Ind. Eng. Chem. Res. 1997, 36, 3647-3655
3647
Experiments on Electrostatic Dispersion of Air in Water Won-Tae Shin and Sotira Yiacoumi School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0512
Costas Tsouris* Chemical Technology Division, Oak Ridge National Laboratory,† P.O. Box 2008, Oak Ridge, Tennessee 37831-6226
The objective of this work is to investigate bubble generation of air in water through electrified metal capillaries. Many important factors that affect the formation of bubbles, including capillary size, capillary tip configuration, electrode distance, and flow rate, are studied. It is found that the bubble size decreases with increasing applied voltage and decreasing airflow rate. A dimensional analysis of the system parameters is also pursued. The dimensionless numbers are correlated into an empirical model that can be used for the prediction of the bubble size as a function of the applied voltage and airflow rate. It is found that the bubble size decreases with decreasing Reynolds number and increasing Weber number. Three different modes of bubble formation are observed: a spraying mode obtained at low airflow rate and high applied voltage, a dripping mode observed at high flow rate and low applied voltage, and a mixed spraying-dripping mode. Introduction In many chemical and environmental applications, the use of bubble column reactors is common and often essential in such processes as absorption, coal liquefaction, catalytic slurry reactions, and bioreactions. The gas-liquid interfacial area depends on the shape of the column, the operating conditions, and the physical properties of liquid media (Shah et al., 1982). One means of increasing the gas-liquid interfacial area, as well as the gas holdup, is to decrease the bubble size. Smaller bubbles provide not only higher interfacial area but also longer residence times due to lower rising velocity. The surface area is more important in systems that are mass-transfer-limited, such as ozonation, while longer residence times are desirable in reaction-limited processes. Several methods of producing fine bubbles are currently in use, including electroflotation, dissolved air flotation, mechanical agitation, and bubble diffusers. Devices traditionally used to contact two phases make use of mechanical agitation with various types of impellers (e.g., Rushton et al., 1950a,b) and fluid pulsation through perforated plates installed in column contactors (e.g., Lo et al., 1983). Although such devices achieve some bubble size reduction, they represent inefficient use of energy because most of the energy is used for liquid agitation, not for an increase of the interfacial area. Another method of producing gasliquid dispersion is by electrostatic spraying. This method is investigated in the present work. Electric-field-driven separation processes have been known for many years. Common industrial applications are solid-solid separation in the mining industry, coalescence of water-in-oil emulsion in the petroleum industry, and cleaning of exhaust gases from solid particles in various technologies. Ptasinski and Kerkhof (1992) reported several advantages in direct utilization * To whom all correspondence should be addressed. Telephone: (423) 241-3246. Fax: (423) 574-6442. E-mail:
[email protected]. † Managed by Lockheed Martin Energy Research Corp. S0888-5885(97)00008-0 CCC: $14.00
of electrical energy, especially in multiphase systems. These advantages result from the fact that electrical energy supplied to the system interacts selectively with an interface and, to a lesser degree, with the bulk. This interaction may lead to increased rates of heat or mass transfer across an interface. Also, a superimposed field exerts electric body forces that contribute to the existing gravity force and can be used for levitation or stabilization of the dispersed phase. Until recently, only electrostatic spraying of conductive fluids, such as water, into nonconductive fluids, such as air or organic solvents, was successful. In many industrial processes, however, it is practical to have a conductive fluid as the continuous phase and a nonconductive fluid as the dispersed phase. These processes include extraction, distillation, stripping, flotation, and oxidation. Recently, Sato and co-workers (1979, 1980, 1993) and Ogata and co-workers (1979, 1980) conducted successful experiments in which nonconductive fluids were sprayed into relatively conductive fluids. The mechanism for electrostatic spraying has been elucidated by Tsouris et al. (1994), who showed that the two contrasting spraying systems obey electrohydrodynamic theory. In the course of electrostatic spraying of air into water, it was found that the formation of bubbles follows certain modes. Cloupeau and Prunet-Foch (1994) pioneered the classification of such modes in electrostatic spraying. Their classification is based on observations of electrostatic spraying experiments of liquids into air or vacuum. In their paper, the proposed terminology includes dripping, cone-jet, multijet, microdripping, ramified jet, simple jet (including fan configuration), and spindle (including harmonic spraying). Because the present work involves the contrasting (air-into-water) system, the terms cone-jet, multijet, simple jet, ramified jet, and spindle are not applicable. Experimental observations, however, suggest that the terms dripping, microdripping, and spraying modes can properly be used to describe the behavior of spraying air into water. Instead of microdripping, a “mixed” mode is used when referring to simultaneous formation of a bimodal distribution of bubble sizes, some of which are on the order © 1997 American Chemical Society
3648 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 Table 1. Capillary Sizes and Flow Rates Used in Experiments capillary outside diameter (in.)
a
Figure 1. Experimental assembly for electrostatic dispersion of air in water.
of 10 µm, while others are much larger. Thus, three terms, dripping, mixed dripping-spraying, and spraying modes, are proposed in the present study and used for the air-into-water system. Dripping occurs when relatively large bubbles are produced and released oneby-one. Spraying occurs when small bubbles are produced and many are released at the same time. Mixed dripping-spraying occurs when a bimodal distribution of large and small bubbles is produced. The main objective of this paper is to identify the conditions under which electrostatic spraying can produce bubbles of micron size. Toward this goal, experiments have been conducted using various geometrical configurations and operating conditions. System parameters that have been varied include capillary inside and outside diameters, distance between the capillary tip and insulation tip, and distance between electrodes. The operating conditions that have been examined are airflow rate and applied voltage. Based on the experimental results, a dimensional analysis has been pursued to provide an empirical model for the prediction of the bubble size. Materials and Methods Electrostatic spraying can be achieved using the experimental assembly shown in Figure 1. A cylindrical glass column of 70-cm height and 6-cm inside diameter was used. Air was introduced at the bottom of the column through the capillary electrode shown. Either the laboratory air supply or a syringe pump (Sage Instruments, Model 361) was used as the source of air. The laboratory air supply was used for the high flow rate (i.e., dripping mode experiments), while the syringe pump was used for the low flow rate (i.e., spraying mode experiments). The airflow rate was regulated using a flow meter (Cole-Parmer) having a maximum airflow rate of 100 mL/min. The high-voltage power supply (Spellman, SL 1200) was operated in a voltage range of 0-10 kV and a current range of 0-20 mA and provided digital readings of applied voltage and electrical current. Bubbles generated at the tip of the electrode capillary were videotaped by using a high-speed video camera (Xybion video camera and adapter, Model ESC-02-3) with a magnifying lens (Nikon, Nikkor 200 mm, f4D CD1F AF Micro-Nikkor) for the dripping mode (e.g., high airflow rate and low applied voltage) and a long-distance microscope (Questar, QM-100, 250×) for the spraying mode (e.g., low airflow rate and high applied voltage)
1/
32
1/
16
a
flow rate
inside diameter (in.) 0.005 0.01 0.02 0.005a 0.01a 0.02
mode dripping spraying
flow rate (mL/min) 10 15 20 1 2 5
Capillaries used in spraying mode experiments.
experiments. A video recorder (Panasonic, AG 1970 Proline), a monitor (Dotronix Inc., Dot-X), and an image printer (Mitsubishi, video copy processor P-78 U) were used to monitor and store the images of sprayed air bubbles. A sensitive pressure transducer (ENDEVCO Σ, Model 8510B-1) of a pressure range of 0-1 psig was used to obtain pressure measurements during electrostatic spraying. A light source was located behind the reactor to illuminate the tip of the capillary for better imaging. Deionized water of conductivity range between 0.3 and 0.5 µS/cm was used throughout this project. The bed height was filled with deionized water to a height of 50 cm. A close-up view of the electrode capillary, which was sheathed in a ceramic capillary for insulation, is shown in Figure 1. Insulation was needed to reduce electric current so that a strong electric field could be maintained at the very tip of the electrode capillary (Tsouris et al., 1995). The outside and inside diameters of the electrode capillaries were varied to determine their effect on the bubble size reduction. The sizes of the flat-tip electrode capillaries examined in this work (Figure 1) are provided in Table 1. Capillaries with different outside diameters (1/32 and 1/16 in.) and different inside diameters (0.005, 0.01, and 0.02 in.) were used. For the spraying mode experiments, two capillaries were used, with 1/16-in. outside diameter and 0.005- and 0.01-in. inside diameter. The electrode capillary was constructed of electropolished and electrolytically cut tubing obtained from Valco Instruments (tubing kits T10N5D, T10N10D, and T10N20D). Two sizes of ceramic capillaries (3/16- and 1/16-in. outside diameter) were used to fit the outside diameter of the electrode capillaries for better insulation and minimum current leakage. Airflow rate was changed for the two different flow regimes (e.g., dripping and spraying), as shown in Table 1. Three different flow rates were used for each regime. For the dripping mode experiment, flow rates of 10, 15, and 20 mL/min were used; for the spraying mode experiment, flow rates of 1, 2, and 5 mL/ min were used. Table 2 lists the physical properties of water and air. The conductivity of water was measured using a conductivity meter (Fisher Scientific, Inc., Model 09-3262). Other properties were obtained from the CRC Handbook of Chemistry and Physics (1990). Also in Table 2, the charge relaxation time, defined as the ratio of permittivity over conductivity, was calculated for air and water. The role of the charge relaxation time in electrostatic dispersion of air in water is discussed in the Experimental Results section. To measure the bubble size for both dripping and spraying mode experiments, the images of bubbles were first printed using the video copy processor. The diameters of the bubbles were then measured using a ruler for dripping mode experiments and image analysis for spraying mode experiments. In dripping mode
Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3649 Table 2. Physical Properties of Air and Water (25 °C) material
density (kg/m3)
kinematic viscosity (m2/s)
surface tension (N/m)
permittivity (C2/J‚m)
conductivity (S/m)
charge relaxation time (s)
air water
1.175 998.23
1.55 × 10-5 9.127 × 10-5
0.074
8.85 × 10-12 7.08 × 10-10
8.85 × 103 1.57 × 10-5
experiments, the mean diameter was obtained from vertical, horizontal, and diagonal diameter measurements for each bubble. This method provides reliable results for the dripping mode because the bubble sizes are relatively large and the number of daughter bubbles (satellite bubbles) is negligible. In these measurements, calibration was provided by the outside diameter of the ceramic insulation surrounding the metal capillary. For spraying mode experiments, computer-based image analysis equipment (Leica Cambridge Ltd., Quantimet 570 image analysis system) was used to provide the bubble size distribution. The image analysis equipment is composed of a control computer, an image monitor, an image processor, and a camera (Burns et al., 1997). In spraying mode experiments, bubble sizes are significantly smaller than those in the dripping mode. Over 200 bubbles were randomly selected; the mean diameter was then measured, and the Sauter diameter (d32) was calculated. The Sauter mean diameter, used as an important parameter in mass-transfer calculations, is expressed as N
d32 )
Figure 2. Typical bubble images for various values of applied voltage: electrode capillary inside diameter ) 0.01 in.; electrode capillary outside diameter ) 1/16 in.; ceramic capillary diameter ) 3/16 in.; flow rate ) 1 mL/min; applied voltage ) (a) 0 kV, (b) 2 kV, (c) 4 kV.
N
db 3/∑db 2 ∑ i)1 i)1 i
i
(1)
where db is the bubble diameter. Experimental Results The results of the experiments conducted in this work confirm that electrostatic spraying of air into water is as successful as that of water into air. These results were made possible by using the capillary configuration shown in Figure 1, which was designed for the conductive continuous phase. Sato et al. (1993) also suggested that the nozzle design is the most important factor for the atomization of highly insulating fluids and that success of the process is based on a nozzle geometry that creates a very intense nonuniform electric field in the vicinity of the nozzle tip. The bubble size reduction obtained in this work is shown in a series of pictures of air bubbles sprayed into distilled water at various levels of applied voltage (Figure 2). The size of bubbles issued from the capillary decreases as the applied voltage increases, a finding consistent with the results reported by other investigators, for example, Sato et al. (1993) and Tsouris et al. (1994, 1995). Effect of Capillary Inside Diameter on Bubble Size Reduction. Three different inside diameters are examined for both dripping and spraying mode experiments (see Table 1). The results are shown in Figures 3 and 4 for capillaries of 1/16- and 1/32-in. outside diameter, respectively, for dripping mode experiments and in Table 3 for spraying mode experiments. As shown in these figures, at an applied voltage of 0 V, the bubble diameter increases with increasing capillary inside diameter. This fact agrees with the bubble equation given by Mersmann (1962), which is obtained from a force balance. When there is no voltage applied,
Figure 3. Effect of capillary inside diameter on bubble size reduction: capillary outside diameter ) 1/16 in.; flow rate ) (a) 10 mL/min, (b) 20 mL/min.
the bubble equation is expressed as (Ptasinski et al., 1995):
[ x( )
3diσ + db ) Fwg
3diσ Fwg
2
]
15Q2di + g
1/3
(2)
where di is the capillary inside diameter; σ is the surface tension of water; Fw is the density of water; g is the gravity constant; and Q is the flow rate. In this equation, the bubble diameter is a function of the
3650 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997
Figure 4. Effect of capillary inside diameter on bubble size reduction: capillary outside diameter ) 1/32 in.; flow rate ) (a) 10 mL/min, (b) 20 mL/min. Table 3. Bubble Diameter Generated from Spraying Mode Experiments 6 kV Q (mL/min) db (µm) 1 2 5
dave d32 dave d32 dave d32
8 kV
di (in.) ) 0.005
di (in.) ) 0.01
di (in.) ) 0.005
di (in.) ) 0.01
33.1 73.5 39.0 121.2 41.3 161.6
29.0 82.0 31.9 76.4 37.0 112.3
31.4 80.8 36.0 87.5 36.2 99.9
37.0 80.1 31.4 73.3 35.5 95.9
capillary inside diameter and flow rate. A larger capillary inside diameter gives a larger bubble diameter, as shown by the experimental data in Figures 3 and 4. Equation 2 was also found to be quantitatively in agreement with the experimental data of Figures 3 and 4 when no voltage was applied. The effect of the capillary inside diameter is minimized when voltage is applied to the system, as can be seen in Figures 3 and 4. This occurs because the electric force that appears as a result of the applied voltage overcomes the forces caused by surface tension and drag. At applied voltages over 3 kV, the bubble sizes generated by each capillary have approximately the same size. For spraying mode experiments, the average bubble diameter, as well as the Sauter mean diameter defined by eq 1, is presented in Table 3. As seen in Table 3, the bubble sizes vary slightly and even display some fluctuations at applied voltages of 6 and 8 kV. At such high applied voltages, the effect of capillary inside diameter becomes negligible. This result is also discussed later in this paper. Some general observations can be made regarding bubble diameter produced by the spraying mode: (i) the bubble diameter increases slightly
Figure 5. Effect of capillary outside diameter on bubble formation: flow rate ) 10 mL/min; capillary inside diameter ) (a) 0.005 in., (b) 0.02 in.
with increasing airflow rate; (ii) the effect of capillary inside diameter on bubble size is insignificant; and (iii) the effect of applied voltage on bubble diameter is very small. In general, a higher applied voltage results in a slightly smaller bubble size; the large values of the Sauter mean diameter, d32, as compared to the average bubble diameter, dave, indicate broad size distributions for the bubble size, in contrast to the narrow size distribution in the dripping mode. Effect of Capillary Outside Diameter on Bubble Size Reduction. Figure 5 shows the effect of capillary outside diameter on bubble size reduction for the dripping mode. The electrode thickness is important because of the higher strength of the electric field for smaller-size electrodes at a given applied voltage. Figure 5 shows that the difference in bubble sizes is significant for two different outside-diameter capillaries; the smaller outside-diameter capillary (1/32-in.) gives smaller bubble sizes and reaches the system limit in electric current more rapidly than the larger outsidediameter capillary (1/16-in.). In all the experiments presented so far, the electric current is shown to follow one of two regimes: (i) a linear regime, in which the current increases linearly with applied voltage, followed by (ii) a nonlinear regime, in which the current increases exponentially with applied voltage as a result of corona discharge (Ptasinski et al., 1995). Effect of Flow Rate on Bubble Size Reduction. The experimental results in parts a and b of Figure 6 show that the effect of the flow rate is not significant for dripping mode experiments. This finding, however, should be applied only to the specific narrow range of flow rates that has been used in this work. The flow rate is included in the Reynolds number, which is used
Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3651
Figure 8. Effect of electrode distance on bubble size reduction: capillary inside diameter ) 0.01 in.; flow rate ) 10 mL/min.
Figure 6. Effect of flow rate on bubble size reduction: capillary inside diameter ) 0.01 in.; outside diameter ) (a) 1/16 in., (b) 1/32 in.
Figure 7. Effect of three capillary-tip configurations on bubble size reduction: capillary inside diameter ) 0.01 in.; flow rate ) 10 mL/min.
to determine the bubble formation mode. Experimental observations indicated that there is a specific flow rate below which a spraying mode can be obtained. This subject is discussed later in this section. Effect of Capillary Geometry on Bubble Size Reduction. Figure 7 illustrates the effects on bubble size and current of three different configurations of the metal capillary tip distance from the tip of the insulation tube. In the first configuration, the distance between the two tips is zero; in the second configuration, the capillary tip is 1 mm inside the ceramic tip (-1 mm); and in the third configuration, the capillary tip is extended 1 mm outside the ceramic tip (+1 mm). For
the case of the protruded (+1 mm) capillary tip, bubble size reduction can be achieved; however, the consumption of current is very high. For the case of the flat and recessed (-1 mm) tip configurations, the bubble size reduction is about the same; however, the energy consumption is slightly lower in the latter case. Thus, the recessed capillary tip configuration gives better results in both bubble size reduction and energy consumption. Tsouris et al. (1995) showed similar results for the effect of capillary tip distance. Up to 2 kV of applied voltage, however, the bubble size is very large compared with other cases because the inside diameter, di, is now that of the ceramic tube, which is much larger than the inside diameter of the metal capillary tube, and, as eq 2 predicts, the bubble size increases rapidly with di. This effect can be considered a disadvantage of the recessed-tip capillary. Effect of Electrode Distance on Bubble Size Reduction. In this work, deionized water of electrical conductivity between 0.3 and 0.5 µS/cm was used. If a perfect conductive fluid were used, the fluid would be at an equipotential state regardless of the location of the immersed ground electrode. According to Tsouris et al. (1995), however, a small variation in the strength of the electric field is expected because of the everpresent finite resistance of the “conductive fluid”, which is not very conductive in this case. Two electrode distances, 50 and 5 cm, were used in this work. Figure 8 shows that electrode distance has an effect on bubble size reduction. The bubble size becomes smaller at lower applied voltage for the 5-cm electrode distance than for the 50-cm distance. Although the 5-cm electrode distance provides smaller bubble size than the 50-cm distance, the power consumption is higher. It has been found that approximately the same amount of energy (voltage × current) is required by these two configurations to produce the same size bubbles. Dripping and Spraying Modes. The distinction of three modes of electrostatic spraying of air into water (e.g., dripping, mixed dripping-spraying, and spraying modes) is made here for the first time. Based on observations during the experiments, the Reynolds number (Re) and the modified Weber number (We) are used to distinguish between the three modes. From the analysis of the system parameters that affect bubble formation, it is found that the Reynolds number (inertial over viscous forces) and the modified Weber number (destructive over cohesive forces) play significant roles in electrostatic spraying of air into water. These two
3652 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997
Figure 9. Classification of three modes of bubble generation using Reynolds and Weber numbers.
numbers were used to develop an empirical model and were defined as follows:
QaFa Qa ) diµa diνa
(3)
diaE2 + u2diFa σ
(4)
Re ) and
We )
where subscript a denotes air, νa is the kinematic viscosity, E is the electric field (applied voltage/electrode distance), a is the permittivity, and u is the airflow velocity. The modified Weber number is simply the summation of the electric Bond number and the original Weber number. Figure 9 shows the three regimes that can be observed in electrostatic spraying of air into water. At a relatively low Reynolds number (below 20), spraying mode can be achieved with a relatively low Weber number (around 10-15). If the Reynolds number is increased, the Weber number must be increased to achieve a spraying mode. This observation implies that, for a higher flow rate, more input power is needed to obtain a spraying mode. At higher flow rates (i.e., above 10 mL/min), a pure spraying mode was not observed. This occurs because the system limit in electrical current is reached before a spraying mode is obtained. Thus, a pure spraying mode can be obtained using relatively low flow rate, or a Reynolds number below 20. The occurrence of dripping and spraying modes of bubble formation under electric fields can be explained in terms of the charge relaxation time. If the bubbleformation characteristic time is assumed to be the inverse of the frequency of bubble formation, then it should be much smaller than 1 s. If, for example, we use 100-µm bubbles as the upper end of the size distributions shown in Figure 10, we can calculate the characteristic time of bubble formation to be 3 × 10-5 s for 1 mL/min and 1.57 × 10-5 s for 2 mL/min. These characteristic times are of the same order as the charge relaxation time of water shown in Table 2. A significant increase in the airflow rate will result in a smaller characteristic time of the bubble formation, leading to the formation of some large bubbles which are observed experimentally. Thus, the following can be concluded: (i) Air spraying in water is due to charge action in water under the influence of an electric field, since the bubbleformation characteristic time and the charge relaxation
Figure 10. Cumulative bubble size distributions obtained from spraying mode experiments: capillary inside diameter ) 0.005 in.; capillary outside diameter ) 1/16 in.; flow rate ) (a) 1, 2, and 5 mL/min; applied voltage ) (a) 6 kV, (b) 6 and 8 kV.
time in water are of the same order of magnitude (,1 s), while the charge relaxation time in air is .1 s. (ii) As the airflow rate is increased, the bubble-formation characteristic time is decreased and, as a result, the mode of bubble formation changes from spraying to dripping. Figure 10 shows the cumulative size distributions for the spraying mode with different flow rates and input powers. These measurements reveal that the bubble size in the spraying mode cannot be reduced greatly by applying higher input power (Figure 10b). More than 80% of the bubbles have diameters less than 50 µm, but the greater number of large bubbles is produced at the higher airflow rate (5 mL/min), as can be seen in Figure 10a. This indicates that a practical limit in input power exists for the spraying mode. To avoid excess power consumption, the spraying mode should be operated at 6 kV of applied voltage. In general, it was found that, at a low airflow rate (on the order of 1 mL/min), the spraying mode occurred above 3-4 kV of applied voltage, while at high airflow rates (beyond 10 mL/min), a much higher applied voltage was needed. As the applied voltage is increased, however, the electric current increases exponentially, indicating that other electrostatic phenomena, such as corona discharge, have occurred. Under these conditions, enhanced power consumption results in undesirable phenomena, including electrochemical reactions and temperature increase, which lead to interruption of the electrostatic spraying process. Thus, above a certain airflow rate, the spraying mode may not be reached. A criterion was defined as the bubble surface area produced per specified period of time and per specified amount of power consumed. This criterion was calculated for both dripping and spraying modes under various operating conditions. Surprisingly, these cal-
Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3653
Figure 11. Measurements of pressure and current during electrostatic dispersion of air into water. Table 4. Surface Area Produced per Energy Consumed per Time mode
dripping
spraying
flow rate (mL/min) 10 15 20 1 2 5 area/power‚h 0.548 0.764 0.525 0.190 0.416 1.336
culations showed that the surface area of bubbles produced in the dripping mode is comparable to that produced in the spraying mode when equal amounts of energy are consumed, as shown in Table 4. Only at the limits of the spraying mode (i.e., at the highest possible airflow rate) was the surface area larger than that produced at higher flow rates in the dripping mode. This finding suggests that a dripping-mode operation may be more economical in some systems, while the opposite may be true in others. For instance, an ozonation reaction that is mass-transfer-limited should be favored by a spraying mode, which produces smaller bubbles, rather than by a dripping mode. Pressure Measurements. According to Tsouris et al. (1994, 1995), the electric stress on the interface, which causes electrostatic spraying, results in an electric force with direction from the conductive to the nonconductive fluid. Thus, in the case of air spraying into water, there should be an electric force acting inward with respect to the gas-liquid interface or the meniscus at the tip of the capillary. This electric force has a significant effect on pressure inside the meniscus, causing a pressure increase. The measurements in this work, however, reveal that the pressure behavior inside the capillary is slightly different from that reported by Tsouris et al. (1994, 1995). Figure 11 shows the pressure behavior inside the capillary versus applied voltage. The pressure increases initially, reaching a maximum at approximately 6 kV, and then decreases as the voltage is increased further. The explanation for this pressure drop at higher applied voltages is the electrohydrodynamic (EHD) flow generated near the tip of the capillary (Ogata et al., 1979, 1980). Ptasinski et al. (1995) reported similar results, but the pressure drop was attributed to corona discharge that occurred in their experiments. This phenomenon has not been observed during the experiments of this work. From these experimental results and the reported mechanisms, it is concluded that the pressure increase at the first stage of applied voltage is caused by the electric stress and that the pressure drop at higher applied voltage is caused by the EHD flow component near the tip of the capillary. It should be noted, however, that the pressure variations shown in Figure 11 are on the order of a few centimeters of water, which
by itself cannot cause spraying in the absence of an electric field. This result can easily be shown by increasing the pressure inside a capillary in the absence of a field. Thus, it is the electric stress at the gas-liquid interface that causes electrostatic spraying rather than the EHD flow. Prediction of Bubble Size. A dimensional analysis has been developed in this work. This approach is applied for the dripping mode. The system parameters that affect the formation of bubble are as follows: db, di, do, νa, νw, g, F, E, a, σ, Qa. The subscripts a and w imply air and water, respectively, and do is the capillary outside diameter. These system parameters are then used in Buckingham’s π theorem to obtain dimensionless numbers. The resulting important dimensionless numbers are the Reynolds number, the modified Weber number, the capillary diameter ratio, and the dimensionless bubble diameter. The Reynolds number is defined by eq 3. The electric Bond number is defined as electric force over surface tension force:
Be ) diaE2/σ
(5)
This electric Bond number is added to the Weber number to compensate for the situation in which there is no electric field (Pamperin et al., 1995). The modified Weber number is obtained by eq 4. The capillary diameter ratio (the ratio of outside diameter to inside diameter) is defined as
Cr ) do/di
(6)
The dimensionless bubble diameter is defined as the ratio of bubble diameter to capillary inside diameter:
Y ) db/di
(7)
The dimensionless numbers were correlated as follows:
Y ) RReβWeγCrγ
(8)
where the model constants R, β, γ, and δ can be obtained from experimental data using a nonlinear optimization technique. In this research, the SQP (Sequential Quadratic Program; Biegler, 1985) computer program was used to minimize the difference between the correlation and experimental data. From the optimization of experimental data, the following empirical equation was obtained:
Y ) 0.25Re0.4We-0.28Cr0.75
(9)
This empirical model includes a relative error of 21% with the experimental data. Note that the dimensionless bubble diameter is proportional to the Reynolds number and to the capillary diameter ratio and inversely proportional to the Weber number, which implies that the bubble size can be reduced by maintaining a small Reynolds number and a large Weber number. This is an expected result, since the Reynolds number decreases with decreasing airflow rate and the Weber number increases with increasing applied voltage. Figure 12 shows one sample bubble size prediction obtained from eq 9, while all data are shown in Figure 13. If the correlation were exact, data points would lie on the diagonal line in Figure 13. Although most of the data points lie close to the diagonal line, some are located far from it, indicating that important parameters may have been left out of the correlation. Future
3654 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997
Figure 12. Comparison of the correlation with experimental data: capillary inside diameter ) 0.01 in.; capillary outside diameter ) 1/16 in.; flow rate ) 10 mL/min.
is introduced into a nonconductive fluid, the electric force acts outward, while in the inverse case of a nonconductive fluid, such as air, introduced into a conductive fluid, such as water, the electric force acts inward. Thus, the pressure increase at low applied voltage during electrostatic spraying of air in water is due to the inward electric force, while the pressure drop at higher applied voltage is due to the EHD flow near the tip of the capillary electrode. However, the pressure variations alone are incapable of causing spraying in the absence of an electric field, leading to the conclusion that it is the electric stress at the gas-liquid interface that causes electrostatic spraying rather than the EHD flow. An empirical model has been developed to provide the bubble size as a function of applied voltage. The relative error of the correlation is 21%. Finally, it was found that under certain conditions either dripping mode or spraying mode operations may be more efficient in generating interfacial area. Acknowledgment
Figure 13. Accuracy of the correlation developed in this work for the size of air bubbles formed in water by electrostatic means.
work should focus on improving the correlation and developing a physically sound theoretical approach. Summary and Conclusions Microbubbles can effectively be generated in water using electric fields. Air bubble dispersion by electric fields in water can be classified into dripping, mixed, and spraying modes. In the dripping mode, the effects of capillary inside and outside diameters and flow rate are less significant compared with the effects of applied voltage. Also, in the dripping mode, a short distance between the electrodes gives better results in terms of bubble size versus applied voltage because of the relatively low conductivity of deionized water. This result complements previously reported data (Tsouris et al., 1995), which were obtained at a short range of applied voltage and electrode distance. It was also found that the capillary tip distance should either remain flat or be receded inside of an insulating capillary to avoid significant current leakage. A pure spraying mode can be obtained at a Reynolds number of below 20 and a Weber number of over 10-15. In the spraying mode and at applied voltages of 6-8 kV, microbubbles of sizes ranging between 30 and 80 µm can be easily generated. The various modes of bubble formation are connected to the relation between the charge relaxation time and the bubble-formation characteristic time. If the charge relaxation time is smaller than the bubble-formation time, then the spraying mode occurs. When the airflow rate is increased, the bubbleformation characteristic time becomes comparable to the charge relaxation time, leading to a mixed drippingspraying mode. In the case in which the airflow rate is significantly increased, the dripping mode occurs. Pressure measurements gave insight into the mechanism of electrostatic spraying. When a conductive fluid
This research is sponsored by the Division of Chemical Sciences, Office of Basic Energy Sciences, and the Environmental Management Science Program (EMSP), U.S. Department of Energy, under Contract DE-AC0596OR22464 with Lockheed Martin Energy Research Corp., and the School of Civil and Environmental Engineering of the Georgia Institute of Technology (GT). The authors are also thankful to Professor J. David Frost (GT) for the use of his image analysis equipment, Susan E. Burns (GT) for her assistance in measuring the bubble size, Merry Spurrier (ORNL) for her assistance in the experiments, and Marsha K. Savage (ORNL) for editing the manuscript. Finally, the authors thank the reviewers for their comments which improved the presentation of the paper. Literature Cited Biegler, L. T. Improved Infeasible Path Optimization for Sequential Modular Simulators. I. The Interface. Comput. Chem. Eng. 1985, 9, 245. Burns, S. E.; Yiacoumi, S.; Tsouris, C. Microbubble Generation for Environmental and Industrial Separations. Sep. Purif. Technol. 1997, in press. Cloupeau, N.; Prunet-Foch, B. Electrohydrodynamic Spraying Functioning Modes: A Critical Review. J. Aerosol Sci. 1994, 25, 1021. CRC Handbook of Chemistry and Physics, 70th ed.; Weast, R. C., Lide, D. R., Astle, M. J., Beyer, W. H., Eds.; CRC Press, Inc.: Boca Raton, FL, 1990. Lo, T. C.; Baird, M. H. I.; Hanson, C., Eds. Handbook of Solvent Extraction; Wiley: New York, 1983. Mersmann, A. Druckverlust und Schaumho¨hen von Gasdurchstro¨ten Flu¨ssigkeitsschichten auf Siebbo¨den. VDI-Forschungsh. 1962, 491, Ausgabe B, Band 28. Ogata, S.; Yoshida, T.; Shinohara, H. Small Air Bubble Formation in Insulating Liquids Under Strong Nonuniform Electric Fields. Jpn. J. Appl. Phys. 1979, 18, 411. Ogata, S.; Tan, K.; Nishijima, K.; Chang, J.-S. Small Bubble Formation by Using Strong Nonuniform Electric Field. IEEE Trans. Ind. Appl. 1980, 16, 766. Pamperin, O.; Rath, H.-J. Influence of Buoyancy on Bubble Formation at Submerged Orifices. Chem. Eng. Sci. 1995, 50, 3009. Ptasinski, K. J.; Kerkhof, P. J. A. M. Electric Field Driven Separations: Phenomena and Applications. Sep. Sci. Technol. 1992, 27, 995. Ptasinski, K. J.; Geurts, F. L. S.; Staring, A. J. P. M.; van Heesch, E. J. M.; Kerkhof, P. J. A. M. Formation of Small Bubbles in an Electric Field. Sep. Sci. Technol. 1995, 30, 2127.
Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3655 Rushton, J. H.; Costich, E. W.; Everett, H. J. Power Characteristics of Mixing Impellers. Part I. Chem. Eng. Prog. 1950a, 46, 395. Rushton, J. H.; Costich, E. W.; Everett, H. J. Power Characteristics of Mixing Impellers. Part II. Chem. Eng. Prog. 1950b, 46, 467. Sato, M. Cloudy Bubble Formation in a Strong Nonuniform Electric Field. J. Electrostat. 1980, 8, 285. Sato, M.; Kuroda, M.; Sakai, T. Effect of Electrostatics on Bubble Formation. Kagaku Kogaku Ronbunshu 1979, 5, 380. Sato, M.; Takano, Y.; Kuroda, M.; Sakai, T. A New Cloudy-Bubble Tracer Generated Under Electrostatic Field. J. Chem. Eng. Jpn. 1980, 13, 326. Sato, M.; Saito, M.; Hatori, T. Emulsification and Size Control of Insulating and/or Viscous Liquids in Liquid-Liquid Systems by Electrostatic Dispersion. J. Colloid Interface Sci. 1993, 156, 504. Shah, Y. T.; Kelkar, B. G.; Godbole, S. P.; Deckwer, W.-D. Design Parameters Estimations for Bubble Column Reactors. AIChE J. 1982, 28, 353.
Tsouris, C.; DePaoli, D. W.; Feng, J. Q.; Basaran, O. A.; Scott, T. C. Electrostatic Spraying of Nonconductive Fluids into Conductive Fluids. AIChE J. 1994, 40, 1920. Tsouris, C.; DePaoli, D. W.; Feng, J. Q.; Scott, T. C. Experimental Investigation of Electrostatic Dispersion of Nonconductive Fluids into Conductive Fluids. Ind. Eng. Chem. Res. 1995, 34, 1394.
Received for review January 6, 1997 Revised manuscript received June 2, 1997 Accepted June 11, 1997X IE970008Q
X Abstract published in Advance ACS Abstracts, August 15, 1997.
