid phase is modeled as a distributed plug-flow model, whereas the fixed bed is assumed to be homogeneous. The mass-transfer processes are assumed to be convection, axial dispersion, and film diffusion in the boundary layer of the particles:

∂cA ∂2cA u0 ∂cA cA ∂u0 kf[6(1 - L)] ) Dax 2 ∂t L ∂z L ∂z dPL ∂z {cA - cA,equ[r ) (dP/2)]} (3) Internal mass transport in the adsorbent assumes surface diffusion to be dominant, which is a common assumption for high-affinity solutes.17 For the adsorption of benzoic acid on a polymeric resin, Huang et al.18 show that better simulation results are obtained by applying a surface-diffusion model compared to a porediffusion model. Axial disperion is assumed to be constant. The local surface-diffusion coefficient is described by the Eyring’s rate theory:19 Implying a temperature-dependent Freundlich isotherm

q ) k0eA/TcAn

(4)

leads to a temperature- and surface-concentrationdependent surface-diffusion coefficient

The local adsorption equilibrium is best described by a temperature-dependent Redlich-Petersen isotherm:20

q)

k1,0eA1/TcA 1 + k2,0eA2/TcAn1

(6)

Presuming a Freundlich isotherm and a constant temperature inside the particles leads to a radially constant surface diffusion, thus giving the known equation for

( )]

(7)

The initial conditions are

[(1 - L)FScpP + LFFlcpFl]

The heat balance of the adsorber wall contains axial heat conduction and heat transition inside and outside the adsorber wall:

] [

∂q ∂2q 2 ∂q 1 ∂ ∂q ) DS 2 r2 ) DS 2 + ∂t r ∂r ∂r r ∂r ∂r

q(z,r,t)0) ) q0

(8)

cA(z,t)0) ) cA,0

(9)

TF(z,t)0) ) TW(z,t)0) ) T0

(10)

The boundary conditions are

|

∂q )0 ∂r r)0

(11)

kf ∂q ) {c - cA,equ[r ) (dP/2)]} ∂r r)dP/2 FPDS A

(12)

cA(z)0,t) ) cA,in

(13)

TF(z)0,t) ) TF,in

(14)

|

2.2. Ultrasound. Ultrasound represents mechanical waves, i.e., a variation of pressure or density, with frequencies above the human hearing threshold (ca. 18 kHz). During propagation, it is attenuated by absorption in the propagation medium,21,22 by cavitation bubbles,23 by particles,24 and at interfaces.25 The inner porosity can increase the attenuation of ultrasound in solid materials to such an extent that the dissipated energy can be used for ultrasonic drying of porous material.26 Depending on the frequency and particle diameter, ultrasound is reflected backward or focused in the direction of propagation by particles. Apart from this, particles get stimulated by ultrasound to surface oscillations. At the resonant frequency

fr )

x

cP πdP

FP 3 FFl

(15)

particles transform most of the ultrasonic energy into oscillationary energy, leading to heat dissipation due to friction with the propagation medium. 2.3. Inception of Cavitation. Because ultrasound is not perceived, high sound intensities are feasible. Hence, nonlinear phenomena like acoustic cavitation occur: Because of high sound intensities, the tensile stress of the liquid is exceeded. Little gas bubbles are formed during the expansion cycle of the sound wave and grow over one or several cycles to many times its initial size. When having reached a critical size, they collapse intensively during the compression cycle. During the collapse, energy is set free, inducing extreme thermodynamic conditions of several thousand kelvin and a few hundred bar in the vicinity of the imploding bubble.27 Depending on the intensity/pressure amplitude and frequency of the sound wave, cavitation bubbles act differently to the excitation: Transient cavitation bubbles grow and implode within one sound cycle, whereas stable bubbles exist over several sound cycles. Cavitation diagrams are helpful to estimate the dynamic

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Figure 1. Cavitation diagrams for air bubbles in air-saturated water at 25 °C and a static pressure of 105 Pa at different ultrasonic frequencies: (a) 40 kHz; (b) 350 kHz; (c) 1050 kHz.

behavior of a bubble in a sound field. Such diagrams are shown in Figure 1 for three different frequencies. The bubble diameter is plotted logarithmically on the x axis; the y axis inversely logarithmically shows the pressure amplitude of the sound waves. Cavitation diagrams can be divided into several areas: (i) Bubbles in resonance with the exciting sound field oscillate stable and without a phase shift around a characteristic resonance radius.28 (ii) In area I the pressure amplitude is too weak to produce stable bubbles: bubbles smaller than the resonance radius dissolve, and bubbles greater than the resonance radius float to the surface. (iii) In area II bubbles oscillate as a result of the sound waves. During the oscillations, dissolved gas diffuses through the bubble walls; because of the greater surface area of the bubble during the expansion half-cycle, more gas diffuses into the bubble than diffuses out of the bubble in the compression half-cycle.29 In this process, called rectified diffusion, the bubbles grow over several sound cycles.28 (iv) In area IIa bubbles additionally grow as a result of absorption of ultrasonic energy. (v) In area III cavitation bubbles become transient: The sound intensity is sufficient to let the bubbles grow to several times its initial size within one sound cycle and finally implode heavily:30 The cavitation diagrams in Figure 1 show that at higher frequency the spectrum of cavitation bubbles is shifted toward smaller bubble diameters. Also, it becomes obvious that transient cavitation cannot occur inside the pores of the adsorbents, which have diameters

50 nm (macropores).31 Also, high-pressure amplitudes (>106 Pa) are necessary for the inception of transient cavitation inside pores with diameters in the nanometer range. 2.4. Effects of Cavitation. Depending on the frequency and intensity, different mechanical, thermal, and radical effects arising from cavitation dominate. Effects are greater for bigger bubbles (i.e., lower frequencies) because the energy stored within a cavitation bubble is proportional to its size. As more cavitation events occur per time and volume at higher frequencies because of quicker oscillations and smaller wavelengths, an optimum frequency for any cavitational effect exists. This frequency depends on the energy required to evoke a desired effect. Mechanical effects of cavitation, e.g., erosion of solid surfaces or acceleration of heat and mass transport, arise from pressure waves emitted by imploding bubbles and from microjets, which occur as a result of an asymmetric collapse of cavitation bubbles at interfaces. They form liquid jets directed toward the surface of the interface, which reach speeds up to 500 m/s.27 Because mechanical effects, e.g., the erosion of solid surfaces, need a lot of energy, these effects dominate at the lowfrequency range. In contrast, chemical effects dominate in the midfrequency range between 200 and 400 kHz.32,33 They arise from the high temperatures of (theoretically) up to 1000 K within the center of a cavitational collapse. These extreme conditions promote chemical reactions, like the cracking of water into hydrogen and hydroxyl radicals:27 cavitation

H2O 98 H• + •OH

(16)

3. Experimental Section 3.1. Chemicals. The polymeric resin Dowex Optipore L-493 (Dow Chemicals, Midland, MI) serves as the adsorbent. It consists of a styrene-divinylbenzene copolymer with a specific surface area of 1100 m2/g (Brunauer-Emmett-Teller), a total porosity of 1.16 cm3/g, and an average pore diameter of 90 nm.34 The resin is in the form of chemical inert rigid spheres, which are wet sieved to particle sizes between 630 and 800 µm in these studies. Preliminary tests had shown that the resin does not get damaged by ultrasound of the applied frequencies.35 As a model substance for water pollutants, benzoic acid is used as the adsorbate in these studies. Adsorption and desorption experiments are performed with fully desalted water. The temperature-dependent isotherm and mass transport parameters of these substances are experimentally determined by frontal analysis in a high-performance liquid chromatograph between 25 and 40 °C. The temperature-dependent Redlich-Petersen isotherm has the following parameters (see Figure 2):

q)

0.017810e1512.40/Tc 1 + 4.436464e260.95/Tc0.710053

(17)

A temperature-dependent Freundlich isotherm20 is only accurate at high concentrations of >0.08 g/L. The temperature- and surface-concentration-dependent surface-diffusion coefficients are estimated using Eyring’s rate theory (see eq 5) with a vaporization

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Figure 2. Temperature-dependent isotherms for the system benzoic acid/water/Dowex Optipore L-493.

Figure 3. Experimentally and simulatively determined breakthrough curves for the system benzoic acid/water/Dowex Optipore L-493 with different loading concentrations at different temperatures.

energy of benzoic acid of36

∆Evap ) 63819.807 J/mol

(18)

and a temperature-dependent solubility of benzoic acid in water of (values from refs 37 and 38)

cA,s(ϑ) ) 2.170477 exp(0.004400ϑ1.451080) [g/L]

(19)

The parameters a and b in eq 5 are estimated with gEST from the breakthrough curves

a ) 0.823935

(20)

b ) 1.97731 × 10-4 m2/K/s

(21)

This set of parameters leads to surface-diffusion coefficients between 10-13 and 10-11 m2/s, which is consistent with values published in the literature.15 The external mass transport is estimated using the correlation of Wakao and Funazkri:39

Sh ) 2 + 1.1Sc1/3ReP0.6 for L ) 0.4 and 3 < ReP < 10.000 (22) The temperature-dependent diffusion coefficient is calculated with the correlation of Wilke and Chang40 using the correlation of Gunn and Yamada40 to estimate the molar volume at the normal boiling point. Figure 3 shows the good conformity between experimentally and simulatively determined breakthrough curves at different temperatures and concentrations

using this set of parameters and correlations. This proves the assumption of surface diffusion as the ratelimiting step inside the particles: pore diffusion would lead to a more symmetric breakthrough curve17 as well as to another temperature dependency of the intraparticle mass transport.41 3.2. Experimental Setup. A peristaltic pump delivers the solution/water from a tempered reservoir to a six-port valve. The experiment starts by turning the valve, so that the solution/water flows through the adsorber column in an upflow configuration. By this procedure, a defined starting point of the experiment is set. The outlet concentration is measured by a UV/ vis detector at wavelengths of 269 or 290 nm. The adsorber column is placed in a water bath, tempered by an external thermostat, which constantly exchanges warm water with cold water. Temperatures entering and leaving the column as well as in the water bath are recorded. An ultrasonic transducer of L-3 Communications ELAC Nautik, Kiel, Germany (frequencies between 40.3 and 1040 kHz), is flanged onto one side of the water bath. To achieve a homogeneous standing-wave field, the water bath is built as a pentagon. The adsorber column (Figure 4) consists of three parts: an inlet and an outlet piece, both of which are built of poly(vinyl chloride) and are covered by metallic shielding, and the adsorption part (inner diameter: 11 mm) with walls of 1-mm-thick acrylic glass. Preliminary experiments had shown that ultrasound passes this material. The inlet and outlet temperatures of the adsorber are both measured at the rear side of the glass frits. Inside the adsorber is a dry mass of ca. 0.47-0.49 g of adsorbent. For loading of the adsorbent, a 0.061 06 g/L benzoic acid solution is pumped through the column at a volumetric flow rate of 4.0 mL/min at 25 °C until equilibrium is reached. The corresponding equilibrium loading of the resin is 0.057 g/gwet. Desorption experiments are performed with degassed desalted water, which passes through the column at a volumetric flow rate of 1.2 mL/min. 4. Experimental Results 4.1. Power Input into the Adsorber. Although the geometrical setup of the sonicated adsorber is the same for all frequencies, the ultrasonic and cavitational fields, which evolve in the water bath, are different. For a comparison of desorption results at different frequencies, it is essential to conduct the experiments at the same power input into the adsorber. The temperature rise of water passing the sonicated adsorber (1.2 mL/min) is a measurable variable for the calorimetric power input into the adsorber. In Figure 5, the temperature rise in dependency of the ultrasonic frequency and calorimetric power (for definitions, see, e.g., ref 27) is shown for an empty adsorber (a) and for adsorbers packed with different adsorbents (b-d). The water heats without ultrasound, because the water enters the adsorber with 22 °C while the temperature inside the water bath is kept at 25 °C. When passing the empty adsorber (with the same residence time inside the sonicated part of the adsorber as in the packed adsorbers), the water heats with increasing ultrasonic power input as a result of sound absorption in the acrylic glass and water (Figure 5a). The higher temperature rise at 355.5 kHz can be

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Figure 4. Experimental setup of the adsorber: (a) placement in a water bath; (b) constructive realization.

Figure 5. Calorimetric power input into the adsorber at different frequencies and different power settings at the transducer: (a) empty adsorber; (b) with the adsorbent Serdolit PAD-I; (c) with large particles of the adsorbent Dowex Optipore L-493; (d) with small particles of the adsorbent Dowex Optipore L-493.

explained by the more focused ultrasonic field. The other frequencies lead to an approximately similar energy input. The temperature rise of the water changes significantly when the adsorber is packed with adsorbent particles. Dependent on the particle size, the temperature rise is more pronounced at different frequencies: (i) When passing the adsorber packed with a large particle fraction of Dowex Optipore L-493 (dP ) 0.6773 mm; Figure 5c), the temperature rises up to 27 °C at the outlet of the adsorber when being sonicated with maximum power at 355.5 kHz. When being sonicated with other frequencies, the heating of the water is less

pronounced but is still higher than that in the empty adsorber as a result of higher sound absorption inside the packed bed. (ii) If the particle size is reduced to 0.3360 mm (Figure 5d), the frequency-dependent heating of the water resembles the characteristics in the empty adsorber whereas a slightly higher sound absorption occurs in the fixed bed. (iii) The heating of the water is completely different in an adsorber packed with Serdolit PAD-I with a mean particle diameter of 0.1930 mm (Figure 5b). At 1046.0 kHz the temperature at the outlet of the adsorber rises, while it decreases at all other frequencies (as a result

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Figure 7. Iodine concentration inside the adsorber after sonicating potassium iodide at different frequencies for 40 min. Figure 6. Calculated resonance frequencies of adsorbent particles with different particle sizes (eqs 15 and 23).

of the limited penetration depth at smaller particle sizes and higher porosity). These findings indicate that resonance effects in the sound absorption occur depending on the particle size and ultrasonic frequency as a result of the frequencydependent surface oscillations of the particles. Substituting the velocity of sound in eq 15 by

cP )

x

EP

3FP(1 - 2νP)

(23)

leads to the results shown in Figure 6, where the resonance frequency is shown for different particle sizes for two different Young’s moduli and νP ) 0.3. The full line shows the results when applying experimentally determined Young’s moduli of dry particles (63.7 N/mm2);35 the broken line shows results for an adjusted Young’s modulus. The findings clearly indicate that the resonance frequency increases with decreasing particle sizes. Because the experiments in Figure 5 are performed with wet particles in a fixed bed, the particles are stiffer than those in a dry condition. Therefore, the experimentally determined Young’s moduli of Breitbach et al.35 give too low resonance frequencies. When the modulus is adjusted to a higher value of 228.5 N/mm2, the resonant surface oscillation occurs at ca. 355 kHz for the large particles and at ca. 750 kHz for the small particles of the Optipore adsorbent. Particles with diameters of ca. 0.2 mm have resonance frequencies in the low megahertz region. This frequency-dependent behavior of surface oscillations at different particle sizes explains the different outlet temperatures in Figure 5: (i) The large particles of the Dowex adsorbent are in resonance with the applied sound field at 355.5 kHz. (ii) The small particles of the same adsorbent are not in resonance with any of the applied frequencies. (iii) The very small particles of Serdolit PAD-I are in resonance at 1046 kHz. 4.2. Cavitation inside the Adsorber. To get information about the mechanisms of ultrasonically enhanced desorption, it is important to know if cavitation occurs inside the fixed bed of adsorbent and if the cavitational intensity is frequency dependent. In a homogeneous reaction system, Busnel and Picard32 found a maximum of the cavitation intensity at 350 ( 50 kHz when exploring the oxidation of a iodide solution by cavitationally induced hydroxyl radicals.

This system is also used in these studies in the heterogeneous solid-liquid system. An iodide solution (0.1 mol/L) is sonicated for 40 min at the same calorimetric power input in a reaction vessel, which is filled with adsorbent particles and has the same geometry and materials as the adsorber in the desorption experiments. After the sonication, the whole setup is washed with 0.95 mL of a Na2S2O4 solution before this solution is titrated with an iodine solution (5 mmol/L). The median iodine concentration after sonication of at least three experiments is shown in Figure 7. These results show that cavitation is introduced in the packed adsorber at every frequency. The intensity of cavitation is frequency dependent with a maximum in the midfrequency range around 355.5 kHz, which corresponds to the findings of Busnel and Picard32 for a homogeneous reaction system. 4.3. Frequency Dependency of Sonicated Adsorption and Desorption. The frequency dependency of sonicated adsorption processes is a valuable measure to distinguish between the different effects of ultrasound and cavitation. Changes of the adsorption equilibrium and mass transport kinetics can be investigated simultaneously: The area in Figure 8 between the breakthrough curve and the loading concentration is determined by the adsorption equilibrium, whereas the course of concentration results from the mass-transfer mechanisms. Thus, adsorption experiments are performed for each frequency at the same calorimetric power input into the adsorber (same ∆T in Figure 5c). Additionally, an experiment with similar inlet and outlet temperatures without ultrasound is conducted. The courses of outlet concentrations and temperatures are shown in Figure 8. The identical courses of concentration for each frequency lead to the conclusion that the ultrasonic effects on the adsorption equilibrium as well as on the masstransfer kinetics are not frequency dependent. Because the cavitation intensity is strongly frequency dependent at identical conditions in the adsorber (see section 4.2), interparticle cavitational effects can be neglected. Furthermore, the identical concentrations during the sonicated and unsonicated experiments show that the ultrasonic effect is solely of a thermal nature: (i) Stable cavitation bubbles inside the pores would affect the equilibrium toward lower loadings because these bubbles would block adsorption pores. Because the equilibrium is unaffected by ultrasonication, this effect can be neglected in this adsorption system.

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Figure 10. Concentrations (above) and outlet temperatures (below) during sonicated desorption experiments at different volumetric flow rates at 355.5 kHz and 200 Wnominal. Figure 8. Concentrations (above) and temperatures (below) during sonicated adsorption experiments at different frequencies at identical power inputs into the adsorber.

examined experimental setup because the course of concentration is identical with and without ultrasonication. Sonicated desorption experiments (not shown) confirm these results: When applying ultrasound of the same power input (into the adsorber) during desorption, the courses of the outlet concentration are identical at each frequency. 4.4. Variation of Power during Desorption. The influence of ultrasonic power input is investigated at 355.5 kHz because this frequency shows the highest efficiency. The courses of concentration and temperature rise in the adsorber are shown in Figure 9. In the first phase of ultrasonic desorption, an upgrading of the solution

Ac ) cout,max/cloading > 1

Figure 9. Concentrations (above) and temperature differences (below) during sonicated desorption experiments at different powers at 355.5 kHz.

(ii) In the literature microturbulence inside pores due to oscillation of the particles is given as an explanation for different mass-transfer kinetics during adsorption/ desorption.8,9 Because the courses of concentration are unaffected by sonication in Figure 8, no significant effect of microturbulences on the mass transport processes can be found in this study. (iii) Diffusion processes in the boundary layer of the particles are not accelerated by ultrasound in the

(24)

takes place; i.e., the outlet concentration exceeds the concentration during loading. With increasing power, the outlet concentrations rise as a result of the higher temperatures inside the adsorber. These temperature differences inside the adsorber grow with increasing ultrasonic power to 30 K at 200 Wnominal. 4.5. Variation of the Volumetric Flow Rate during Desorption. The influence of the volumetric flow rate is investigated at 355.5 kHz and a maximum power of the transducer (200 Wnominal) between 0.2 and 4.0 mL/ min. The courses of concentration and temperature at the outlet of the adsorber are shown in Figure 10. For a better comparison, the x axis of the diagram shows the volume that has passed the adsorber:

V ) Qt

(25)

With decreasing flow rates, the outlet temperature of the water increases as a result of a longer residence time in the sonicated part of the adsorber until it reaches a maximum at 1.2 mL/min. Decreasing the flow

5642 Ind. Eng. Chem. Res., Vol. 42, No. 22, 2003

Figure 11. Courses of concentration during hot-water desorption experiments at 40, 50, and 60 °C in comparison to an ultrasonic desorption experiment at 355.5 kHz and 200 Wnominal.

rate further leads to a drop of the outlet temperatures as well as to a nervous course of temperature at the outlet. In contrast to the temperatures, the maximum concentrations grow with decreasing flow rate. The upgrading of the solution at different volumetric flow rates reaches a maximum value of ca. 6 (at 0.2 and 0.5 mL/ min), which corresponds to the upgrading when desorbing with hot water at 100 °C, which will be shown in the following dynamic simulations (see section 5.2). These results also show that the dominating effect of ultrasonication during desorption is a heating effect because the maximum possible upgrading of a hot-water desorption is not exceeded. Also, the results show that the temperature measured at the outlet of the adsorber does not necessarily correspond to the temperature at the rear end of the fixed adsorber bed: Because of a much higher residence time in the unsonicated part of the adsorber (i.e., glass wool and frit) at low flow rates, the water has more time to cool, leading to misleading temperature measurements. 4.6. Comparison of Ultrasonic and Hot-Water Desorption. For a comparison of ultrasonic desorption with hot-water desorption, the loaded adsorber is regenerated with hot water between 40 and 60 °C, which corresponds to the outlet temperatures reached during ultrasonic desorption experiments (see Figure 10 below). In Figure 11 the courses of concentration of three hotwater desorption experiments as well as one ultrasonic desorption experiment are shown. When applying hot water for desorption, the outlet concentration increases with growing desorption temperatures. The agreement of the maximum concentration during hot-water desorption and the equilibrium concentrations at these temperatures (eq 17) confirms the reliability of the adsorption and desorption experiments. Also this shows that equilibrium is reached during hot-water desorption at the flow rate of 1.2 mL/min (compare to work of Bercˇicˇ et al.20). The desorption with ultrasonication seems to be much more effective than the hot-water desorption: The concentrations are much higher, thus leading to higher desorption rates, although the temperature at the outlet of the adsorber is only around 50-53 °C. These findings could lead to the conclusion that not only a thermal effect is responsible for the ultrasonic desorption. Simulative studies have to be taken into account in order to verify these contradictory results.

Figure 12. Comparison of experiment and simulation for hotwater desorption experiments at 40, 50, and 60 °C (for parameters, see Figure 11).

Figure 13. Simulation study of the influence of desorption temperature during hot-water desorption.

5. Simulative Results 5.1. Verification of the Model for Hot-Water Desorption. The courses of concentration for the hotwater desorption experiments are simulated with the model introduced in section 2.1 and the temperaturedependent adsorption equilibrium and mass transport kinetics given in section 3.1. The simulated results are compared to the measurements in Figure 12. It is evident that the model is well suited for simulating hot-water desorption processes. 5.2. Influence of the Desorption Temperature during Hot-Water Desorption. Simulations at various desorption temperatures are given in Figure 13. The parameters for the simulations are the same as those during the ultrasonic desorption experiments. Figure 13 shows that the maximum outlet concentration at ca. 100 °C is 0.35 g/L, which corresponds to an upgrading of the solution of ca. 6. This is the limit that is possible with ultrasonic desorption experiments at ambient pressure (see Figure 10). 5.3. Measurement of the Longitudinal Power Distribution inside the Fixed Bed. The longitudinal power distribution inside the fixed bed cannot be measured by thermocouples inside the fixed bed because the ultrasonic field would be disturbed immensely. Therefore, a method was developed in these studies that determines the distribution by varying the flow rate through the adsorber and estimating the distribution by simulating the temperature response at the outlet. In the experiments, water passes the sonicated adsorber with a low flow rate of 1.2 mL/min. The water heats as a result of ultrasonic energy dissipation inside the adsorber and leaves with a higher outlet temperature. The temperature profile inside the fixed bed is

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Figure 14. Comparison between simulation and experiment for a jump of the flow rate while sonicating with 40.3 kHz and 200 Wnominal: temporal course of the outlet concentration (left) and longitudinal power distribution and temperature distribution (for 1.2 mL/min) inside the fixed bed (right). Table 1. Temperatures Measured at the Outlet of the Adsorber at 1.2 mL/min as Well as the Maximum Temperatures in the Adsorber Determined by Simulation experiment 1

experiment 2

experiment 3

f [kHz]

P [Wnominal]

Tout [°C]

Tmaxa [°C]

∆T [K]

Tout [°C]

Tmaxa [°C]

∆T [K]

Tout [°C]

Tmaxa [°C]

∆T [K]

40.3 204.0 355.5b 610.0 1046.0

200 200 100 200 200

29.7 33.5 40.2 28.8 29.8

33.1 37.0 (100.0) 31.4 49.9

3.4 3.5 g59.8 2.6 20.1

29.9 33.4 40.7 29.0 31.1

33.7 36.1 (100.0) 33.0 39.0

3.8 2.7 g59.3 4.0 7.9

29.7 32.7 39.9 28.9 29.5

35.6 37.6 99.4 35.2 37.5

5.9 4.9 59.5 6.3 8.0

a Outlet temperature at 1.2 mL/min (in thermal equilibrium). b Temperature distribution cannot be calculated because the model is only valid up to 100 °C.

dependent on the energy distribution due to ultrasonication and on the heat losses through the adsorber wall. When increasing the flow rate abruptly (in these studies, 4.0 mL/min), the temperature profile is pushed out of the adsorber, before the new equilibrium adjusts. If the heat losses through the adsorber walls and in the periphery are known, it is possible to estimate the longitudinal power distribution inside the adsorber from the temporal course of the outlet temperatures after the increase of the flow rate. The temporal course of the outlet temperatures is approximated by varying the longitudinal power distribution inside the fixed bed using the energy balances given in section 2.1 (i.e., eqs 1 and 2). A comparison of the outlet temperatures during three experiments and by simulation for a jump of the flow rate while sonicating with 40.3 kHz and 200 Wnominal is shown in the left diagram of Figure 14. The longitudinal power distributions inside the fixed bed that are used for these simulations are given in the right diagram. The beginning of the temperature rise and the maximum temperature are calculated well with the simulation model. Differences between experiment and simulation occur after approximately 10 s, when the measured values tend to smaller temperatures. This happens for two reasons: (i) In the experiments, the change of the volumetric flow rate takes several seconds, whereas the simulations calculate with an instant increase from 1.2 to 4.0 mL/ min. (ii) The periphery of the adsorber, i.e., glass wool and frit (see Figure 4, left), is simplified in the modeling. Also, Figure 14 shows the very inhomogeneous longitudinal power distribution due to ultrasonication with a maximum close to the inlet of the adsorber. The position of the maximum results from the geometrical arrangement because the inlet of the adsorber is closer

to the center of the sound-emitting surface (see Figure 4, left). This leads to maximum temperatures inside the adsorber that are 3-6 K higher than the measured outlet temperatures at 1.2 mL/min. The diagrams show that the power/temperature distribution inside the adsorber varies to a fair amount under the same conditions. The reason for this lies in instationary cavitation and ultrasonic field inside the pentagonal water bath, which leads to instationary power distributions inside the fixed bed. Experiments and simulations with the other frequencies give similar results. This proves that the proposed method is a valuable tool to estimate the longitudinal power/temperature distribution. Table 1 gives the temperatures measured at the outlet of the adsorber at 1.2 mL/min as well as the maximum temperatures in the adsorber determined by simulation. The differences between the maximum and outlet temperatures are in the range between 2 and 8 K for 40.3, 204.0, 610.0, and 1046.0 kHz at 200 Wnominal, whereas maximum temperatures above 100 °C occur at 355.5 kHz despite a lower nominal power (100 Wnominal). Such high temperatures are confirmed by the occurrence of white parts in the acrylic glass after sonicating with 355.5 kHz. The softening temperature of this material lies between 100 and 105 °C.42 The simulations are not valid for higher temperatures because they do not take into account a phase change liquid-gas. As a consequence, the temporal courses of the outlet temperature at 355.5 kHz can only be roughly estimated at 1.2 mL/ min. These results show that the temperatures inside the adsorber are much higher than those at the outlet. This information is very important for the simulation of adsorption and desorption processes because the adsorption isotherm as well as the mass transport processes are strongly temperature dependent.

5644 Ind. Eng. Chem. Res., Vol. 42, No. 22, 2003

Figure 15. Comparison between simulation and experiment for two ultrasonically enhanced desorption experiments with 355.5 kHz and 200 Wnominal at different flow rates (dotted line, 4.0 mL/ min; solid line, 2.5 mL/min).

5.4. Verification of the Model for Ultrasonic Desorption. A comparison between simulation and experiment of ultrasonic desorption at 355.5 kHz at 200 Wnominal at two different volumetric flow rates is given in Figure 15. The simulation only takes into account the longitudinal temperature distribution due to the inhomogeneous ultrasonic field in the adsorber and temperature-dependent isotherms as well as mass transport parameters. Because the ultrasonic power input varies in time, heavy temperature changes in the adsorber occur (see Figure 15 below). Therefore, two simulations with a minimum and a maximum power input of 55 and 75 Wcal.,adsorber are stated in the diagram, which correlate with the minimum and maximum outlet temperatures during the experiments. The simulations reflect the trend of the experimental values quite well. The simulated outlet concentrations are in the same range as the measured values. This substantiates the experimentally obtained results that the heating effect of ultrasound enhances desorption because only this effect is taken into consideration for the modeling. Another effect of ultrasound or cavitation is not significant. 6. Conclusion and Prospects The objective of these studies was to find the effects of ultrasound on adsorption and desorption processes in a fixed-bed adsorber by experimental and simulative studies. The dominating intraparticle mass transport mechanism was by surface diffusion. Experiments concerning the ultrasonic power input clearly indicate that adsorbent particles absorb the ultrasonic energy very effectively if they are in resonance with the ultrasonic field. The resonance frequency of the particles depends on size and mechanical (elastic) properties. The ultrasonic energy is dissipated into heat. Hence, desorption processes are promoted because at

elevated temperatures the equilibrium loading is lower and mass-transfer processes are quicker. Desorption experiments at different frequencies between 40 and 1046 kHz show that no frequency effect occurs. The consequence hereof is that neither particle oscillations nor cavitation effects are significantly responsible for ultrasonically enhanced desorption processes. The ultrasonic power has a major effect on the efficiency of the desorption process. A model based on mass and heat balances has been derived, and the temperature-dependent adsorption equilibrium and mass-transfer kinetics have been determined. The ultrasonic power distribution in the fixed bed was measured with a new method, which only demands information about the temperature development at the outlet of the adsorber after changing the flow rate through the adsorber. The results clearly show that the power distribution is very inhomogeneous over the adsorbent bed and that much higher temperatures occur inside the adsorber than at the outlet. With these information, the trend of the measured concentrations can be calculated. Thus, simulations substantiate the experimental results that only a thermal effect is responsible for an enhancement of desorption processes by ultrasound for an adsorption system with surface diffusion as the rate-limiting step. Because water can be heated in a cheaper way than by ultrasonication, this desorption variant only makes sense when additional heat exchangers cannot be introduced in an adsorption process. This is, for example, the case in ultrapure water processes, in which any additional apparatuses lead to additional pollution spots. In these studies, an adsorbent-adsorbate system with surface diffusion as the rate-limiting step was applied. Future studies should be conducted with a pore-diffusion-limited adsorption system. Because of the different transport mechanism, a “true” ultrasonic effect by, for example, acoustic vortex streaming could be possible. Acknowledgment The authors thank Deutsche Forschungsgemeinschaft (DFG) for the financial support of the project “Desorption durch Ultraschall” (BA 2012/1-1) and the MaxBuchner Foundation of DECHEMA eV for supporting the project “Untersuchungen zur Desorption durch Ultraschall” (MBFSt 2192) as well as INAQUA Vertriebsgesellschaft mbH, Mo¨nchengladbach, Germany, for providing the adsorber resin. Nomenclature a ) parameter of temperature-dependent surface-diffusion coefficient A ) parameter of temperature-dependent Freundlich isotherm (K) A1 ) parameter of temperature-dependent Redlich-Petersen isotherm (K) A2 ) parameter of temperature-dependent Redlich-Petersen isotherm (K) Ac ) upgrading of a solution b ) parameter of temperature-dependent surface-diffusion coefficient (m2/K/s) b ) damping constant (theory of Eller28) (s-1) c ) concentration (kg/m3) cA ) concentration of the adsorbate (kg/m3) cA,0 ) initial concentration of the adsorbate (kg/m3)

Ind. Eng. Chem. Res., Vol. 42, No. 22, 2003 5645 cA,equ ) concentration of the adsorbate in equilibrium (kg/ m3) cA,in ) concentration of the adsorbate at the inlet (kg/m3) cA,s ) solubility of the adsorbate in water (kg/m3) cGas ) concentration of dissolved gas (kg/m3) cGas,s ) saturation concentration of dissolved gas (kg/m3) cloading ) inlet concentration during adsorption (kg/m3) cout ) concentration at the outlet of the adsorber (kg/m3) cout,max ) maximum concentration at the outlet of the adsorber during desorption (kg/m3) cP ) sound velocity in the particles (m/s) cpFl ) fluid heat capacity (J/kg/K) cpP ) particle heat capacity (J/kg/K) cpW ) heat capacity of the wall material (J/kg/K) dB ) bubble diameter (m) dP ) particle diameter (m) D ) diameter of the adsorber (m) D12 ) diffusion coefficient in the solution (m2/s) Dax ) axial fluid dispersion coefficient (m2/s) DS ) surface-diffusion coefficient (m2/s) ∆Evap ) molar vaporization energy (J/mol) EP ) Young’s modulus of particles (N/m2) f ) frequency (Hz) fr ) resonance frequency (Hz) h ) Planck constant (J‚s) ha ) heat-transfer coefficient at the outside of the adsorber wall (W/m2/K) hi ) heat-transfer coefficient at the inside of the adsorber wall (W/m2/K) k0 ) parameter of temperature-dependent Freundlich isotherm [(m3/kg)n] k1,0 ) parameter of temperature-dependent Redlich-Petersen isotherm (m3/kg) k2,0 ) parameter of temperature-dependent Redlich-Petersen isotherm [(m3/kg)n1] kB ) Boltzmann constant (J/K) kf ) film-transfer coefficient, external mass-transfer coefficient (m/s) mS,dry ) mass of dry adsorbent in the adsorber (kg) mS,wet ) mass of wet adsorbent in the adsorber (kg) n ) parameter of temperature-dependent Freundlich isotherm n1 ) parameter of temperature-dependent Redlich-Petersen isotherm p0 ) hydrostatic pressure (Pa) pB ) threshold pressure for transient cavitation after Blake (Pa) pD ) threshold pressure for rectified diffusion (Pa) pdiff ) differential power input (W/m) pI ) pressure of transient bubbles after Apfel with critical size (Pa) pmax ) maximum pressure during collapse of cavitation bubble (Pa) pT ) threshold pressure for transient cavitation after Apfel (Pa) P ) power (W) Pcal.,adsorber ) calorimetric power input into the adsorber (W) Pcal.,transducer ) calorimetric power of the transducer (W) q ) loading (kg/kg) q0 ) initial loading (kg/kg) Q ) volumetric flow rate (m3/s) r ) coordinate in the direction of the particle radius (m) RB ) radius of the bubble for transient cavitation after Blake when in resonance (m) RD ) radius of the bubble for rectified diffusion when in resonance (m) RI ) critical inertial radius of the bubble for transient cavitation after Apfel (m) Rmin ) minimum bubble radius of the cavitation bubble during collapse (m) Rr ) resonance radius (m)

RT ) radius of the bubble for transient cavitation after Apfel when in resonance (m) ReP ) Reynolds number of a particle ()u0dP/νFl) s ) wall thickness (m) Sc ) Schmidt number ()νFl/D12) Sh ) Sherwood number ()kfdP/D12) t ) time (s) T ) temperature (K) T0 ) initial temperature (K) Te ) temperature of the environment (K) TF ) temperature inside the fixed bed (K) TF,in ) temperature at the inlet (K) Tin ) temperature at the inlet of the adsorber (K) Tout ) temperature at the outlet of the adsorber (K) TW ) temperature of the wall (K) u0 ) superficial velocity (m/s) V ) volume (m3) z ) coordinate in the direction of flow through the adsorber (m) L ) external porosity P ) particle porosity ϑ ) temperature (°C) κ ) polytropic index λ ) distance between two neighboring adsorption sites (m) λD ) heat dispersion coefficient (W/m/K) λW ) heat-transfer coefficient of the wall (W/m/K) µS ) tortuosity for surface diffusion νFl ) kinematic viscosity (m2/s) νP ) Poisson ratio FFl ) fluid density (kg/m3) FP ) wet particle density (kg/m3) FS ) dry solid density (kg/m3) FW ) density of the wall material (kg/m3) σFl ) surface tension of the liquid (N/m3) ω ) circular frequency (Hz) ωr ) resonance circular frequency (Hz)

Literature Cited (1) Bathen, D.; Breitbach, M. Adsorptionstechnik; Springer: Berlin, Germany, 2001. (2) Slejko, F. L., Ed. Adsorption Technology: A Step Approach to Process Evaluation; Marcel Dekker: New York, 1985. (3) Ba¨ssler, C. Influence of ultrasound on the adsorption and desorption behavior of polymeric adsorbents in watery media (in German). Gewa¨ sserschutz, Wasser, Abwasser 1997, 169, 1. (4) Ba¨ssler, C.; Reichert, J. K.; Fischwasser, K. Influence of ultrasound on the adsorption and desorption behavior of polymeric adsorbents in watery phase (in German). Vom Wasser 1996, 87, 15. (5) Ba¨ssler, C.; Reichert, J. K.; Fischwasser, K. Ultrasound for the regeneration of adsorbents (in German). Metalloberflaeche 1997, 51 (7), 511. (6) Rege, S. U.; Yang, R. T.; Cain, C. A. Desorption by Ultrasound. AIChE J. 1998, 44 (7), 1519. (7) Schueller, B. S.; Yang, R. T. Ultrasound enhanced adsorption and desorption of phenol on activated carbon and polymeric resin. Ind. Eng. Chem. Res. 2001, 40 (22), 4912. (8) Yu, S.; Gao, D.; Qin, Z. Ultrasonic desorptionsa new regeneration technology. Int. Sugar J. 2000, 102 (1216), 202. (9) Feng, D.; Aldrich, C. Elution of ion-exchange resins by use of ultrasonication. Hydrometallurgy 2000, 55 (2), 201. (10) Qin, W.; Yuan, Y. H.; Dai, Y. Y. Effect of ultrasound on desorption equilibrium. Chin. J. Chem. Eng. 2001, 9 (4), 427. (11) Chmutov, K. V.; Alekseev, N. G. Effect of irradiation by supersonic waves on the adsorption of fatty acids by finely porous carbons (in Russian). Nauk USSR 1949, 67, 321. (12) Qin, W.; Wang, D.; Dai, Y. Effect of ultrasound on resin adsorption dynamics of acetic acids. Qinghua Daxue Xuebao, Ziran Kexueban 2001, 41 (4/5), 28. (13) Li, X.-b.; Li, Z.; Xi, H.-x. Effects of Ultrasound on Adsorption Equilibrium of Phenol on NKA II Resin. J. Chem. Eng. Chin. Univ. 2001, 15 (4), 363. (14) Breitbach, M.; Bathen, D. Influence of ultrasound on adsorption processes. Ultrason. Sonochem. 2001, 8 (3), 277.

5646 Ind. Eng. Chem. Res., Vol. 42, No. 22, 2003 (15) Sontheimer, H.; Frick, B. R.; Fettig, J.; Ho¨rner, G.; Hubele, C.; Zimmer, G. Adsorptionsverfahren zur Wasserreinigung; DVGWForschungsstelle am Engler-Bunte-Institut der Universita¨t Karlsruhe (TH): Karlsruhe, Germany, 1985. (16) Ruthven, D. M. Principles of Adsorption and Adsorption Processes; John Wiley: New York, 1984. (17) Ma, Z.; Whitley, R. D.; Wang, N. H. L. Pore and Surface Diffusion in Multicomponent Adsorption and Liquid Chromatography Systems. AIChE J. 1996, 42 (5), 1244. (18) Huang, R.-T.; Chen, T.-L.; Weng, H.-S. Adsorption of o-Cresol and Benzoic Acid in an Adsorber Packed with an IonExchange Resin: A Comparative Study of Diffusional Models. Sep. Sci. Technol. 1994, 29 (15), 2019. (19) Miyahara, M.; Okazaki, M. Correlation of concentrationdependent surface diffusity in liquid-phase adsorption. J. Chem. Eng. Jpn. 1993, 5 (26), 510. (20) Bercˇicˇ, G.; Pintar, A.; Levec, J. Desorption of phenol from activated carbon by hot water regeneration. Desorption isotherm. Ind. Eng. Chem. Res. 1996, 35 (12), 4619. (21) Kuttruff, H. Physik und Technik des Ultraschalls; Hirzel: Stuttgart, Germany, 1988. (22) Millner, R. Ultraschalltechnik: Grundlagen und Anwendungen; Physik-Verlag: Weinheim, Germany, 1987. (23) Keil, F. J.; Swamy, K. M. Reactors for sonochemical engineering - present status. Rev. Chem. Eng. 1999, 15 (2), 85. (24) Malecki, I. Physical foundations of technical acoustics; Pergamon Press: Oxford, U.K., 1969. (25) Rozenberg, L. D. Physical Principles of Ultrasonic Technology, Vol. 2; Plenum Press: New York, 1973. (26) Kamenkovich, V. V.; Mednikov, E. P. Mechansims of the acoustic drying of capillary-porous materials. Sov. Phys.sAcoust. (Engl. Transl.) 1968, 13, 382. (27) Mason, T. J. Practical Sonochemistry: User’s guide to applications in chemistry and chemical engineering; Ellis Horwood: Chichester, U.K., 1991. (28) Young, F. R. Cavitation; McGraw-Hill: New York, 1989. (29) Leighton, T. G. Bubble population phenomena in acoustic cavitation. Ultrason. Sonochem. 1995, 2 (2), S123. (30) Apfel, R. E. Acoustic cavitation prediction. J. Acoust. Soc. Am. 1981, 69 (6), 1624.

(31) IUPAC (International Union of Pure and Applied Chemistry) Manual of symbols and terminology for physicochemical qualities and units, Appendix II, part I. Pure Appl. Chem. 1972, 31, 576. (32) Busnel, R. G.; Picard, D. Relationship between the wave length and the oxidation of potassium iodide by ultrasound (in French). C. R. Acad. Sci. 1952, 235, 1217. (33) Pe´trier, C.; Francony, A. Ultrasonic waste-water treatment: incidence of ultrasonic frequency on the rate of phenol and carbon tetrachloride degradation. Ultrason. Sonochem. 1997, 4, 295. (34) Dow Chemicals. Product Information DOWEX OPTIPORE L493 and V493; Dow Chemicals: Midland, MI, 1997; issue 3. (35) Breitbach, M.; Bathen, D.; Schmidt-Traub, H.; Ebener, H. Stability of Adsorber Resins under Mechanical Compression and Ultrasonication. Polym. Adv. Technol. 2002, 13 (5), 391. (36) Weast, C. R., Ed. CRC handbook of chemistry and physics, 67th ed.; CRC Press: Boca Raton, FL, 1986/7. (37) Stephens, H., Stephens, T., Eds. Solubilities of inorganic and organic compounds. Vol. 1: Binary systems. Part 1; Pergamon Press: Oxford, U.K., 1979. (38) Merck Index: http://cdroms.digibib-nrw.de/icafiles/MerckIndex.ica; Internet site, 11.2001. (39) Wakao, N.; Funazkri, T. Effect of fluid dispersion coefficients on particle-to-fluid mass transfer coefficients in packed beds. Chem. Eng. Sci. 1978, 33, 1375. (40) VDI (Verein deutscher Ingenieure), Ed. VDI-Wa¨ rmeatlas, 7th ed.; VDI-Verlag: Du¨sseldorf, Germany, 1994. (41) Breitbach, M. Wirkmechanismen von Ultraschall auf Adsorptions- und Desorptionsprozesse; VDI Verlag: Du¨sseldorf, Germany, 2003. (42) Oberbach, K. Kunststoffkennwerte fu¨ r Konstrukteure; Karl Hauser: Mu¨nchen, Germany, 1975.

Received for review April 21, 2003 Revised manuscript received August 7, 2003 Accepted August 25, 2003 IE030333F