Cassell, R. E , , Jr., “Axial Dispersion in Turbulent Flow through a Piping System Containing 90” Elbows,” master’s thesis, TTniver4tI. o.,.f Tennessee Marrh 1966. - ...~~, .~~ _. . - .._. .___ - _...._____ , Knnxville. ~ - -,- Tenn.. Knudsen, J. G., Katx, I). L., “Velocity Profiles in Annuli,” First Midwestern Conference on Fluid Dynamics, J. W., Edwards., ed.., .. D D . 175-203. Edwards Bros., Ann Arbor, Mich., ~
~~
~
~
1951.
Levenspiel, O., Ind. Eng. Chem. 60, 343-6 (1958). Levenspiel, O., Bischoff, K. B., Advan. Chem. Eng. 4, 95-199 (1963). Okiishi, T. H., Serovy, G. K., “Experimental Velocity Profiles for Fully Developed Turbulent Flow of Air in Concentric Annuli,’ A.S.M.E. Paper 64 W.4/FE-32, New York, 1964.
Olson, R. M., Sparrow, E. M., A.I.Ch.E. J. 9, 766-70 (1963). Rothfus, R. R., “Velocity Gradients and Friction in Concentric Annuli.” unoublished Ph.D. dissertation.’ Carneeie Institute of Technolo&, Pittsburgh, Pa., 1948. Smith, J. V., “Axial Mixing of Fluids in Turbulent Flow t,hrough Concentric Annuli,” master’s thesis, University of Tennessee, Knoxville, Tenn., June 1967. Taylor, G. I., Proc. Roy. Soc. (London), Ser. -4, 223, 446-48 ( 1954). Tichacek, L. J., Barkelew, C. H., Baron, T., -4. I.Ch.E. J . 3, 439-42 (1957). RECEIVED for review August 28, 1968 ACCEPTEDMay 27, 1969 0
FIBROUS B E D C O A L E S C E N C E OF W A T E R Steps in the Coalescence Process R. N . H A Z L E T T Naval Research Laboratory, Washington, D. C. 20390
The coalescence phenomena in a fibrous filter bed have been analyzed on the basis of three major steps: approach of a dispersed water droplet to a fiber, attachment of the droplet, and release of enlarged droplets from the downstream side of the filter. For approach the interception process is important, while diffusion and inertial impaction processes ore insignificant in the total efficiency of this step. Surfactants that increase the water-hydrocarbon interfacial viscosity may interfere with the attachment of the small water droplets in the initial part of the filter or the attachment of a coalesced water thread as it snakes through the fibrous bed. They also interfere with the release process by altering the interfacial tension. The latter property influences the size of a water thread at rupture and thus controls released water droplet size. Rayleigh instability can occur when the interfacial tension is decreased.
HE removal of emulsified water from an organic liquid is a Trequirernent in many phases of today’s technology. The requirement of removal of free water is particularly stringent with aircraft fuels, since free water in a fuel system results in corrosion and microbiological growth as well as icing problems a t low operating temperatures (Krynitsky and Garrett, 1961). Particulate, or free, water is readily emulsified in fueling systems which use high-speed centrifugal pumps and are characterized by turbulent flow in fuel lines. A centrifugal pump readily produces a water-in-fuel emulsion in which 90% of the droplets are less than 4.8 microns and 100% are less than 8.6 microns in diameter (Bitten, 1967). Water droplets of this size do not settle out of fuel in a reasonable length of time, particularly if there is any agitation or sloshing in the storage tank or if thermal gradients are present. The drop size may be increased by passage of the emulsions through a fibrous bed. I n this situation, small droplets are retained until growth occurs by coalescence. The larger drops are then swept from the fiber bed by dynamic forces and ideally are of such size that they can separate by gravitational forces. Fueling equipment employing this principle is known as a filter-separator. I n addition to coalescing and separating emulsified water, this equipment serves as a filter for solid matter which is retained in the fibrous bed. A filter-separator typically consists of two
stages: a resin-bonded glass-fiber bed which retains solid matter and coalesces water drops and a hydrophobic screen or paper, included to strip water drops of an intermediate size which are too small to settle by gravity forces but too large to pass through the pores of this separator stage along with the continuous fuel phase (Redmon, 1963). Filter-separators with fueling rates of 10 to 600 gallons per minute are typical. The physical size of a particular installation is controlled by the fiber-bed flow velocity, which has an upper limit of 0.5 to 1.0 cm. per second. The performance of a filter-separator may be inadequate if the jet fuel contains surface active materials (Krynitsky and Garrett, 1961) This requires care on the part of the refiner, the transporter, and the user to ensure absence of undesirable surfactants from the fuel. Another consequence of this behavior is that additives, such as corrosion inhibitors and antioxidants, which might otherwise be useful in controlling certain fuel properties, must be selected carefully. The complex events occurring in a filter-separator are not adequately understood. The work described here examines the steps in the coalescence process in an effort to understand the physical and chemical phenomena involved and to determine the critical factors for coalescence. The process of coalescence in a fibrous bed may be divided into three main steps: approach of a droplet to a fiber or to a droplet attached to a fiber, attachment of a droplet to a fiber I
VOL.
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or to a droplet already attached to a fiber, and release of an enlarged droplet from a fiber surface. Each step involves considerable complexity or alternate mechanisms. Approach Mechanisms
A water droplet in a fuel emulsion must arrive a t a proper location before the subsequent steps of coalescence can occur. In the principal mechanisms of approach, which can be termed direct interception, a particle following the streamlines of the laminar flow can be captured by a fiber because both the particle and fiber have finite sizes. Superimposed on the process of interception are diffusion, inertial impaction, electrostatic attraction, and the effect of gravity. Vinson (1965) has examined these phenomena as they relate to finemesh screens. His conclusions that gravity and electrostatic effects are not significant for the approach mechanism with fine-mesh screens can be accepted for fibrous beds. Reiman (1961) has likewise concluded that electrostatic phenomena are not important in the efficient operation of a filter-separator, although Sareen et al. (1966) and Bitten (1967) feel that electrostatic phenomena participate in coalescence. The efficiencies of interception, diffusion, and inertial impaction are presented in this article for a water emulsion in jet fuel (kerosine type, JP-5). The fuel density of 0.795 gram per ml. and fuel viscosity of 1.463 centipoises used in the calculations are typical for JP-5 fuel a t 25' C. Interception. In laminar flow, a fluid passing a submerged cylinder, such as a glass fiber, will follow flow streamlines such as those depicted in Figure 1, a, where F is the cross section of a fiber. A water droplet, W1, will follow these flow lines. The droplet shown on streamline S4 will be int,ercepted by the fiber when it reaches position WZ. A droplet of somewhat smaller size, Wa, following streamline SZ, which is equidistant with S4 from the center line, will pass the fiber without opportunity for interaction, even at closest approach, W 4 . Such a smaller droplet will be intercepted, however, if it follows a streamline closer to the center line of the fiber. In evaluating the interception mechanism, the equation developed by Langmuir (1942) is useful:
r
1
where E, = efficiency of collection by a single isolated fiber from a fluid stream of a width equal to the diameter of the fiber R = interception parameter = dp/dJ d p = particle diameter, cm. d f = fiber diameter, cm. N R = Reynolds number The Reynolds number includes the velocity term and uses d, as the characteristic dimension. The need for including the Reynolds number arises from the fact that the streamlines are influenced by it, being affected a t a greater distance upstream from the fiber and displaced further from the fiber laterally as the Reynolds number (or velocity for a fixed particle diameter) decreases. The effects of fiber and droplet size on the efficiency of a single isolated fiber for interception of small water droplets in JP-5 fuel, based on the Langmuir equation, are shown in Figure 2. The efficiency increases as the flow velocity increases, but does not change very rapidly in the 0.3- to 3.0cm. per second range, the velocity region of practical irnportance. The efficiency of interception varies greatly with fiber diameter, the smaller fibers being significantly more efficient. Thus a 2-micron fiber is about 15 times more effective than a 10-micron fiber in removing 1-micron water drops from a jet fuel stream of a width equal to that of the respective fiber diameters and flowing a t 0.9 cm. per second. The efficiencies of the 1- and 2-micron fibers are appreciable, whereas that of the IO-micron is low. Diffusion. A particle moving with a fluid will tend to depart from the flow streamline. The most important mechanism effecting this departure is the random transverse motion due to diffusion. Capture of particles by the diffusion mechanism is important a t lower flow velocities in aerosol filtration. The higher viscosity of liquids would lower the efficiency, while the generally lower flow velocities used in liquid filtration would raise the efficiency by this
1
FLOW VELOCITY (CMISECI
Figure 2. (bl
Figure 1. Flow patterns for interception and inertial impaction mechanisms 626
I h E C
FUNDAMENTALS
Efficiency for interception mechanism
Fuel density. 0.795 g./ml. Fuel viscosity. 1.463 cp. Number to right of each curve indicates fiber diameter in microns
mechanism in water coalescence in a fuel. The viscosity of the fluid is incorporated in the formula for the diffusion coefficient along with the temperatures and particle size,
D=- kT 3 d P
where D = diffusion coefficient IC = Boltzman constant T = absolute temperature 11 = absolute viscosity (poise) for fuel phase p50
By using a value of 25' C. for the temperature and 0.01463 poise for the fuel viscosity, the diffusion coefficient can be related to the water droplet size as follows:
D=
3.0
x
4
d
10-13
dP
Langmuir (1942) has related the efficiency of the diffusion mechanism for a single, isolated fiber to the diffusion coefficient of an aerosol particle a t low flow velocities with the formula
E, = 2.16
1
( 31
2 (2 - In N E )
where V = flow velocity of fuel, centimeters per second. This equation was used to obtain the data in Figure 3. The efficiency decreases with an increase in flow velocity, in particle size, and in fiber size. At a flow velocity of 0.9 em. per second , which is typical of filter separator flows, diffusion would be important only for droplets less than 1 micron in diameter and then only if the fiber diameter were less than 1 micron. Inertial Impaction. h particle with a density different from that of a fluid with which it is flowing will deviate from the flow streamlines should the latter be diverted. A more dense particle tends t o move in a line less curved than that of the streamline. A possible path for a more dense particle
I
Figure 4.
ZU
0 I' 5
I-
1
--+ 5cu
7
- - - - D - -I O / '
L
IO-~
c
rVATER C R O P S I Z E
_ . A--_..
*--
-
0 2P 0 lp
-I LLLLIL 5 3
Figure 3.
-
I O FLON \LLOC17t
1
l-th/
See Figure 2 for legend
I
1
I
I
1 1 1 1
300
is illustrated in Figure 1, b, where the broken line indicates the departure from streamline 272. Particle W E ,in deviating from the streamline, approaches close enough to the fiber to be captured when it reaches position Wg. Thus the greater the density a particle has with respect to the continuous phase, the higher the probability that the particle will be captured. This approach mechanism has been called the inertial impaction process. In aerosol filtration, inertial impaction is a significant mechanism for particle removal (Ramskill and Anderson, 1951). Because of the low viscosity and density of air, inertial impaction is the most important mechanism at high flow velocities. Since the density of jet fuel is close to that of water and the viscosity of a liquid is much higher than that of a gas, the significance of inertial impaction must be somewhat less for water-in-fuel emulsions than for aerosols. To evaluate the contribution of this mechanism to coalescence, the inertial parameter, K , of aerosol technology (Dorman, 1966) was calculated for various conditions using the equation:
= p~ =
PH$O
density of water, grams per ml. density of fuel, grams per ml.
A density difference of 0.2 gram per ml. and a fuel viscosity of 0.01463 poise were used for the calculations plotted in Figure 4. The value of K increases with velocity and with water drop size. I t decreases, however, as the fiber diameter increases. The application of the inertial parameter to efficiency calculations has been on an empirical basis. Landahl and Hermann (1949) used the formula
OC
E,
1 ' )
Efficiency for diffusion mechanism
A611
Inertial parameter as a function of flow velocity
I L L ~ - .
I
39
I
Density difference. 0.20 g./ml. See Figure 2 for legend
where
10-4
I
10 30 100 FLOW V E L O C I T Y ( C M / S E C )
03
=
(KI3
+ 1.54K2+ 1.76
(K3)
to determine filtration efficiencies for aerosols a t high Reynold3 numbers (10 and above). Use of this formula, which has VOL.
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Table 1.
Combined Efficiencies for DiffurionandInterceptiona Efeciency
a
IO-^
I
I
01
I
I
IO WATER DROP SIZE (MICRONS)
Figure 5. diffusion Flow velocity.
I
I I I I I
I
I
I I I I I
100
Comparison of efficiencies for interception and
0.9 15 cm./sec,
supporting experimental work, shows that the efficiency of inertial impaction falls rapidly as K decreases and that this mechanism is inefficient a t most of the conditions shown on Figure 4. The velocity must be high and the drop size large to attain a significant efficiency. The actual efficiencies in coalescence would probably be somewhat less than those derived from Equation 5, since the Reynolds number is usually less than 1 in coalescers. Although inertial phenomena have not been dealt with satisfactorily, a study by Davies and Peetz (1956) has indicated a much lower efficiency for aerosol filtration at N R 0.2 than a t N R 10. If this effect holds true for liquid filtration, it can be concluded that inertial impaction contributes very little to the coalescence of the emulsions considered in this report. Combination of Approach Mechanisms. The previous discussion has indicated that an interception mechanism is the most important approach mechanism examined. Inertial impaction is clearly insignificant, but diffusion may supplement direct interception as a primary mechanism for very small water droplets. The efficiency of the mechanisms as a function of drop diameter at a flow velocity of 0.915 cm. per second is shown in Figure 5. At this flow velocity, interception predominates down to a drop diameter of about 0.2 micron. The higher efficiency of small fibers is apparent in both mechanisms. If it is assumed as a first approximation that the efficiencies of diffusion and interception are additive, the combined efficiency can be determined for different fiber diameters. These are listed in Table I for 2-micron11-micron, and 0.2-micron drops. A 1-micron fiber is almost 14 times as effective as a 5-micron fiber in capturing a 1-micron water drop and 6 times as effective in capturing a 0.2-micron drop. The relative efficiency of 1- us. 5-micron fibers is greater for larger drop sizes, since the contribution of diffusion decreases sharply as the drop size increases. A detailed evaluation of combined approach mechanisms has been made for aerosol filtration by Stechkina and Fuchs (1966). Efficiency of Filter us. Single Fiber. Extrapolation from 628
I&EC
FUNDAMENTALS
---
Fiber Diameter, p
2-c( drop
1-c( drop
0 . 2 - p drop
0.5 1 2 5
0.706 0.270 0.0967 0.0227
0.246 0.088 0.0291 0.00857
0.0201 0.0075 0.00314 0.00127
Flow velocity 0.915 cm./sec.
a single-fiber efficiency to a filter-bed efficiency requires many assumptions. The flow pattern around a single fiber in a bed is constrained compared to the isolated case. Adjacent fibers, as well as upstream fibers, restrain the streamlines to a position closer to the fiber. Evaluation of this effect is difficult, but the efficiency of interception and diffusion mechanisms both increased, the former more than the latter. The packing fraction of the filter would influence this increase, since a streamline would be more constrained as the number of fibers per unit volume increased. Hence, the efficiency should be higher as the packing fraction increases. This effect has been observed by Bitten (1967) for some types of filter material. An object, such as a cylindrical fiber, submerged in a flowing fluid, disturbs the flow pattern. At low Reynolds numbers, this results only in a displacement of streamlines and laminar flow pertains. As the Reynolds number is increased, eddies occur on the downstream side of the object. Further increases result in flow of the eddies downstream and finally more severe turbulence. These phenomena are reported to develop with single isolated cylinders a t Reynolds numbers above 2; hence they should not play a part a t the flow velocities and fiber diameters used in a filter-separator. This may not be a realistic appraisal for a filter bed, however, since Sareen et al. (1966) observed turbulence in a fibrous bed. Zebel (1966) states that turbulence can augment the coagulation of aerosols, since particles of different sizes move a t different velocities relative to each other and thus have opportunity to collide. In the field of water coalescence in a fuel, turbulence in a filter bed may have the opposite effect of emulsification. The degree of turbulence in a filter bed and effect of such turbulence on water drops in fuel need further investigation. Although the studies of Spielman and Goren (1968) give hope of overcoming some of the difficulties of evaluating approach efficiencies for a fibrous bed, the efficiencies for single, isolated fibers are used here to obtain a feel for the structural details of a filter bed. A completely ordered array of fibers is assumed in such calculations, so that the distance between adjacent fibers in any direction is the same. On the basis of a fiber bed with a cross section of 1 sq. cm. and a 1-cm. depth, the number of fibers 1 cm. long is given by
where n = number of fibers and P.F. = volume packing fraction for fibers. The number of fibers per layer and the number of layers per centimeter equals the square root of n,
N =
2/11 = 1.13
,&$ P.F.
where N = number of fibers per layer and number of layers per centimeter. The thickness per layer of fiber bed is the
reciprocal of N and the area coverage fraction per layer of fiber bed is the product of N and d f . The efficiency per layer is found by multiplying the efficiency of a single, isolated fiber by the area coverage fraction. T o determine the number of layers required for a desired bed efficiency, Farrow (1966) suggests an exponential function,
P
= exp
(-ELNP)
Table II. Influence of Temperature on Approach Efficiencies Typical JP-5 Jet Fuel" Temp., O
(8 )
where P = fraction of particles penetrating through a fiber bed EL = efficiency per layer N p = number of layers in bed The efficiency of a filter bed must be considered in conjunction with the pressure drop across the bed. Of importance for this discussion are the bed depth and the fiber diameter. The filtration pressure is a function of these two parameters RS follows (Dorman, 1966) : (9)
where A P = differential pressure across filter bed and b = bed depth, cm. = N p / N . The relative pressure drop through a completely ordered fiber bed as related to the penetration of 2.0-micron water drops is shown in Figure 6. The fiber packing fraction used was 0.075 (12 pounds per cu. foot packing density for glass
i
c
L
Olk
t
L
c.
50 25 0 a
V
=
EBciency ( E , )
Fuel Density, G./hll.
Fuel Viscosity, Poise
Interception
Diffusion
0.777 0.795 0.813
O.OO987 0.01463 0.0251
0.283 0.269 0.252
0.000794 0.000568 0.000365
0.915 cm./sec.: d f
=
1.0 p ; d, = 2 . 0 p
fibers with an absolute density of 2.5 grams per cc.) and this affords an area coverage fraction per layer of 0.31. The performance improves as the fiber diameter decreases but the differences are not large for fiber sizes between 0.5 and 2 microns. If the removal of smaller droplets were critical, higher relative pressure drops would be required to attain the same penetration behavior. The removal of smaller drops is not considered typical of fuel filtration. A large percentage of the particles in a water-in-fuel emulsion may be less than 2 microns (Bitten, 1967), but on a weight basis such particles constitute only a small part of the free water in an emulsion. A coalescer designed to be effective for a small droplet would be much more effective for larger droplets. A bed with a penetration of 0.1 for 1-micron droplets affords a penetration of 0.001 for 2-micron droplets a t the same bed pressure drop. Temperature and Approach Processes. The efficiencies for interception, diffusion, and inertial impaction are all decreased a t lower temperatures. The latter process is the most sensitive to a temperature change, since the inertial parameter (Equation 4) decreases directly with a decrease in density difference and with an increase in fuel viscosity. Since inertial impaction is unimportant a t normal temperatures, it need not be considered further a t lower temperatures. Efficiency by the diffusion process is affected in a complex way by temperature. Not only i s the diffusion coefficient a direct function of the absolute temperature and an inverse function of the fuel viscosity (Equation 2 ) , but the fuel density and viscosity are factors in the Reynolds number (Equation 3 ) . The predominant effect is a reduction in efficiency as the temperature decreases. Table I1 shows that E, for the diffusion process a t 0" C. is less than one half that a t 50' C.
The change in fuel viscosity and density with temperature affects only the Reynolds number in Equation 1. These parameters alter the efficiency of interception only slightly over the temperature range 0" to $50" C. (Table 11). Thus, the primary approach process for coalescence in a fibrous bed is the direct interception process a t the flow velocities and temperatures characteristic of filter-separator operation. Other processes in the filter-separator are not as independent of temperature. The settling of coalesced water droplets under the influence of gravity is particularly sensitive to a temperature change, primarily due to the change in fuel viscosity.
001 \
\ \
9
c
c
I i0.001
Figure 6.
\ I
2 3 4 5 RELATIVE PRESSURE DROP
6
7
Filter bed penetration as related to pressure drop
Flow velocity. 0.91 5 cm./sec. Packing fraction. 0.075 W a t e r drop size. 2.0 microns Fiber diameter indicated b y number adjacent to each curve
Attachment
Once a water drop in an emulsion has arrived at a fiber, the stage is set for further activity. The desired action is for attaching the drop to the fiber and spreading the drop on the fiber. Resisting this process is a film of fuel located between the fiber and the drop. This film must thin to a certain minimum thickness before rupture occurs and attachment takes VOL.
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place. The rate of film drainage decreases as the film becomes thinner because of the drag associated with two interfaces, the fuel-water interface and the fiber-fuel interface. Rupture times of seconds and even minutes have been observed in liquid-liquid coalescence (Hartland, 1967; MacKay and Mason, 1963). The rupture distance for lowviscosity liquids was found by illlacKay and Mason (1963) to be less than 0.05 micron, but Hartland (1967) concludes that the film thickness a t rupture is much greater for viscous liquids. Princen (1963) established that the continuous phase can be trapped in a dimple as a liquid drop approaches a solid surface. The drop is deformed by the excess pressure developed by the film drainage process. It would seem that an easily deformed drop might have a longer film drainage time. The interfacial tension would affect the deformability of a drop and some additives that degrade coalescence may do so by lowering the interfacial tension and increasing the deformability of a drop. Another possible effect of surfactants could be the change in interface viscosity. An additive locked in an interface 'should raise the viscosity tangential to the surface. An increased drag on the adjacent fluids should result, and the rate of film drainage be reduced. Surfactants can considerably reduce the rate of film drainage (Allan et d., 1961). Film rupture of the thinned film is another important consideration in the attachment process. AlacKay and Mason (1961) state that the rupture time can be reduced by various means, some of which work by decreasing the film thickness a t a localized spot. Undulations moving across a deformable interface, specks of solid debris in the interface, or sharp points or edges on a fiber are means of reducing the film thickness a t a localized spot. Imposing an electric field such that a spark can penetrate the film and produce a bridge to a droplet also appears to enhance film rupture (Allan and Mason, 1961). Weatherford (1967) concludes from his theoretical and experimental study that the film-drainage process is not controlling coalescence for low-viscosity liquids but that film rupture is the limiting step. A fiber bed which has been exposed to an emulsion retains water attached to the fibers. Such attached water increases the effective fiber size. This increase affects the efficiency in a complex way, since the larger effective fiber would cause more displacement and disturbance of the flow patterns, thus reducing the efficiency, while the greater effective area for interception would increase the efficiency. The attachment process for a small droplet approaching an attached drop is more complicated than the similar process for a droplet and a fiber. Both interfaces are deformable and two interfacial films must be ruptured for coalescence. The discussion on film drainage and rupture presented should be applicable to this more complicated process also. The experimental studies on film drainage and rupture phenomena have been restricted to relatively large drops. With small drops ( < l o microns), the volume of film which must drain is greatly reduced and the dimpling phenomenon may be less significant. On the other hand, the driving force for film drainage is less. Lawson (1967) has concluded on the basis of his studies that the drainage time is proportional to the 1.5 power of the drop radius. If this relationship holds down to the drop sizes of interest in fuel emulsions, film drainage time should be very short and probably insignificant in the initial attachment of water drops to fibers or other drops attached to fibers. Film drainage time may be important, however, in restrict630
l&EC
FUNDAMENTALS
ing attachment of coalesced water to downstream portions of a fibrous bed. The coalesced water, as either a drop or channel, would, in effect, be a greatly enlarged drop compared to the original drops in the emulsion. In addition, the reduction in interfacial area would result in more complete coverage of the interface when surfactants were present. The film drainage time would be increased by both factors. For attachment to be effective, the water drop must displace the fuel film from the fiber and preferentially wet the fiber. This process is encouraged as the surface energy of the fiber increases. A water droplet should readily displace fuel on hydrophilic surfaces, such high energy ones as glass or metal. The displacement on a low energy surface such as polyethylene or Teflon should be considerably less. This is confirmed by the measurement of contact angles of water on various surfaces in the presence of organic liquids (Bascom and Singleterry, 1962). Typical contact angles reported by Beatty and Walcutt (1965) and Beatty (1966) for a distilled water-JP-5 system are 44' for glass, 89' for nylon, 89' for cellulose acetate, 123' for phenolic resin, and 180" for Teflon. Lindenhofen and Shertzer (1967) give a contact angle of 50' for glass and 119' for phenolic resin for a water-RF-1 system. (RF-1 is a mixture of 15% toluene and 85% Bayol. The latter is a highly refined kerosine.) The glass fibers in a filter-separator element are bonded together with a phenolic resin which gives an intermediate contact angle. I t has been assumed that this afforded the desired wetting, sufficient to allow displacement of the fuel by water, but a t the same time being characterized by a modest fiber-water adhesion which permitted release of the coalesced water. A solid which gives a high contact angle with a water-fuel combination has been considered a poor coalescing material, in the belief that water droplets would not displace fuel and attach to such a surface. Suggestions have been made that surfactants degrade coalescer performance by absorption on the fibers, with a resulting increase in the contact angle and decrease in wettability. Some recent studies do not support the suggestion that a surfactant absorbs a t a bonded glass-fiber surface, raises the contact angle, and reduces the coalescing ability of a fiber. Single fiber experiments with flowing water-in-fuel emulsions indicate that water droplets will attach and grow on all materials examined (Beatty, 1966; Bitten, 1967). Plastic fibers, even Teflon, which give high contact angles were effective in these coalescence studies. Furthermore, corrosion inhibitors and other surfactants do not absorb on bonded glass fibers although they do on unbonded glass (Beatty and Walcutt, 1965; Lindenhofen and Shertzer, 1967). Lindenhofen and Shertzer (1967) interpret their work to shorn that a surfactant in a fuel is active a t the fuel-water interface and not a t the fuel-solid interface. Release
RIotion pictures taken by the Army Engineering Research and Development Laboratory revealed some of the phenomena occurring after initial coalescence. Brown (1966) used a short section from a filter-separator element as a coalescer for this work. Installation of this section in a transparent plastic cell permitted photography of u-ater droplet release at the outer surface of the coalescing medium. In addition, passage of water along the interface between the transparent wall and the fiber glass could be followed. Observation of the water drops was enhanced by preparing the water-in-fuel emulsion with water containing a soluble dye.
The color movies indicate that in a fiber bed of reasonable packing density, the coalesced droplet size appears to be large enough so that it bridges to a fiber downstream and attaches before releasing from the first fiber. I n fact, these movies of coalescence with a high quality fuel indicate that the water does not move through the fiber bed as discrete droplets once attachment has occurred (Brown, 1966). Rather, threads of water snake through the coalescer. The thread size varies, since the water readily deforms to fill the passageway through the coalescer. At the downstream face of the fiber bed, the water is realeased in individual drops. Three factors which affect the size of the droplets released are the flow velocity, the surfactant content, and the fiber size. Beatty (1966) has shown in single fiber studies that detachment occurred more readily from small than from large diameter fibers. A higher velocity removed smaller drops. The nature of the material had little effect on the detachment flow velocity except for polyethylene filaments, for which detachment was somewhat easier. iidditives in the fuel usually encouraged detachment. At high concentrations (60 p.p.m.) of powerful surfactants, Beatty found that droplets slid on the fibers and detached much more readily than drops in a fuel containing no additives. Beatty (1966) suggests that the hydrodynamic force acting on a drop must overcome the adhesive force between the droplet and fiber before detachment can occur. The insensitivity of release to the fiber material indicates, however, that the fuel-water interfacial force is the one which must be overcome by the hydrodynamic force of the flowing fuel. The observation by Beatty (1966) that a small drop of water remained on the fiber after detachment supports this viewpoint. The following treatment examines three possible mechanisms for release which are based on breaking a thread of water: drop-volume rupture, drop-elongation rupture, and jet rupture. In the first mechanism, the detaching force for a water droplet in a moving fluid, is found by equating the drag exerted on the droplet with the restraining force of the interfacial tension :
where C = drag coefficient a = orifice radius a t the downstream face of a water channel through the fibrous bed, em. y = interfacial tension, dynes per em. AV = difference between fuel and droplet velocity, em. per second By assuming that the orifice radius is less than 0.1 the droplet radius, the latter can be approximated by
The drag coefficient of interest here is in the Reynolds number range (0.3 to 1000) between the Stokes' law region and the Newton's law region (Perry, 1963) where
Thi:., gives the following equation for water droplet size a t releitse : (13)
If the release of droplets is controlled by this mechanism, the interfacial tension, orifice, and radius would greatly influence droplet size. Measurement of interfacial tension by the ring method is not applicable to many coalescence systems because of the large difference in water-fuel ratios and interfacial areas used in the ring method vs. those characteristic of typical water-infuel emulsions. The pendant drop method, however, has been shown by the Coordinating Research Council (1964) to be useful for examining the effect of water-soluble surfactants on coalescence. This study indicated that some surfactants a t a concentration of 0.5 p.p.m. in fuel could lower the interfacial tension below 10 dynes per em. and drastically interfere with coalescence. In a fibrous bed, the dimensions of a channel for water passage would be related to the fiber size. At a constant packing density, a bed of large fibers would afford a larger diameter channel than that found for small fibers. This suggests that coalescence would be improved with a bed having large fibers built into the downstream portion of the bed. This arrangement is typical of filter-separator elements and the results of laboratory studies support such a design. Equation 13 indicates that the velocity difference between fuel and particle influences particle size a t release. An increase in this parameter leads to a decrease in the droplet diameter. The value for the fuel velocity is readily established for an emulsion with a low water content, but the droplet velocity is not defined. The latter depends upon the fraction of the filter cross section utilized by the water threads. Further, passage of water through the fibrous bed is irregular and this results in a variable velocity difference. In the studies by Beatty (1966) on the detachment of a drop from a single fiber, the velocity was well defined. Aplot of the product of the droplet diameter times the fuel velocity a t detachment vs. the square root of the fiber diameter gives a linear relationship for most fiber materials. This is remarkable, since the cross section of the water thread a t the point of attachment is probably not circular. Comparison of data for clean kerosine and kerosine containing 60 p.p.m. of a corrosion inhibitor shows that detachment is easier for the latter material, as would be expected from its lower interfacial tension. A second treatment of droplet release examines the elongation effected by the moving fluid surrounding a droplet. Taylor (1934) studied the effect of the properties of viscous liquids on the elongation of freely suspended drops and rupture of the threads formed. The ratio of the viscosity of the drop to that of the continuous phase had a significant control on the stretching phenomena. For a viscosity ratio in the range 0.5 to 1.0, which is typical of water-jet fuel systems, the elongation a t small distortions is proportional to a dimensionless number, F ,
where G is the shear rate, in reciprocal seconds. The elongation becomes more sensitive to an increase in F a t distortions near those where rupture takes place. The rupture of the extended thread, which occurs by Rayleigh instability (Rayleigh, 1879), produces a series of drops of uniform but smaller size. Rayleigh instability has been observed in coalescence studies with fuels containing additives (Hazlett, 1968). The control of elongation by the interfacial tension is apparent in Equation 14. A reduction VOL.
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of y would increase F and under certain circumstances could shift the thread from a stable but extended equilibrium configuration to a condition of instability with respect to rupture. The elongation release mechanism is directly proportional to t,he shear rate and hence the velocity difference between the fuel and wat,er droplet. The problem of assigning values to t,his parameter is discussed above. Ejection of water from a fibrous bed by jet action can also be considered a droplet release mechanism. This mechanism is more complex, but more realistic than the drop-volume and drop-elongation mechanisms, in that water input is a n integral part of the process. At the relatively low velocities characteristic of filter-separator operation, the jet behavior is described as varicose and breaks up into small drops as a result of Rayleigh instability (Merrington and Richardson, 1947). The drop size is fairly uniform for a part’icular set. of conditions and pair of liquids. This size is governed by interfacial tension and nozzle size. Although their experimental studies did not extend t’o the low velocit’iesof interest here, Merrington and Richardson suggest that the drop size formed by jet rupture is independent of velocity below a critical value. Rayleigh instability has been observed with fuel containing some additives (Hazlett’, 1968). This is associated with irregular water release from a glass fiber bed and is thought to be the result of \vater jet instability and rupture, although the jet prior to rupture has not been observed outside the filter bed. Experimental work related to the three release mechanisms discussed is not directly related to water detachment from a fibrous bed. The velocity regime, orifice diameter, and/or liquid physical properties have been considerably different from those of interest as related to coalescence in a fibrous bed. Subsequent studies will adjust the conditions to those typical of filter-separator operation in an effort to define the role played by the three release processes. Conclusions
The interception process is the predominant mechanism for approach of a water drop to a fiber from a Rowing fuel emulsion. The interception theory explains the reason for the importance of small fibers in a fiber bed and predicts that the bed pressure drop for a desired penetration will be less for a small-fiber bed. The attachment process is not considered critical in this type of coalescence. Surfactants are thought to interfere with release of coalesced water from the downstream face of the fibrous bed and/or movement of coalesced water through the middle portion of the bed. The effects of fuel velocity, surfactant type, surfactant concentration, fiber size, and fuel properties on the size of
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water droplets released from a coalescence filter will aid in evaluating the various processes and mechanisms discussed. Acknowledgment
Thanks are extended to Naval Air Systems Command for support of this work under project A33-536/652/ 69F32.543.301. literature Cited
Allan, R. S., Charles, G. E., Mason, S. G., J. Colloid Sci. 16, 150 (1961). Allan, R. S., Mason, S. G., Trans. Faraday SOC.67, 2027 (1961). Bascom, W. D., Singleterry, C. R., J. Phys. Chem. 66, 236 (1962). --,. j-l
Beatty, H. A., Ethyl Corp., Ferndale, Mich., Interim Tech. Rept. GR-6640 (July 1966). Beatty, H. A., Walcutt, C., Ethyl Corp., Ferndale, Mich., Final Tech. Re&. GR66-1 (March 1965). Bitten, J. &F.,IIT Research Institute, Chicago, Ill., Annual Report, Project C6088-4, May 19G7. Brown, R., Engineer Research and Development Laboratories, Ft. Belvoir, Va., private communication, 1966. Coordinating Research Council, New York, N. Y.. CRC No. 376, Febrcary 1964. Davies, C. N., Peetz, C. V., Proc. Roy. SOC.A234, 269 (1956). Dorman, R. G., “Aerosol Science,” C. N. Davies, ed., Chap. VIII, Academic Press, New York, 1966. Farrow, R. >I., Filtration & Separation 3, 490 (1966). Hartland, S., Trans. Inst. Chem. Eng. 46, T102 (1967). Hazlett, R. N., Naval Research Laboratory, Washington, D. C., unpublished work, 1968. Krynitsky, J. A., Garrett, W. D., Kava1 Research Laboratory, Washington, D. C., Rept. 6686 (August 1961). Landahl, H., Hermann, K., J.Colloid Sci. 4, 103 (1949). Langmuir, I., OSRD Rept. 866 (September 1942). Lawson, G. B., Chem. Process Eng. 48, 45 (1967). Lindenhofen, H., Shertzer, R. H., Aeronautical Engine Laboratory, Philadelphia, Pa., NAEC-AEL-1862, NAEC-AEL-1866 (April 17, 1967; July 7, 1967). MacKay, G. D. M., Mason, S. G., Can. J . Chem. Eng. 41, 203 (1963). Merrington, A. C., Richardson, E. G., Proc. Phys. SOC.69, 1 fj 1947) -”-.,.
Perry, J. H., ed., “Chemical Engineers’ Handbook,,’ 4th ed., Sec. 5, p. 59, McGraw-Hill, New York, 1963. Princen, H. hi., J . Colloid Sci. 18, 178 (1963). Ramskill, E. A., Anderson, W. L., J. Colloid Sci. 6, 416 (19511. Ravleieh. Lord. Proc. Row. SOC.29. 71 11879). Sareen, S. %., Rose, ’€ A.I.Ch.E.J. 12, 1045 (1966). Spielman, L., Goren, S.L., Environ. Sci. Technol. 2, 279 (1968). Stechkina, I. B., Fuchs, X. A., Ann. Occup. Hyg. 9, 59 (1966). Taylor, G. I., Proc. Roy. SOC.146, 501 (1934). Vinson, C. G., Jr., Ph.D. thesis, University of Michigan, Ann Arbor, Mich., 1965. Weatherford, W. D., Jr., Southwest Research Institute, San Antonio, Tex., Tech. Rept. AFAPL-TR-67-3 (February 1967). Zebel. G.. in “Aerosol Science.” C. N. Davies, Chao. 11, Academic Press, New York, 1966. RECEIVED for review August 14, 1968 ACCEPTED April 16, 1969
