The mechanism of scavenging of waterborne bacteria by a rising bubble

Transcription

1 Litnnol. Oceanogr., 28(l), 1983, 1983, by the Americnn Society of Linmolagy and Oceanography, IN. The mechanism of scavenging of waterborne bacteria by a rising bubble Martin E. Weber Department of Chemical Engineering, McGill University; Montreal, Quebec 113A 2A7 Duncan C. Blanchard and Lawrence D. Syxdek Atmospheric Sciences Research Center, State University of New York at Albany, Abstract It is shown that interception can account for the number of bacteria which are collected by a rising bubble. In the first Few centimeters of rise the collection rate is large because the bubble surface is mobile. As the bubble picks up surface-active materials, its surface loses mobility and the collection rate decreases. The first cm of rise are the most important. In a previous paper (Blanchard et al. 1981), we showed that the bacteria in the jet drops produced by a bursting bubble were the result of scavenging by the bubble during its rise, Our purpose here is to show that interception (Weber 1981) is the mechanism responsible for the collection of bacteria by a rising bubble. Collection of particles by a rising bubble If a particle is to be collected it must first collide with a bubble and then become attached to it. The collection efficiency EC is the fraction of the particles in the cylindrical volume swept out by the bubble which is collected by it, The collection efficiency is conveniently written as the product of a collision efficiency E and an attachment efficiency E, : Ec = E E, (1) where E is the fraction of the particles in the path of a bubble which collides with it and E, is the fraction of the colliding particles which becomes attached. We may consider E to account for hydrodynamic effects and E, for surface chemical effects, e.g. the hydrophobic nature of the bacterial surface. Particles may reach the bubble surface by one or more of four mechanisms: gravitational deposition, inertial impaction, convective diffusion, and interception. The relative importance of each mechanism is governed by the size of the bubble and the size and density of the par- 101 ticles. When more than one mechanism is important, their combined collision efficiency is well approximated by the sum of their individual collision efficiencies (Yao et al. 1971). Gravitational deposition occurs when the particle density is different from the fluid density. Equations giving the collision efficiency in terms of the terminal velocities of the bubble and the particle are available (Weber 1981). Since bacteria are essentially neutrally buoyant, gravitation is not an important mechanism of collection. Inertial impaction occurs when the inertial force on the particle is large compared to the drag force. In this circumstance the particles deviate from the fluid streamlines as they curve around the bubble and collisions occur (Flint and Howarth 1971). For particles of the order of 1 pm in size, like bacteria, inertial forces are small, the particles follow the fluid streamlines, and essentially no inertial collisions occur, Convective diffusion becomes important when the particles exhibit Brownian motion. The smaller the particle the more important is convective diffusion. The collection efficiency for diffusion is given by Reay and Ratcliff (1973): Ed = 4KK.J (2) where the subscript d denotes diffusion, K is the mass transfer coefficient for the convective diffusion of the particle to the bubble, and U is the rise velocity of the

2 102 Weher et al. hubblc. Typically K is proportional to the diffllsion coefficient raised to a power between 0.5 and 0.67 (Clift et al. 1978). The diffusion coefficient of the particle, D,, is given by the Stokes-Einstein expression: DP =&- where k is Boltzmann s constant, 7 is absolute temperature, p is fluid viscosity, and u is radius of the particle. Hence, E,! increases as particle size decreases. For particles of the size of bacteria convective diffusion is not an important mechan ism; however for smaller particles, like viruses, it may be the dominant mechanism of collection. Interception occurs because particles have finite size. If the particles are small, their centers move along fluid streamlines around the bubble. The situation is depicted in Fig. 1 for a spherical particle of radius CL and a bubble of radius A. A particle moving along a streamline which approaches the bubble surface more closely than one particle radius will collide with the bubble. The streamline whose closest approach to the bubble is equal to one particle radius is called the grazing streamline. All particles closer to the axis of rise than this streamline collide with the bubble. For particles of bacterial size, interception is the principal mechanism of collection. I( Collision efficiency by interception In terms of R,, the distance of the grazing streamline from the axis of rise far ahead of the bubble (see Fig. I), the collision efficiency is Ei = (R,/A)2 (4) where the subscript i denotes interception. The calculation of the collision efficiency for interception reduces to finding the location of the grazing streamline far ahcad of the bubble. Fig. 1. A grazing collision of a spherical particle with a spherical bubble RT (5) 2 The collision efficiency for a spherical particle with an inviscid sphere having a mobile interface has been derived and can be obtained from M.E.W. The following equation approximates these results for all bubble Reynolds numbers: Such calculations have been made for The e.fficiency for interception is a spherical particles colliding with a rigid strong function of the ratio of the size of sphere (Weber 1981). For a bubble Reyn- the particle to the size of the bubble. For olds number, Re, ~300 the results are a fixed particle size, smaller bubbles have well approximated by higher efficiencies. (6)

3 Bubble scavenging 103 Collection of bacteria by bubbles Blanchard and Syzdek (1972, 1974) passed air bubbles through suspensions of Serrutia murcescens and counted the bacteria carried by the bubbles and the jet drops. These bacteria are rodlike with diameters of about 0.5 pm and lengths (excluding flagella) of l-2 pm. It is impossible to calculate the interception efficiency for a rodlike particle because of the complexity of this shape. In -order to test whether interception is the dominant mechanism, we back-calculate an interception diameter, i.e. the diameter of a spherical particle which has the collection efficiency measured for the bacteria. If interception is the most important mechanism, this diameter will be in the range of the actual cell dimensions. We assume that E,, the attachment efficiency, is unity. In the bubble tube experiment of Blan- chard and Syzdek (1974), bubbles of l.o5- mm diameter rose through a suspension of S. marcescens at a concentration of 3 X 105* ml-. The bubbles were released every 2.5 s from a capillary tip submerged either 2.2 or 20.3 cm. The number of bacteria collected by a bubble is shown in Fig. 2. The rate at which bacteria were collected decreased with bubble rise distance. This behavior is similar to that exhibited by the enrichment factor for bacteria in the top jet drop (see fig. 1 of Blanchard et al. 1981). The rate of collection of bacteria decreases with height of rise because the bubble surface loses mobility as it picks up surface-active materials, The bubble changes gradually from a sphere with a mobile surface to one with a rigid surface. Direct evidence for this change comes from the work of Aybers and Tapucu (1969) and many others (e.g. Bachhuber and Sanford 1974; Detwiler and Blanchard 1978) who noted a decrease in rise velocity with height. For bubbles of 0.83-mm diameter, released every 2 s, Aybers and Tapucu found a rapid initial acceleration up to a maximum velocity of 23 cm. s- after a rise of 1.5 cm, followed ov BUBBLE RISE DISTANCE (Cm) Fig. 2. Effect of distance of bubble rise on number of bacteria (S. marcescens) carried by the bubble. Bubble diameter was 1.05 mm and bulk concentration of the bacterial suspension was 3 x lo * ml-. Points are the mean of fine measurements (vertical bars-sd). by a gradual deceleration. The bubble accelerated to a velocity of 20 cm. s-l after rising 0.5 cm and decelerated to the same velocity at a rise distance of 11 cm. The bubble was still decelerating very slowly after 65 cm of rise where its velocity was 13 cm-s-. On the basis of this evidence it is likely that for the 2.2-cm submergence the bubbles behaved as spheres with mobile interfaces and that even after 20 cm of rise the interfaces were partially mobile. Hence, we use the data for 2.2-cm submergence and Eq. 6 to calculate the interception diameter. Since the bubble was 0.1 cm in diameter, it rose 2.1 cm from the capillary tip to the liquid surface. In this rise it swept out a cylindrical volume containing 5.5 x 10 bacteria. The bubbles collected an average of 18 bacteria, yielding Ei = 3.3 X lo-. Neglecting the initial acceleration of the bubble and taking its velocity to be constant over the 2.1 cm of rise, we find the Reynolds number to be 250. Equation 6 gives 2u = 1.3 pm, i.e. the interception diameter of S. marcescens is 1.3 pm. This value is in the I I

4 104 Weber et al. correct size range, thus providing strong marcescens a bubble of 380~pm diameter evidence that interception is the mecha- with a mobile surface picks up bacteria nism responsible for the scavenging of at a rate about 150 times larger than the bacteria. same bubble with a rigid surface. Another set of data is available for S. The enrichment factor for the jet drops mnrcescens using the same apparatus, but can be oained from Eq. 7 as follows. bubbles of 380-pm diameter (Blanchard Define p as the fraction of the particles and Syzdek unpubl.). In these experi- adhering to the bubble which is transments the bubbles rose 26.5 cm through ferred to the jet drops. Since the enricha suspension of 1.8 x 106* ml-. The a& ment factor, F, is the ratio of the concenerage number of bacteria collected per tration in the drops to that in the bulk, bubble was 175. Assuming that the bub- the rate of increase of the enrichment facble surface is mobile and that the inter- tor With height is ception diameter is 1.3 pm, we calculate the rise distance required to collect 175 (9) bacteria. If interception is the dominant dx Vd a mechanism, this calculated distance will Here VcJ is the volume of the jet drop or be less than the actual rise distance be- drops. Equation 9 can be applied to any cause the bubble surface will not be mo- jet drop or to the entire jet set. For the bile over its entire rise. For bubbles of top jet drop, /3 is the fraction of adhering this size the Reynolds number is approx- particles transferred to this drop and Vcl imately 22 and, from Eq. 6, Ei = 6.1 X is the volume of the drop. For the entire lo-. The bubbl e sweeps out a volume jet set, p is the overall transfer efficiency containing 2.0 x 10 bacteria. cm-- of rise; and Vd is the total volume of the set. hence it will collect 175 bacteria in 14.3 Equation 9 predicts that F should be incm. This is well below the actual rise dis- dependent of concentration. This agrees tance, as expected. with the results reported in fig. 2 of our previous paper (Blanchard et al. 1981), al- Scavenging rate though the concentration was not varied The rate at which a bubble scavenges widely there. particles is given by Assuming that E, = 1, thus making Ec = dn dx = rra2cece, (7) where N is the number of particles attached to the bubble, x is height of rise, and C is particle number concentration. We will assume that E, is unity. If Ec did not change with height, particles would be picked up at a constant rate and their number would increase linearly with bubble rise distance. When a bubble rises, however, Ec decreases as the surface loses mobility. A bubble with a mobile surface is much more effective in picking up particles than one with a rigid surface. For bacteria, where interception is dominant, the ratio of the rates of pickup is 03) The numerator can be obtained from Eq. 6 and the denominator from Eq. 5. For S. Ei, and that the bubble surface is mobile over small rise distances, we can calculate p for the top jet drop from Eq. 9 and the slope at the origin of fig. 1 of Blanchard et al. (1981). From this figure, df/ dx = 140*cm-. Noting that the diameter of the top jet drop is about a tenth of the bubble diameter, that Re = 22 and using Eq. 6, we obtain p = This value is reasonable in light of the few measurements which have been made. Values of 14 and 85% have been reported (Blanchard and Syzdek 1974). Conclusion Interception is the mechanism responsible for the scavenging of bacteria by rising bubbles. The rate at which a bubble collects bacteria is very high during the first few (lo-30 cm) centimeters of rise when the surface of the bubble is mobile. We have provided expressions with which

5 Bubble scavenging 105 to calculate the rate at which suseendcd particles collide with a rising bubble. References AYBERS, N. M., AND A. TAPUCU The motion of gas bubbles rising through stagnant liquid. Waerme- Stofftlebertrag. 2: BACIIIIUBER, C., AND C. SANFORD The rise of small bubbles in water. J. Appl. Phys. 65: BLANCIIARD, D. C., AND L. D. SYZDEK Concentration of bacteria in jet drops from bursting bubbles. J. Geophys. Rcs. 77: , AND Bubble tube: Apparatus for determining rate of collection of bacteria by an air bubble rising in water. Limnol. Oceanogr. 19: , -, AND M. E. WERER Bubble scavenging of bacteria in freshwater quickly produces bacterial enrichment in airborne drops. Limnol. Oceanogr. 26: CLIFT, R. C., J. R. GRACE, AND M. E. WEBER Bubbles, drops and particles. Academic. DETWILER, A., AND D. C. BLANCIIARD Aging and bursting bubbles in trace-contaminated water. Chem. Eng. Sci. 33: FLINT, L. R., AND W. J. HOWARTH The collision efficiency of small particles with spherical air bubbles. Chem. Eng. Sci. 26: REAY, D., AND G. A. RATCLIFF Removal of fine particles from water by dispersed air flotation: Effects of bubble size and particle size on collection efficiency. Can J. Chem. Eng. 5 1: WEBER, M. E Collision efficiencies for small particles with a spherical collector at intermediate Reynolds numbers. J. Separation Process Tcchnol. 2: YAO, K.-M., M. T. HABIBIAN, AND C. R. O MELIA Water and waste water filtration: Concepts and applications. Environ. Sci. Tcchnol. 5: Submitted: 18 February 1982 Accepted: 24 June 1982