7010
Ind. Eng. Chem. Res. 2005, 44, 7010-7018
Effect of Acoustic Standing Wave in a Bubble Column Joline M. Fan and Zhe Cui* Department of Chemical and Biomolecular Engineering, The Ohio State University, Columbus, Ohio 43210
Experiments using nickel magnetostrictive oscillators as transducers that generate acoustic standing waves in a bubble column were conducted in this study. The acoustic frequencies employed are 16 and 20 kHz with power up to 400 W. The column is operated at a constant room temperature, with the heat generated from acoustic excitation removed by the use of a water jacket. The study examines the fundamental behavior of initial bubble size, bubble rise velocity and movement of a swarm of mesobubbles (2-8 mm in diameter), gas-liquid mass transfer, and turbulence under the influence of the Bjerknes force in the acoustic field. The results indicate a smaller initial bubble size, a slower bubble rise velocity, and more concentrated bubble aggregates in the presence, rather than in the absence, of the acoustic field. Furthermore, the gas-liquid mass transfer rate and the liquid-phase turbulence are found to be significantly enhanced when an acoustic field is present. Introduction In a bubble column, a gas or a mixture of gases is introduced and rises in the form of bubbles through a continuous liquid phase. Because of their good heat and mass transfer characteristics, bubble columns are widely used in industry as reactors for chemical, biochemical, and petrochemical processing.1 Bubbles play an important role in gas-liquid process systems by inducing liquid agitation or providing gaseous reactants to the liquid medium. For either agitation or chemical reaction applications, the characteristics of bubble motion and bubble interfacial dynamics dictate the performance of the bubbling systems. Thus, the ability to control the motion of bubbles and their interfacial dynamics is important to enhancing the system performance. Studies have been conducted to view the effect of bubbles in the presence of external force fields such as a magnetic field2 or an acoustic field.3 In the presence of an acoustic standing wave in the liquid medium, small bubbles can be trapped because of the effect of the Bjerknes force at a pressure antinode of the acoustic standing wave when the equilibrium radius, R0, is smaller than the resonant radius, Rres; or these bubbles can be trapped at a node of the acoustic standing wave when R0 > Rres.4,5 The resonant radius, Rres, can be estimated by Rres ≈ 3/f for an air-water system,6 where f is the acoustic frequency and Rres is in units of meters. The bubble sizes used in these studies are mostly in the microbubble size range (100 µm-2 mm in diameter) and involve a single bubble or a low concentration of bubbles. For bubble column systems, bubbles are mainly in the mesobubble size range (2-8 mm in diameter) with a high bubble concentration. The fluid dynamic behavior of bubbles with the influence of the Bjerknes force under this bubbling condition has not been fully explored. Most acoustic applications for chemical reaction systems are in the ultrasonic frequency range.6,7 Under the high-frequency range (5-10 MHz), acoustic fields are used for diagnostic purposes. Under the mediumfrequency range (300 kHz-2 MHz), acoustic fields are used to yield sonochemical effects in which chemical * To whom correspondence should be addressed. Tel.: (614) 292-4935. Fax: (614) 292-3769. E-mail:
[email protected].
reactions are catalyzed via free radical generation under extreme temperatures and pressures through the formation, growth, and collapse of microbubbles formed by cavitation. Under the low-frequency range (20-100 kHz), ultrasonic fields are used for power ultrasound applications such as cutting and welding. This work presents a study of using a relatively lowfrequency acoustic standing wave (16 and 20 kHz) for the modulation of the motion of mesobubbles at a high concentration in a bubble column. The gas-liquid mass transfer in the acoustic field is examined under both reactive/nonreactive conditions. The Reynolds stress in the acoustic field is also probed. Experimental Studies The experiments are conducted in a cast acrylic acoustic assisted bubble column as shown in Figure 1. The total height of the bubble column is 80 cm, with an inside diameter of 10.26 cm. The acoustic transducer is mounted at the bottom and/or placed at the top as shown in Figure 1. Gas is introduced from a 4 mm i.d. sintered metal tube sparger placed at 2 cm above the bottom of the column. The liquid phase is operated under a batch condition. The acoustic transducers are made of a nickel magnetostrictive oscillator that generates acoustic waves at 16 and 20 kHz. The transducer is silver-brazed to a stainless steel plate of 3.2 mm thickness and 10 cm diameter, which vibrates like a diaphragm and transmits the acoustic wave when the transducer is powered. The power supplied to the acoustic transducer ranges up to 600 W, and the power conversion efficiency is ∼6%. While the magnitude of these vibrations is small, i.e., only one or two thousandths of an inch, strong accelerating forces are induced which compress and rarefy the liquid. The pressure fluctuation in the liquid phase due to the acoustic standing wave is measured using a B&K 8103 hydrophone. The sensitivity of the hydrophone is 25.4 µv/Pa. The distance from the boundary of the near-field and of the far-field to the surface of the transducers,6 Ls2/λ, where Ls is the radius of the transducer and λ is the acoustic wavelength, is 2.5 cm. The region within this distance from the transducer
10.1021/ie050125i CCC: $30.25 © 2005 American Chemical Society Published on Web 07/02/2005
Ind. Eng. Chem. Res., Vol. 44, No. 17, 2005 7011
Figure 2. Heating effect on temperature in the system with/ without the water jacket at Ug ) 1 cm/s (posi 1, 2, 3: 1 cm above the bottom transducer and 1, 3, and 5 cm from the wall, respectively; posi 4, 5, 6: 1 cm under the top transducer and 1, 3, and 5 cm from the wall, respectively; posi 7, 8, 9: 28.2 cm above the bottom transducer and 1, 3, and 5 cm from the wall, respectively).
Figure 1. Schematic diagram of the vertical acoustic gas-liquid column.
marks the acoustic near-field, which is unstable. Given the column height and the operating conditions of this study, the acoustic field in the bulk part of the bubble column is stable. When the acoustic wave is introduced to the bubble column, the liquid temperature increases because of acoustic heating effects. Thus, the present experiments are performed under controlled conditions in order to minimize such a heating effect on the flow and transport properties measured. In the controlled experiments, as shown in Figure 1, water cooling coils are jacketed around the column. The effect of the water jacketing on the temperature uniformity in the column can be assured by monitoring the temperature at various locations of the column. As shown in Figure 2, for the controlled experiments, the measured temperature is constant at 9 locations over the column including, those near and away from the transducers. For the noncontrolled experiments, in which the water cooling coils are not used, Figure 2 shows that, in the first 10 min, the temperature in the column rises by a maximum of 0.5 °C. However, the temperature rises under the controlled experiments are only 0.1 °C. The resulting changes of the physical properties of the fluids as the temperature increases from 23.5 °C to 23.6 °C are negligibly small. Thus, the effects of the temperature rise due to the acoustic heating in the present controlled experiments on the liquid density, the solubility of the gas, and the mass transfer coefficient are considered insignificant. When the acoustic wave is applied to the stationary liquid medium, natural convection would occur. Fur-
Figure 3. Effect of the acoustic-induced temperature rising on the axial liquid velocity at h ) 28.2 cm and 5 mm from the wall.
thermore, when the natural convection or buoyancy flow effect in the temperature-controlled system is examined, the Grashof number, Gr ) gR∆TL3/ν2 (where g is gravity, R is the thermal expansion coefficient, ∆T is the temperature difference, L is the length scale, and ν is the kinematic viscosity), is calculated to be ∼2.5 × 104, which is ,109, the value demarcating the laminar from the turbulent flows. The calculated value indicates the flow field induced by the natural convection due to the temperature rise in the present system is laminar. Thus, with agitated mesobubbles and nearly unchanged physical properties of the fluids as in the present experiments, the flow field would be dominated by the bubble-induced flow versus the natural convective flow when the acoustic field is present. To further elaborate this point, measurements are made of the liquid velocity using the LDV (laser Doppler velocimetry) in the column with and without bubble flows in the conditions with acoustic heating and without water cooling. Figure 3 shows the effect of the natural convection due to the acoustic-induced temperature rise on the time-averaged
7012
Ind. Eng. Chem. Res., Vol. 44, No. 17, 2005
Figure 4. Experimental setup with funnel for studying acoustic effect on levitated bubbles (Vl ) 64 cm3/s).
axial liquid velocity measured at 5 mm from the wall and at 28.2 cm above the distributor. There is no gas flow introduced during the first 3 min. It is seen that the liquid velocity due to the natural convection induced by the temperature rise is very small and is near constant. When the gas flow is introduced into the system thereafter, a steady increase in the temperature is observed. A sharp increase in the liquid velocity is observed along with a constant liquid velocity with the time variation. The figure clearly indicates the dominance of the rising-bubble-induced flow over the naturalconvection-induced flow and the negligible temperature effects on the liquid flow field. It is expected that, with water cooling or with temperature control, the effect of the natural convection can further be neglected. It is noted that, in the present study, with the exception of the measurements involving optical techniques or direct visualization, experiments are conducted under the temperature-controlled condition. Experiments are conducted in a nonreactive system and a reactive system. Nitrogen and oxygen-water and ozone-potassium iodide solution are used as gas-liquid phases, respectively. The gas-liquid mass transfer is measured using the oxygen desorption method.8 In this method, the liquid is first saturated with oxygen through air flow. The oxygen desorption takes place when the air flow is switched to the nitrogen flow. An optical fiber oxygen probe is utilized to measure the oxygen concentration in the liquid phase. A 470 nm light source is used to activate the fluorescent dye coated on the tip of the probe. When the fluorescent gel is excited, it emits a 590 nm wavelength light. As oxygen molecules collide with the excited fluorescent dye, energy is transferred to the oxygen molecule (fluorescence quenching). The extent of energy transfer is proportional to the collisionnumber frequency between the oxygen molecules and the fluorescent dye. Therefore, the light intensity can be translated into the partial pressure or the concentration of oxygen. A two-point calibration of the optical fiber oxygen probe is performed by applying atmospheric air and an aqueous solution of sodium dithionite. The
addition of sodium dithionite to water chemically removes the dissolved oxygen to generate a zero-oxygen environment. The superficial gas velocity used in this study varies up to 7.5 cm/s, covering both bubbling and turbulent flow regimes. In the reactive experiments, an ozone reaction is conducted. Ozone produced from an ozone generator (made by Ozomax) is introduced into a solution of potassium iodide with starch as an indicator. Ozone diffuses from the gas bubble to the liquid and instantaneously reacts with potassium iodide to form iodine, which turns to a dark purple color in the presence of starch. The rate of the color change depends on the rate of ozone transfer from the gas-liquid interface. Thus, the faster appearance of the dark purple color reflects the higher interfacial transfer rate. The effect of the acoustic field on the movement of a swarm of bubbles is studied through bubble levitation using an inverse funnel through which the liquid flows downward as shown in Figure 4. The visualization of the bubble-aggregation phenomenon is made by using a CCD (charge-coupled device) camera with a recording speed of 240 frames/sec. The rise velocity of a single bubble in an acoustic field is also studied. The effect of the acoustic field on the flow field and turbulence properties in the liquid phase is probed using an LDV system. The LDV technique is used in backscatter mode in the measurements. The liquid axial velocity profiles and normal stress profiles are obtained at 40 cm above the bottom of the bubble column. Results and Discussion Properties of Acoustic Standing Wave. When the acoustic transducers are placed at the top and bottom of the column, an acoustic standing wave can be developed between the two acoustic transducers, as shown in Figure 5. For an acoustic frequency of 16 kHz, the wavelength is 9.4 cm, with the distance between two pressure nodes at 4.7 cm. Thus, for an acoustic field distance of 56.4 cm between two transducers, which is
Ind. Eng. Chem. Res., Vol. 44, No. 17, 2005 7013
Figure 5. Image and schematic diagram of the acoustic standing wave field in the bubble column.
presence of an acoustic field of 16 kHz at 200 W (Figure 6b). Specifically, in this case, the velocity of the rising bubble in the acoustic field decreases by ∼20% versus that in the absence of the acoustic field. The initial bubble size from the gas distributor plays an important role in determining the gas holdup and gas-liquid mass transfer behavior in bubble columns. The effect of the acoustic standing wave on the bubble formation is examined experimentally in this study using a 1 mm i.d. stainless steel nozzle. In the presence of the acoustic standing wave, the initial bubble size from a single nozzle is seen to be smaller than that in the absence of the acoustic standing wave, as shown in Figure 7. In Figure 7b, it is indicated that the initial bubble size decreases with an increase in the acoustic intensity at a given gas flow rate. Little effect of the acoustic frequency is observed on the initial bubble size. The smaller initial bubble size can be explained by considering the balance of various forces that act on the bubble in its formation process as given below
FB + FM + Fp ) FD + Fσ + FBasset + FI,g
Figure 6. Effect of the acoustic wave on the rise velocity of a 6 mm bubble with line separation distance h ) 6.3 cm and bubble rising time t ) 333.3 ms (a) without acoustic field and (b) with acoustic field (16 kHz).
six times the acoustic wavelength in the liquid phase, a total of 12 standing waves can be established. The major forces that dictate the movement of bubbles are buoyancy force, drag force, and acoustic radiation force or Bjerknes force in the acoustic field. The Bjerknes force, Fp, is related to the pressure gradient by3
FP ) -Vb∇Ps
(1)
Ps ) ∆P cos(ωt) sin(kx)
(2)
where Vb is the volume of the bubble; Ps is liquid pressure around the bubble; and ∆P, ω, and k are the amplitude, the angular frequency, and the wavenumber of the driving acoustic pressure generated from the acoustic transducer, respectively. With the variation of Vb with Ps and that of ∇Ps with time, the values for Fp fluctuate between the positive and the negative, yielding a net deterrent effect on the rise velocity of bubbles. As shown in Figure 6, a single bubble of 6 mm diameter in water rises, reaching a marked line faster in the absence of an acoustic field (Figure 6a) than it does in the
(3)
where FB is the effective buoyancy force, FM is the gas momentum force, FD is liquid drag force, Fσ is the surface tension force, FBasset is the Basset force, and FI,g is the bubble inertial force. In these forces, FB and FM are upward forces, while FD, Fσ, FBasset, and FI,g are downward forces. The direction of Fp varies between upward and downward depending on if the bubble is exposed to the high- or low-pressure region of the acoustic field. However, it is noted that bubbles oscillate in the acoustic field in the same time scale as that of the acoustic pressure fluctuation, and a bubble is to release from the nozzle as soon as the force balance relationship is first established in the fluctuating pressure field. The pressure force is first established when the acoustic force directs upward, leading to a smaller initial bubble size compared to that in the absence of an acoustic field. The precise simulation to predict the initial bubble size is not within the scope of this study. Expressions for various forces except the acoustic Bjerknes force given in eq 1 are described in the models by Ramakrishan et al.9 and Fan et al.10 Simulations can, thus, be readily carried out. Furthermore, it is also shown that, in Figure 7a, in the presence of the acoustic field, bubbles aggregate and stay longer around the nozzle area while retaining their near-spherical shape. In the absence of the acoustic field, bubbles do not aggregate and they rise as soon as they disengage from the nozzle. Near the nozzle area, the deformation of the bubble takes place during the rise, while the bubbles are more spherical when the acoustic field is present. Figure 8 shows the pressure fluctuation signals measured under the conditions with and without an acoustic field. It is seen that the magnitude of the pressure fluctuation without an acoustic field, which is primarily induced by the motion of the bubbles, is significantly smaller than that with an acoustic field, signifying that the flow field is regulated by the acoustic standing waves. Figure 9 shows the axial profile of the pressure magnitude of the acoustic standing wave, measured using the hydrophone for two superficial gas velocities (0 and 0.375 cm/s). The wavelengths of the acoustic standing wave field for both velocities are measured to be ∼4.5 cm, which is consistent with the estimated wavelength, 4.7 cm, shown above. The mag-
7014
Ind. Eng. Chem. Res., Vol. 44, No. 17, 2005
Figure 7. Effect of the acoustic standing wave on the initial bubble size from a 1 mm single nozzle: (a) bubble formation images and (b) bubble size with different acoustic intensity.
nitude for the gas velocity of 0.375 cm/s is smaller than that for the gas velocity of 0 cm/s. Figure 10 shows the effect of the liquid flow and the further effect of the presence of gas bubbles on the pressure fluctuation in the bubble column. In Figure 10a, in the absence of gas bubbles, with an increase in the liquid velocity, the change of the pressure fluctuation behavior is negligible. However, when the gas bubbles are introduced, a significant effect is seen as shown in Figure 10b. With an increase in the gas velocity, the acoustic reflection by the increasingly concentrated bubbles increases. As a result, the sinusoidal pressure signals are somewhat distorted and the amplitudes of the fluctuation are reduced. However, the frequency of the pressure fluctuation is clearly identified as remaining unchanged at 16 kHz. Figure 11 shows images of the bubble swarm confined under the funnel by the downward liquid flow. Without an acoustic field, Figure 11a reveals the aggregation of bubbles near the axis area. Because the highest liquid velocity is located at the axis, a lift force due to the local pressure gradient induces the motion of bubbles toward
the axis. Figure 11b reveals a decrease in the elevation of levitation of bubble aggregates to the node area of the standing wave when an acoustic field of 16 kHz at 30 W is applied. Clearly, the behavior is a result of the acoustic Bjerknes force. Mass Transfer. In the mass transfer experiments for a nonreactive system, the oxygen flow rate varies from 37.5 to 562.5 cm3/s, corresponding to superficial gas velocities, Ug, of 0.5 to 7.5 cm/s. Figure 12a shows the oxygen concentration in the liquid phase when nitrogen is introduced into the system with and without an acoustic field. It is shown that, with an acoustic field, the oxygen concentration in the liquid phase decreases much faster than that without an acoustic field. It indicates a significant enhancement in the gas-liquid mass transfer rate in the presence of the acoustic field. Considering a completely well-stirred liquid medium in a gas-liquid system, the mass transfer balance yields
klaV(1 - g)(Cl - HCg) ) -
dCl V(1 - g) dt
(4)
Ind. Eng. Chem. Res., Vol. 44, No. 17, 2005 7015
Figure 8. Pressure fluctuation signals measured by hydrophone located at h ) 16.5 cm and 1 cm from the wall at 100 W with Ug ) 0.375 cm/s.
Figure 9. Axial profile of the magnitude of the pressure in the acoustic standing wave at 16 kHz and 100 W.
where kl is the gas-liquid mass transfer coefficient, a is the interfacial area per unit volume, Cl is the oxygen concentration in the liquid phase, H is the Henry’s law constant, Cg is the oxygen concentration in the gas phase, g is the gas holdup, and V is the volume of the liquid phase. Considering Cg to be negligible, for a given Cl, kla with an acoustic field and without an acoustic field can be related by
( ) ( )
dCl dt withacousticfield ≈ dCl (kla)withoutacousticfield dt withoutacousticfield (kla)withacousticfield
-
(5)
where dCl/dt is the slope of the oxygen concentration curve as described by Figure 12a. It is shown that the enhancement of the mass transfer property in terms of kla in the initial stage of the mass transfer process is ∼120% in the presence of the acoustic field under the present operating conditions. Further, eq 4 can be expressed by
Cl ) Cl0 exp[-klat]
(6)
where Cl0 is the initial oxygen concentration in the liquid phase. The mass transfer coefficient kla can be calculated as the slope of the -ln(Cl/Cl0) versus t plot,
Figure 10. Effects of liquid and gas flow on the pressure fluctuation: (a) effect of liquid velocity and (b) effect of superficial gas velocity.
as shown in Figure 11b. In the presence of the acoustic field, a good-fitted slope over an entire range of the mass transfer process gives the value of kla as 0.0060 s-1, which is 190% of that without the acoustic field, 0.0032 s-1, as shown in Figure 12b. The effect of the acoustic standing wave on the gasliquid mass transfer under different superficial gas velocities for both frequencies of 16 and 20 kHz and powers of 200 and 400 W is shown in Figure 13. The figure indicates that, at a given acoustic power, there is no significant difference in kla between the frequencies of 16 and 20 kHz. It is also seen that the gas-liquid mass transfer is enhanced with an increase in the acoustic power. Under the operating conditions of 200 W and 16 kHz, the kla increases by ∼100% in the presence of the acoustic field at a lower Ug (
