929
Ind. Eng. Chem. Res. 1994,33, 929-933
Energy Effects in Bubble Nucleation Melbourne L. Jackson Department of Chemical Engineering, University of Idaho, Moscow, Idaho 83843
The size and number of bubbles produced by the desorption of supersaturated gases from water are shown to be a primary function of the energy available for bubble formation in a flowing system; this energy is that not dissipated in turbulence and friction. The number of nucleation sites is greatly increased when certain impurities are present, particularly surface-active agents. Low saturation pressures can produce very large numbers of very small bubbles when added energy is provided for discharge. High gas concentrations produce excess large bubbles which pass up rapidly through the much slower rising bubble mass. A combination of low saturation pressure followed by higher pressure for flow, such as by liquid pumping, results in bubble characteristics which can be controlled for applications. PRESSURE GAGE
Introduction Bubble size and number produced by desorption are important considerations for certain industrial processes such as flotation, gas stripping, and some types of chemical reaction and mass transfer. This study was undertaken to observe the relationship between the pressures applied and the characteristics of the bubbles formed from supersaturated solutions. The desorption of a gas from water by slow pressure release occurs only slowly by diffusion at a water surface and from nucleation points on a wall. In sharp contrast, a rapid drop in pressure in a flowing system can produce immediate bubble formation in copious quantities which completely fill a receiving vessel. Clift et al. (1978)termed the process effervescence and considered it to be similar to the process of cavitation and a process of heterogeneous nucleation. An early paper by Dean (1944) proposed that bubble nucleation was the result of turbulent flow and vortex formation. Also, mechanical shock such as a blow on the wall of an open container was found to produce bubble swarms in supersaturated liquids. Although pure liquids have high tensile strengths, Knapp (1958) concluded that "weak spots" occur in ordinary water and that "free gas" was the most likely cause of cavity formation. Baasiri and Tullis (1983) observed separation in a liquid column as a function of the amount of dissolved air, the presence or absence of free air, and agitation. When free air was absent, no dissolved air was released until the system pressure fell to the vapor pressure of the liquid. Keller (1972)used a light scattering method to determine the presence of bubble nuclei in tap water. Fresh water showed a larger number of bubbles formed upon cavitation as compared to filtered water. Bubble nuclei were considered to persist only as the result of contamination by "solids or organic substances". Holl (1970) reviewed studies on cavitation nuclei as resulting from the presence of gas bubbles, gas in crevices of solids, or gas bubbles with an organic skin. A theory that microscopic bubbles covered by an organic skin prevented bubbles from dissolving is discussed but discounted as a likely source of cavitation nuclei. Jackson et al. (1975) showed that the presence of a surfactant stabilized either large or small bubbles as initially formed. Coalescence was minimized or eliminated with little apparent size change during rise up a 23-m column.
Experimental Methods The apparatus developed is shown in Figure 1and was designed to provide accurate saturation conditions in a 0888-588519412633-0929$04.50/0
OFFGAS A
FILL AND SHUT-OFF A
T Figure 1. Pressure and flotation columns (levels at end of filling).
pressure column with transfer to a flotation column for bubble formation. The transfer pressure ( p d ) can be set either above or below the saturation pressure (P).Both are given as gauge pressure because both desorption and transfer are to barometric pressure. The saturation column was a glass pipe 1.2 m high with a 7.6-cm inside diameter mounted on a tee with bottom ports for gas inlet and liquid withdrawal. A gas to be saturated enters the bottom of the column through a ceramic ball and flows continuously with pressure controlled by a regulator. The flow rate is limited by a flowmeter. Valves permit alternate passage of the gas to the top of the column to force liquid to the second column for gas desorption and bubble flotation. This column was also 7.6 cm in inside diameter but only 0.9 m high. Transfer of liquid was through 0.9 m of 0.65cm-i.d. plastic tubing and a 'Iz-in. nominal size quickopening ball valve and piping to the bottom of the flotation column. The rate of filling to a constant level in the empty flotation column was controlled by opening the ball valve to a preset fixed stop. The filling time was recorded and checked for consistency in succesivedeterminations. The 0 1994 American Chemical Society
930 Ind. Eng. Chem. Res., Vol. 33, No. 4, 1994
water level in each column at the end of filling is indicated in Figure 1. Gases were introduced through one or two flowmeters, the latter operating at the same pressure. Gases were supplied from high-pressure tanks with most determinations made at measured temperatures from 22 to 24 "C. Most observations were for use of nitrogen gas. Initial observations indicated that a number of conditions affected the size and number of bubbles produced including column filling rate, ball valve opening, dissolved gas concentration, applied transfer pressure, and presence of contaminants. Thus, many combinations of variables are possible and observations were limited to a few fixed values to demonstrate the effect of energy availability on bubble formation. Desorption from strictly clean water resulted in only a few relatively large bubbles formed which rose rapidly and were difficult to evaluate. In contrast, incomplete rinsing of a column after cleaning resulted in numerous and very small bubbles formed which rose slowly. The contaminants appeared to provide nucleation sites and reduce the energy necessary for nucleation. Because industrial waters may contain a variety of dissolved substances, including detergents, most runs were made with 1-5 mg/L commercial detergent added (Woolite, alkylaryl sodium sulfate). Unsteady-state transfer of oxygen from air through the ball diffuser at atmospheric pressure required 4 min to attain 98% saturation as measured by a YSI Clark type oxygen meter. At P = 400 kPa the corresponding time required was 9 min. In contrast, a coarse bubble system required 14 and 33 min for this near approach to saturation. The saturation time used was 10 min or more to provide a known concentration of dissolved gas. For most conditions imposed, very small bubbles form rapidly as a dense mass, white in appearance, which a light beam does not penetrate. Back lighting showedbetter demarcation of the rising bubble mass in comparison to front or side lighting which emphasized the fine, less numerous residual bubbles. A short period was required for nucleation and bubble growth before clear liquid appeared at the bottom of the column. Additional desorption and bubble growth occurred to a small extent during rise. A gradation of sizes resulted at extended rise times, and some thinning of the mass occurred at the upper rise levels. Bubbles were characterized as those observed on initial rise at the lower levels, and the time of rise was measured as the bubble mass passed between two marks. The filling time of the flotation column was usually 15 % or less of the bubble rise time. This appeared to have a negligible effect on bubble characteristics as column contents were well mixed during filling. An estimate of bubble size was made by assuming the applicability of Stokes law for the free rise of bubbles in the viscous region. This is an approximation because of the close packing of the bubbles. The "equivalent bubble diameter" was estimated by d = 176/(t,)1/2for gas bubbles in water at 23 "C where rise time, t,, is in minutes per meter and the size, d, is in microns (pm). Most observations were for rise times longer than 2 minlm which corresponds to a Reynolds number of unity, the viscous limit. The corresponding size would be 125 pm as the largest. The smallest sizes were about 45 pm with a rise time of 14 min/m. Clift et al. (1978) state that the presence of a surfactant does not affect bubble rise characteristics for sizes in the viscous region where bubbles act as solid spheres.
4
I
L
I
Pd=414 kPa
I
Pd=138 kPa gauge
I
** Range of filling times at fixed valve position % 5 mg/L Woolite
.
4
Clean Water
P = 276 kPa
.-C E
Pd = 276 kPa
I $
E
1
Fixed ball valve position SEblected
;
I
4L
:
/
2c
/
0 0
0.25
0.5
0.75
1
1.25
1.5
Filling Time, min/m
Figure 2. Filling times for several valve positions.
Formation of Bubbles The effect of the energy available for nucleation can be demonstrated by observations at selected fixed conditions. The pressure energy for transfer of the supersaturated liquid to flotation is expended in turbulent friction, surface formation in overcoming interfacial tension, expansion of desorbed gas to barometric pressure, and nucleation. Several points are shown in Figure 2 for bubbles formed from clean water. The bubbles are relatively large, fast rising, and small in number with light penetrating the bubble mass. Rise patterns were difficult to follow over a range of saturation and transfer pressures. In contrast, the addition of a small concentration of the detergent increased rise times by a factor of 3 for the same pressure conditions. The corresponding bubble sizes were calculated to be 131 pm for clean water and 74 pm for that with the detergent, both at PIP, = 2761276;the bubble size for P/Pd = 276/414 was smaller a t 53 pm for the added transfer energy. The addition of the detergent appears to provide nucleation sites and to reduce the energy required for bubble formation. The line in Figure 2 is for the saturation and transfer pressures constant at the same value with detergent added. It shows the increase in rise times, and hence the reduction in size of bubbles formed, as the valve controlling the flow rate is reduced from open to nearly closed. Energy losses from turbulence are large at short filling times, but these decrease rapidly as the orifice becomes smaller and the flow rate less. The energy for bubble formation is thus increased as is evident from the smaller and more numerous bubbles produced. A fixed valve position was selected, as shown in Figure 2, for most succeeding runs. Use of transfer pressures from 414 to 138 kPa at the fixed valve position gave filling times from 0.56 to 0.90 minlm, but bubble rise times changed only little. However, an increase in the transfer pressure markedly increased the energy available for bubble formation. For example, increasing the transfer pressure from 276 to 414 kPa almost tripled the rise time from 5.4 to 13.2 min/m. This effect of available energy for bubble formation is most significant. Takahashi et al. (1969) desorbed air from water through very small orifices at pressures of 100-400 kPa. Bubble
Ind. Eng. Chem. Res., Vol. 33, No. 4,1994 931 14
16
* Pd
= 276 kPa gauge
* Pd
= P gauge
121. 12
10110
I + I mg/L Woolite ~
14-'
5 mg/L Woolite added
Clean Water
+
5 mg/L Woolite added
Fixed valve position
12-
. E
P = 276 kPa gauge
C
/ E
/
/
U
,,
4
0-
w
/i
2i
"
0
100 I?
200
4 I
21 300
400
Saturation Pressure, kPa gauge
Figure 3. Effect of transfer pressure,Pd,for arangeof gas saturations.
distributions were from 30 to 180 pm with sizes smaller and numbers larger as pressure was increased. The present study with detergent added, a large orifice, and rapid transfer gave a bubble mass which appeared relatively uniform as to size distribution.
SaturatiodTransfer Pressure Effects Saturation and transfer pressures have independent effects on bubble size and numbers produced. No previous reports were found which distinguished between the two pressure conditions. Some studies used coarse bubble aerators and only short exposure times which would result in only partial saturation. The solid line of Figure 3 is for rise times where the saturation and transfer pressures are the same. The rise time is nearly linear with pressure and equivalent bubble size decreases inversely as the square root of the rise time. The volume of bubbles in the flotation column at the end of filling was determined by marking the filling level initially and then the lower water level after all bubbles had risen and escaped. The product of the difference in height and column area gives the initial bubble volume. This volume is then expressed as a percentage retention of the calculated bubble volume had all supersaturated gas desorbed to barometric pressure. For the solid line of Figure 3 the percentage bubble volume retained at the end of filling amounted to only 39 % of that for complete desorption at the lowest pressure but was 80 % at 276 kPa. Higher pressures showed higher bubble content up to more than 90% at the end of filling. The difference from 100% retained arises from the escape of larger bubbles during filling which was observed for the lower pressures but was minimal or absent at the higher pressure values. Also, the initial retention would not include volume expansion resulting from desorption and bubble growth occurring during bubble rise. Thus, at elevated pressures bubble retention would approach 100% . For a few runs using air, the long rise times of the smaller bubbles produced little residual undesorbed oxygen in the water compared to that for equilibrium with the atmosphere. The effect of keeping the transfer pressure constant at an elevated value,Pd = 276 kPa, while varying the dissolved
0
100
200
300
400
Pd, Transfer Pressure, kPa Figure 4. Effect of transfer pressure for constant saturation.
gas concentration is shown by the dotted line in Figure 3. Bubble sizes remained nearly constant and independent of the amount of gas dissolved except at the lowest saturations. I t is evident that the energy from the applied transfer pressure, above that lost in turbulence, goes to provide energy for bubble formation and growth. For p d constant, the number of nucleation sites appears to be constant. As the saturation pressure is increased, the gas desorbed increasingly appears as excess larger bubbles which rise to the top through the bubble mass. This was confirmed visually as few bubbles broke the surface on filling a t low gas concentrations. The effect of increasing the energy for nucleation is shown in Figure 4, where the dissolved gas concentration is kept constant while the transfer pressure is increased. Bubble size decreases as p d increases, indicating the production of increasing numbers of nucleation sites. Almost all of the fixed amount of dissolved gas goes to small bubble formation for the points lying on the straight portion of the line. Gas volumes retained in the column liquid at the end of filling were 80-95% of that possible except at the lowest p d values. These points depart from the straight line and show low bubble retention on filling. Bubble formation for two levels of detergent added, 1 and 5 mg/L, is also shown in Figure 4. Rise times are essentially coincident and the variation in detergent concentration did not affect bubble size. Several points for clean water, as approximated, are shown and higher transfer pressures did not increase rise times. It is noted that the line of Figure 3, where the saturation and discharge pressures are the same, is also nearly coincident with the line of Figure 4. The departure of the data points from the straight line occurs at the same value of the transfer pressure for the two figures. I t is clear that very small bubbles develop in a flowing system only when excess energy is available for nucleation and also that the number of bubbles formed increases as this extra energy increases. The energy needed for bubble formation was demonstrated further by keeping the transfer pressure on the saturation column constant during filling while imposing a back pressure on the air escaping from the flotation
932 Ind. Eng. Chem. Res., Vol. 33, No. 4, 1994
E
F al VI E 6
0' 0
I
,
1
I
I
,
,
50 100 150 200 250 300 350 400 (Pd
- Back Pressure), kPa
Figure 5. Bubble sizeis reducedfrom energylosttoairdisplaoement.
column. The open flotation column was closed by a t taching a needle valve to vary the air escape rate during filling. The column pressure was determined by either a mercury manometer or a pressure gauge. As shown in Figure 5, the bubble rise time decreases markedly as the back pressure increases from 0 to 70 P a . The back pressure finally consumes almost all of the energy above that for effecting flow with only a few, larger bubbles formed. The threelinesarenearlyparallelwith theslopes, indicating about the same energy requirement to form bubbles of a given size and number. The relative positions are determined hy the different filling times and the three applied transfer pressures. The amount of energy consumed in effecting bubble formation can be estimated from a plot of number of bubbles formed versus net transfer pressure as in Figure 6. The numer of bubbles is calculated from the amount of gas desorbed to barometric pressure in the flotation column, 177 cm3a t P = 276 kPa, by dividing by the volume per bubble to give number of bubbles = 337 X 10'*/dS For the line beginningat 414 kPa and zero back pressure the slope is 0.43 X 108 bubbleslkpa. This is very close to the line starting at 345 which has a slope of 0.46 X 108. The flotation column was filled to a volume of 3.7 L. The energy for the formation of this number of bubbles corresponds to that for 1 kPa acting against the transfer of 3.7 L of water or 37.1 X 106 ergs. This energy is distributed among interfacial tension, expansion of the bubbles against the atmosphere, and nucleation. As an example of the relative energy effects, a bubble size of 62 pm is selected. The energy to create the surface area of 0.44 X lo8bubbles at 70 ergs/cm2is 0.35 X lo6 ergs. The energy expended to form the bubble volume at barometric pressure is 4.8 X lo6ergs. Thus, the energy for nucleation is (37.1 - 0.35 - 4.8) X 106 ergs = 32.0 X 106 ergs. This correspondsto an energyrequirement of0.8ergtonucleate one bubble. Because a range of bubble sizes is involved, rather than a single size, this result serves only to indicate thatthe energy consumed in bubble formation is primarily that for heterogeneous nucleation.
Pd = 345 kPa
6.5
0.7
0.9
1.1
1.3
1.5
Liquid Displacement Time, minlm
Faun, 7. Reduced liquid flowincreases bubble formation.
Bubble formation under liquid flow conditions was simulated by transferring supersaturated water into a full flotation column and displacing the contents by overtlow through outlet piping. After water in the saturation column was depleted, the flow was ?topped and bubble rise time observed. This resulted in additional energy losses as compared to the open column. Transfer was at three pressure levels for constant supersaturation and at several valve positions to vary liquid flow rate (Figure 7). A t Pd = 276 kF'a only large fast-rising bubbles resulted at all flow rates. A t transfer pressures of 345 and 414 kF'a the rise times increased and bubbles became smaller. As the flow rate was reduced, less energy was consumed in turbulencewhichincreasedthe energy availablefor bubble nucleation and growth. Injecting supersaturated water into the full flotation column also permitted observations as to bubble growth
Ind. Eng. Chem. Res., Vol. 33, No. 4, 1994 933 rates. Initial bubble formation appeared instantly as a faint cloud. Over a period of perhaps 10 s the bubbles grew in size and showed the usual, opaque appearance. Other factors influence bubble formation. A highly soluble gas, carbon dioxide, has a solubility 50 times that of nitrogen, and with the Woolite present only very large, rapidly rising bubbles formed. Rise rates were much higher than any observed with the nitrogen and could not be followed. A mixture of 6 7% COz in nitrogen reduced rise times to about half that for pure nitrogen with larger bubbles rising and escaping during filling. A mixture of 3 % COa a t lower pressure saturations resulted in a minimal change in rise times. A liquid soap showed nucleation effects similar to those for Woolite, and the nucleation persisted at dilutions down to 0.05 mg/L. Dextrin also promoted bubble formation, but higher concentrations were required to approach the performance of the detergenb and bubble retention on filling was low at 50%.The solubilities of the gases were obtained from Perry and Chilton (1973) and Metcalf and Eddy (1979).
Some Applications Monitoring the energy available for bubble formation has application for some kinds of industrial processing. The flotation of solids for separation from liquids is an important operation in some industrial processes. Pressure tanks for dissolving gases are operated a t fractional saturations of 50-80% with discharge at the absorbing gas pressure. The present study indicates that lower gas compression energy can be used if higher discharge pressures by liquid pumping are employed. A net saving in energy consumption should be possible by controlling the dissolvingand transfer pressures independently. This would be applicable to either the recycle system, where clear effluent is pressurized and mixed with the incoming suspended solids, or by direct pressurization of the suspension. An additional effect occurs where the solids are in direct contact with the dissolvinggas for an extended time period. The gas penetrates to the interior of the solids, as for biological flocs, and upon pressure release provides an additional effect for flotation. Bubbles adhere to the exterior, but in addition expansion of the flocs by internal gas reduces the solids density and increases the rise rate. Jackson and Shen (1978) and Jackson (1982, 1986) demonstrated this effect in deep tank aeration where use of only the residual nitrogen released at the hydrostatic pressure of the liquid produced effective flotation. Currently, initial observations on the flotation of biological solids in the columns demonstrated that suspensions saturated at low gas pressure and transferred at an elevated pressure showed an increase in solids separation and rate of rise. This confirms results of the present study that the transfer pressure has an independent and controllable effect on bubble formation. Gases other than air or nitrogen find use in industrial processing. Dissolved gases could be released from a pressurized stream to provide a long bubble rise time for extended contact and reaction. For example, methane used in certain biological processes could be formed as minute bubbles for a reaction time much longer than for use of a packed tower and with little excess gas to be discharged. Supersaturated gases in process streams could be desorbed by rapid pressure release across a valve in contrast to the use of packed towers or agitated basins. Conclusions 1. The size and number of bubbles produced by arapid pressure drop in a flowing system depends on the degree
of supersaturation and the energy available for formation. This energy is that not consumed in turbulent flow and can be provided by increasing the system pressure. 2. Nucleation in clean water appears to require a high level of energy with the result that only few large bubbles form. However, the presence of impurities, particularly surface-active agents, lower the nucleation energy and result in the formation of very large numbers of very small bubbles. 3. The energy available for bubble formation goes to that required for surface formation, bubble expansion, and nucleation, with most used in nucleation. 4. Stokes law was used to estimate the equivalent size of the bubbles which ranged from 145 pm for the fastest rising bubbles to 45 pm for the slowest. The corresponding rise times were from 1to 14 min/m. 5. Bubble size and number can be controlled to a degree by using a higher pressure for effecting flow than that used for saturating the liquid. For applications, such as for flotation, energy consumption can be minimized by the use of low saturation pressures in combination with liquid pumping for higher transfer pressures.
Literature Cited Bassiri, M.; Tullis, J. P. Air Release During Column Separation. J . Fluids Eng. 1983,105,113-118. Clift, R; Grace, J. R.; Weber, M. E. Bubbles, Drops and Particles; Academic: New York, 1978; pp 172,337-378. Dean, R. B. The Formation of Bubbles. J. Appl. Phys. 1944, 15, 446-451.
Holl, J. W. Nuclei and Cavitation. J . Basic Eng. 1970,92,681-688. Jackson, M. L. Deep Tank Aeration/Flotation for Fermentation/ Wastewater Treatment. Proceedings of the lthlndustrial Waste Conference; Purdue Univ: Lafayette, IN, 1982; pp 363-374. Jackson, M. L. High Capacity Aeration in a Very Tall Tank. Biotechnol. Prog. 1986,2, 61-66. Jackson, M. L.; Shen, C. C. Aeration and Mixing in Deep Tank Fermentation. AZChE J . 1978,24,63-71. Jackson, M. L.; Leber, B. P., Jr.; James, D. R. Oxygen Transfer in a 23-meter Bubble Column. AIChE Symp. Ser. 1975, 71 (No. 151), 159-165.
Keller, A. The Influence of the Cavitation Nucleus Spectrum on Cavitation Inception, Investigated with a Scattered Light Counting Method. J . Basic Eng. 1972,94,917-925. Knapp, R. T. Cavitation and Nuclei. Trans. ASME 1958,80,13151324.
Metcalf and Eddy, Inc. Wastewater Engineering, 2nd e& McGraw Hill: New York, 1979; pp 222-227. Perry, R. H.; Chilton, C. H. Chemical Engineers Handbook;McGraw Hill: New York, 1973; pp 3-96 to 3-98. Takahashi, T.; Niyarara, T.; Mochizuki, H. Fundamental Study of Bubble Formation in Dissolved Air Pressure Flotation. J . Chem. Eng. Jpn. 1979,24,63-71. Received for review April 5, 1993 Revised manuscript received November 22, 1993 Accepted December 22, 1993. Abstract published in Advance ACS Abstracts, February 15, 1994.
