T = temperature, OC T I = integral time VI = volume of the cooling jacket, cm," V = volume of the reactor, cm:' VI I , Vzn, V:{:< = Liapunov function T = residence time p = density, g/cm:'
pc =
_ --
density of coolant, g/cm:' deviation variables
Subscripts c = coolant i = ith reactor
Berger, A. J., Lapidus, L., AIChEJ., 15, 171 (1969). Berger, J. S., Perlmutter, D. D., Chem. Eng. Sci., 20, 147 (1965). Berger, J. S., Perlmutter, D. D., AlChEJ., I O , 233 (1964). Bilous, O., Block, H. D.. Piret, E. L., AlChEJ., 3, 256 (1957). Bilous, O., Amudson, N. R., AlChEJ.. 1, 513 (1955). Douglas, J. M., Rippin, D. W. T., Chem. Eng. Sci., 21, 305 (1966). Gaitonde, N. Y., Douglas, J. M., AlChEJ., 15, 902 (1969). Lasalle, J., Lefschetz, S., "Stability by Liapunov's Direct Method with Applications," p 31, Academic Press, New York, N.Y., 1961. Leucke, R. H., McGurie, M. L., lnd. Eng. Chem., Fundam. 6, 432 (1967). Luus, R., Lapidus, L., Chem. Eng. Sci., 21, 159 (1966). Perlmutter, D. D., AlChEJ., 12, 130 (1966). Paradis, W. O., Rajagopalan, Seshadri, lnt. J. Control. 17, 161 (1972). Takahasi. Y.. Rabins, M. J., Auslander, D. M. "Control and Dynamic Systems," p 131, Addison-Wesley, Reading, Mass., 1970. Takahasi, Y., Rabins, M. J., Auslander, D. M., "Introducing Systems and Control," p 232, McGraw-Hill, New York, N.Y.. 1974.
L i t e r a t u r e Cited Receiued for reuieu: J a n u a r y 22, 1976 Accepted October 26, 1976
Aris, R., Arnudson, N. R., Chem. Eng. Sci., 7, 121 (1958). Beek, J., AlChEJ., 18, 228 (1972).
Dynamic Spreading of Drops Impacting onto a Solid Surface Lung Cheng Pittsburgh Mining and Safety Research Center, U.S. Bureau of Mines, Pittsburgh, Pennsylvania 152 13
A theoretical and experimental study of the behavior of drops impacting onto a dry solid surface was conducted. For drop sizes and velocities typically encountered with high-pressure sprays, the impacting drop flattens or spreads and then undergoes dampened vibratory motion until it becomes quiescent. Assuming that the impacting drop forms a flat disk, a theoretical maximum dynamic spread factor is derived in terms of the Weber number of the spray and a correction factor C denoting deviation from the simple model. The optimum dynamic spread factor, and the value of C, depends upon the drop size and velocity and the nature of the drop and target surface. For water sprays impacting a dry, lightly dust-laden surface of bituminous coal, the dynamic coverage is about 10 times the static coverage because of the drop flattening upon impact; i.e., adequate dynamic coverage can be achieved without saturating the surface. In a lightly dust-laden surface, the impacting drops essentially completely scavenge the particles in the swept area.
Introduction The coverage of solid surfaces with impacting drops is important in many practical applications, such as foliage and animal spraying for pest control (Hartley and Brunskilll958; Cooper and Nuttall, 1915), drop printing (Carnahan, 1974), measurement of drop size (Cheng, 1977), dust control during mining (Strebig, 1975), road wetting, and numerous other operations. For many engineering purposes, the maximum coverage of the target with the minimum amount of spray is desired. When each drop emitted from a spray nozzle can reach the target surface, the coverage will depend upon the mass concentration of drops, the mean drop diameter, and the manner in which the individual drops spread over the surface after impact. Previous studies of drop impaction, e.g., Ford and Furmidge (1967) and Elliott and Ford (1972), have indicated that an impacting drop spreads and retracts in a vibratory manner and finally comes to rest as a sessile drop. With large, low-velocity drops, the vibration was essentially harmonic in nature. However, most practical applications use high-pressure water sprays, and the drops in these sprays are smaller and have a higher velocity than those hitherto studied. This paper examines the maximum spread of such drops upon impact, with the ultimate objective being to provide guidance for the selection of the line pressure and the type of spray nozzle t h a t gives maximum coverage for a particular engineering operation. 192
Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 2, 1977
This work is part of the research program being conducted by the Federal Bureau of Mines to develop advanced technology directed toward the control of respirable dust in underground coal mining operations and thus the elimination of coal workers' pneumoconiosis. Previous work (Cheng and Zukovich, 1973) has shown that immense amounts of respirable dust (nominally less than 10 pm in diameter) are adhering to ordinary run-of-face broken coal; e.g., enough respirable dust is adhering to 16 Ib of broken coal to contaminate 1 000 000 ft? of air up to the 2 mg/rn:j statutory limit if this dust should become airborne. Water sprays are often used in secondary mining operations to moisten the broken coal in order to reduce the dislodgment of this adhering dust. However, the use of excessive water often is to be avoided because of degradement of the heating value of the coal or the creation of physically uncomfortable conditions in the mine environment. Theory D r o p Spread. Consider a liquid drop perpendicularly impacting onto a solid nonabsorbing surface. We will assume a simple model where the impacting drop flattens into a symmetrical flat, thin disk with a circular profile a t the edge. The height of the flattened drop is h = 2d3/3D2, where d is the diameter of the spherical drop, and D is the diameter of the base of the flattened drop. The spreading of the drop due to impact is visualized as the compression of the fluid by a fic-
titious plate until equilibrium in the vertical direction is reached. The target is assumed to be a free surface that neither promotes nor impedes the liquid flow at the contact line. This model has been successfully used by other workers for force balance in studies of drops resting on a surface (e.g., Charles and Mason, 1960). The external force of the impacting drop causing its spread consists of the impact force and the gravitational force. For a flattened drop with its height in simple harmonic motion, the maximum vertical vibrational velocity u,,, is U,",,
=
v = Ycc
(1)
where 1' = impact velocity, 1' = amplitude of vibration = (I/?) (d - h ), and w = angular frequency of simple vertical harmonic motion. When the maximum acceleration at the zero vibratory velocity is Ycc?,the maximum impacting force F,,,, is F,,,,, = m Y o 2 = mV'/Y (2) where rn is the drop mass. The gravitational force is mg, where g is the gravitational constant. The opposing force is the extra
pressure AP inside the deformed drop and is given by the Laplace capillary equation P = o
where
0
(h'-+- DE,>
(3)
is the surface tension. At equilibrium
The maximum spread factor f of the flattened drop will be defined as the ratio of its maximum base diameter to that of the spherical drop. Assuming that D >> h and (Did) > 1, ey 4 reduces to
where p = drop density, p d V 2 / a = the Weber number, and g d / V ' = the reciprocal of the Froude number. These assumptions result in the value off being l o b less than its exact value for f = 4 and 3% less for f = 2. These errors are negligible for practical purposes. As water drops in sprays from highpressure nozzles typically have a small diameter and a high velocity, the second parenthetical factor is virtually equal t o unity. Therefore, for present conditions, eq 5 reduces t o
Table I. Time Required for Reaching a n Equilibrium %read Time required for equilibrium spread, s Impact velocity, cmls
-
57.8 80.6 354 1537
Drop diameter, Pn
2430 830 735 420
Measured 0.0042 0.00080 0.00028 0.00005 (est)
Calculated, TY/V 0.0044 0.00087 0.00027 0.000042
Specific S t a t i c Spread. The significance of dynamic spread on surface coverage can be deduced by comparing values of specific dynamic spread with those of specific static spread, which is defined here as the area coverage by a sessile water drop resting on the surface and subject only to interfacial and gravitational forces. Taking a contact angle of 57' as a mean value of advancing and receding for a quiescent drop a t the water-coal-air interface (Sun and Schwendeman, 1973), a spherical water drop about 5.8 mm in diameter has a maximum height of 2.6 mm when resting on a coal surface. A water drop larger than this size starts to form a flat top on the sessile drop (Coghill and Anderson, 1923;Padday, 1972). Water drops in high-pressure sprays have diameters far less than this value and therefore form spherical caps while resting on a coal surface. For such sessile drops, the base diameter is approximately a function of the diameter d and the contact angle 8 (Bikerman, 1941; Ford and Furmidge, 1967). For a quiescent drop with a mean contact angle 0 of advancing and receding, the specific static spread then is
and increases hyperbolically with decreasing drop diameter. A comparison of the dynamic with the static spread in terms of SJS, will be shown later.
Experimental Section Single, pure water drops of controlled size and velocity (200 to 1400 pm in diameter, 100 t o 2500 cm/s) were produced (Cheng and Cross, 1975) and vertically impacted onto a dry, horizontal target surface of bituminous coal from the Pittsburgh seam. The coal surface was roughly polished, resulting in multidirectional scratches ranging from 6 t o 14 pm in width. Since an actual impacting drop may deviate from a flat disk Qualitatively, high-speed motion pictures (to 7000 frame&) and a solid surface can never be free from interfacial effects, indicated that drops flattened on impact and that the flatwe will introduce a spread coefficient tened drop underwent oscillatory motion. With a medium impact velocity (-1500 cm/s), the impacting drop initially (7) tended to be a flat disk. Impacting drops initially tended to be plano-convex in shape a t lower impact velocities and where fE.,,]is the experimental value for the maximum spread plano-concave a t higher impact velocities. Vertical heights and of the impacted drop and f is the previously described theobase (horizontal) diameters of impacting drops were measured retical value. from the photographs. Figure 1 gives typical results. For Specific Dynamic Spread. Most engineering applications moderate drop diameters and low drop velocities (Figure l a ) , require knowledge of the coverage of the surface based on the mass of the sprayed liquid. Specific dynamic coverage S,,, the first several vibration cycles after drop impact corresponded to simple harmonic motion. However, for large drops defined as the measured area covered by an impacting drop (Figure l b ) or moderate sized drops at high impact velocities per unit mass of liquid, is given from eq 6 and 7 as (Figure IC),a dampened dissipative vibratory motion was observed. Table I gives the experimental times for an impacting drop to accomplish the first half cycle of vibration and the theoretical times from eq 1. T h e values are in close In this equation, the first factor involves material constants agreement, supporting the assumption of simple harmonic of the liquid, and the second factor involves dynamic variables motion for the early vibration behavior of an impacting and is called here a dynamic spread factor for specific coverdrop. age. Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 2, 1977
193
E E. II
Drop d i a m e t e r
, 830 p m
I m p a c t v e l o c i t y , 80 6 c m / s e c
2 W
I LL W
I5t
c z
W 0
+ Glass
1
Ford and u Cellulose a c e t o t e ] Formidge Beeswax (1967)
*
n
Q
a
- - - - Equolion ( 6 )
z
I O
LL W
IllI
+ W
0 3
8
1
8
1
05
1
I
1
,
I
'
:1
,
1 , :
2
4
6
810
20
30
pdv2
4
7 , io2
05
n
Figure 2. Dynamic spread factor vs. the Weber number for water
W Lo
drops impacting onto various solid surfaces.
4
m 0
I
3
2
5
4
6
T I M E , milliseconds
b
Drop diometer
, 2430 em
impact
, 67 8
velocity
Table 11. Spread Factors Measured at Various Drop Diameters and Impact Velocities Drop diameter, d , gm
E cm/sec
W
213
I Base diameter
300
W 0
468
618 0
10
20
30
40
50
60
918
TIME ,milliseconds 2 4 E E.
1,360
I-
I
2
2 0
W
I LL W W 0
n
z a LL W
c W
I2
Base diameter
oa
I
5
n w
Impact velocity, V, c m l s
1546 2038 2790 827 1517 1988 2233 284 439 879 1311 197 355 745 1015 216 403 552 676 164 274 380
Spread
factor, f e w
4.37 4.56 4.74 3.45 4.57 4.73 4.68 2.62 3.22 3.97 4.70 2.34 3.02 3.96 4.48 2.74 3.49 3.93 4.03 2.54 3.29 3.57
16
I-
z
04
m a m
0
0 4
0 8
12
16
20
24
TIME, milliseconds
Figure 1. Osillatory motion of a water drop impacting onto a coal surface.
In this study, main emphasis was given to investigating the maximum spread of the impacting drop using a stain method. A thin layer of magnesium oxide particles ( < 5 wm in diameter) was deposited onto the coal surface from the smoke of a burning magnesium ribbon using a modified version of the technique described by May (1950). Coverage was less than 10%.After drop impaction, microscopic observation indicated a sharp edge of the coating. The maximum base diameter 194
1
07 09
Coal
Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 2, 1977
measured with the stain method was identical with that directly observed with the high-speed photographic method. No difference in contact angle of a water drop on an uncoated or coated surface was detected using the drop-volume method (Bikerman, 1941). These measurements indicate that the very small amount of magnesium oxide used here was insufficient to produce changes in the physical characteristics of the target surface that affect water spreading. The stain method was much more convenient than the photographic method and was used here to investigate the maximum spread diameter of impacting water drops. Table I1 presents experimental results obtained by the magnesium oxide stain technique. Values of V and f e x r , are the mean values of 10 repeat measurements, for which the variation in impact velocity was 6% and the variation in the maximum value of the base diameter was less than 10%. Figure 2 plots f e x p vs. Weber number for water drops impacting a coal surface and includes theoretical values from eq 6 given. Previous data of f e x p for water drops impacting onto other solid surfaces (Ford and Furmidge, 1967) are also included. For water drops impacting onto a coal surface, the values of the dynamic spread factor predicted by eq 6 were in fair agreement with the measured values for Weber numbers ranging from 500 to 1000. However, the values of fen,, were
I
I
I
I
5000
1i
I00
c
-IN
'!901
N -
80
0
v
u.
0 5
T
8
031 I
L
3
4
v,
,
5 6 ' @ 9 1 3
ic
'6 O 0 L
1 :t
0 6
30
3c
I C ' , c - /set
F i g u r e 3. Spread coefficient vs. impact velocity of a water drop impacting onto various solid surfaces.
'O
t I00
higher than predicted for lower values of the Weber number and were lower than predicted for higher values of the Weber number. Other investigators have found values of fexp higher than predicted for water drops impacting onto various solid surfaces other than coal for low values of the Weber number (Figure 2 ) . The experimental value of the spread coefficient C was virtually independent of the drop diameter (200 to 1400 pm) but did depend on the impact velocity. Figure 3 shows that the observed value of C was approximately equal to 1.0 for an impact velocity of about 1500 cm/s but was greater than 1.0 for lower impact velocities and less than 1.0 for higher impact velocities. Such values agree with qualitative observations from the high-speed photography. T h e results of Ford and Furmidge (1967) also indicated a somewhat higher value of C for low impact velocities. No shattering or splashing of the impacting drop was observed for drop sizes and velocities studied here. A brief study of water drops impacting onto a water film whose thickness was greater than the diameter of the impacting drop indicated that splashing occurred for large drops or high impact velocities. For example, splashing occurred for 600-pm drops having an impact velocity above 600 cm/s and for 2 0 0 - ~ m / sdrops above about 1900 cm/s. T h e secondary drops formed during splashing always were much smaller than the original impacting drop, agreeing with the observations of Levin and Hobbs (1971). The present work used smaller drops and higher velocities than were used in previous studies (e.g., Worthington, 1963).
Discussion T h e present theoretical model analyzes the coverage of a target surface by impacting drops in a dilute spray and assumes that the impacting drop flattens to a maximum diameter and then undergoes dampened harmonic vibration until it becomes a sessile drop. (The model does not include the possibility of an impacting drop touching a previously deposited drop.) T h e model includes the factor C to denote deviation from the present simple model; i.e., a C greater than 1.0 was experimentally observed with low impact velocities, and a C less than 1.0 was observed with high impact velocities. The value of the specific dynamic spread as noted in eq 8 depends upon the square of the value of C, and C therefore must be known with some precision. While the present model hopefully provides a clearer understanding of dynamic spreading, a t present an experimental measurement of C is required.
200
300
400
500
6 0 0 700
800
9 0 0 IOCC
DROP DIAMETER , d , u r r
F i g u r e 4. Optimum drop diameter for various exit velocities of water drops impacting onto a coal surface a t a travel distance of 60.9 cm ( 2 fti.
I
110
- 1 I
I00 -
-i
1
90 -
4000
-
80
'0 -
c 4 a .,.
60
-
50
-
40
-
30 20
-
I0
I
0 I00
200
300
40C SROP
500
600
DIAMETER
700 d >
-
800
903
1000
m
F i g u r e 5. Optimum drop diameter for various exit velocities of water drops impacting onto a coal surface a t a travel distance of 91.4 cm (3 f t ).
The selection of spray nozzles for a desired coverage of a target depends upon the spray characteristics (mean drop size, exit velocity, and mass flow rate of liquid), the distance of the target from the spray nozzle, and also the relative motion between the spray nozzle and the target surface. When a water drop is emitted from a high-pressure nozzle, it is slowed due to drag from the environmental air. Its impact velocity for a given exit velocity and distance of travel can be calculated by standard techniques (e.g., Giffin and Muraszew, 1953). Figures 4-6 plot the dynamic spread factor against drop diameter for several typical exit velocities and travel distances. (According to Lane (1951), the maximum size of water drop t h a t can travel through air without breakup is 680 pm for a velocity of 3000 cm/s and about 400 pm for 4000 cm/s. Therefore, drops over these sizes for these velocities were Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 2, 1977
195
16OC
-1
\
12
: 40-
'\ ,.-a -. IO
8
.
vr
2 6
-
10
0 ZOO
~
l 400
;
1 600
DROP
l
l
1
800
1000
'
, E00
Disloncer of t r a v e l B .
91 4 crn
2
DIAMETER,^,,.^
0
Figure 6. Optimum drop diameter for various exit velocities of water drops impacting onto a coal surface at a travel distance of 121.9 cm (4 ft).
excluded in Figure 4.) The value of the dynamic spread factor and the specific dynamic coverage tends to increase as the exit velocity increases. However, as the drop size decreases, its impact velocity decreases while its dynamic spread factor increases. Therefore, a maximum value of the dynamic spread factor exists for a given travel distance (shown as dotted lines in Figures 4-6). For example, for a travel distance of 91.4 cm (3 ft), the optimum drop diameter for maximum dynamic spread is 630 pm for an exit velocity of 2000 cm/s and 500 pm for 3000 cm/s. Taking the density and surface tension of water as 1.0 g/cm' and 72 dyn/cm, the value of the specific dynamic coverage is 600 and 800 cm2/g, respectively. Figure 7 gives the specific static spread according t o eq 9 and shows the ratios of S d / S , for each of the optimum drop diameters for the three distances noted in Figures 4-6. The value of the ratio ranges from 6 t o 1 2 , with each curve having a maximum value resulting from the increasing steepness of the slope of the curves of the dynamic spread factor with decreasing drop diameter (Figures 4-6). Thus, an impacting drop sweeps an area about 10 times the area covered by the quiescent drop. Most practical situations involve a relative motion between the spray nozzle and the target surface, such as spraying of foliage from an airplane, a set of stationary sprays impacting broken coal on a conveyor belt, or even a set of stationary sprays impacting a stationary target that continuously generates new surface such as occurs when a continuous-mining machine cuts the coal face. Let W = mass flow rate of water through the spray nozzle and A = rate of change of the surface area of the target surface. Then, the mass concentration of water for the sprayed area is W / A ,and the degree of coverage achieved by dynamic spreading 6d is given by
sdw 6d = A
(10)
T h e value of dd can he preselected t o fulfill a coverage requirement. For example, taking & = 2 implies that all of the target area will, on the average, be dynamically covered twice by the impacting drops and is essentially a safety factor of 2. Consider a stationary spray nozzle giving a uniform spray that impacts target material carried by a conveyor belt. T h e degree of coverage is preselected to be 2.0 for impact coverage. Let the water line pressure be 80 lb/in.?, the distance between the nozzle and the target surface be 91.4 cm (3 ft), the spray covers a n area of 56 X 56 cm2, and the belt travels a t a speed of 200 cm/s (400 ft/min). Assuming a plain atomizing nozzle, the drop exit velocity is 3000 cm/s (Cheng, 1973). From Figure 5 , the optimum drop diameter for impact coverage is 500 pm, and consequently, the dynamic spread factor is 6800, which gives Sd = 800 cm2/g. Then, eq 10 gives W = 28 g/s (0.45 196
4
A - 6 0 9 crn
1
Ind. Eng. Chern., Process Des. Dev., Vol. 16,No. 2, 1977
100
300
700
500
900
d.pm
Figure 7. Specific static spread and ratio of specific dynamic spread to specific static spread of water drops on a coal surface.
gal/min). One then selects the spray nozzle that gives the mean drop size of 500 pm with the water flow rate of 0.45 gal/min and the stipulated geometry. Selection of nozzles giving mean drop sizes smaller or larger than 500 pm in the previously described case will require more water for the same coverage or will give less dynamic coverage for t h e same water flow rate. For example, if 6d = 2, a nozzle giving a mean drop diameter of 300 pm requires W = 0.6 gal/ min, whereas a nozzle giving a mean drop diameter of 680 wm requires W = 0.5 gal/min. Alternately, if W = 0.45 gal/min, the 300 pm nozzle gives a coverage of fid = 1.5, and the 680-pm nozzle gives 6d = 1.8. Thus a 40% deviation of the drop diameter from the optimum size will require 10 and 33% more water for the same coverage or will result in a 10 and 25% reduction of coverage for the same water flow rate. An increase in line pressure results in an increase in the dynamic coverage owing to a n increase in the exit velocity of the spray drops and a decrease in mean drop diameter. For example, doubling the line pressure in the aforementioned case leads approximately to a 25% increase in dynamic coverage. The effect of line pressure on coverage is more important for high line pressure because the dynamic spread factor is more sensitive to drop size for small, high-velocity drops (Figures 4-6). T h e user also must decide whether t o emphasize dynamic or static coverage. The static spread, 6,, is given by s s
w
As = -
(11)
A When 6. = 1.0, a sprayed surface, on the average, is saturated with water, and a further increase in W should lead to wastage due to water runoff. In the previous example, where dd was preselected to be 2.0, the optimum drop diameter was 500 pm. According to Figure 7, S d / S , = 10, and thus 6,is 0.2, indicating that optimum dynamic coverage is achieved although the sprayed surface is far from being saturated with water. The interaction between the impacting drop and the particles on a dust-laden target surface obviously superimposes complex processes onto the drop motion. The present results with a lightly dust-laden surface indicate that the small particles do not significantly interfere with the spreading motion of the large impacting drop and that the particles are scavenged by the spreading drop; i.e., the scavenged particles are mostly buried underneath the sessile drop although a few particles lie on the surface of the sessile drop. Previous work (Cheng and Zukovich, 1973) has shown that the respirable dust adhering to ordinary run-of-face broken coal corresponds, on the average, to two layers of particles or about -5-10 pm thick. Such a coating would have negligible
thickness compared with 4 0 0 - p m spray drops, and spray drops impacting onto such a surface may be expected to behave as described here. However, in practice, the surface of broken coal is a mixture of clean or very lightly dust-laden surfaces and thickly dust-laden surfaces. Recent work investigating the behavior of water drops impacting a dry, thick, dust layer on a coal surface has indicated the formation of a circular trench around a central mound of dust a t the impact point similar to the results reported by Engel (1955) with fine moist sand. More important, the smaller particles in the dust layer appear to be preferentially dislodged and become airborne. This work will be reported a t a later date.
Acknowledgments The author appreciates valuable suggestions given by W.
G. Courtney during preparation of the text. Experimental measurements were made by W. G. Cross. Literature Cited
Charles, G. E., Mason, S. G., J. CoIIoidSci., 15, 236 (1960). Cheng, L., Ind. Eng. Chem., Process Des. Dev., 12, 221 (1973). Cheng, L., Environ. Sci. Techno/., in press, 1977. Cheng, L., Cross, W. G., Rev. Sci. Instrum., 46, 263 (1975). Cheng, L., Zukovich, P. O., U.S. Bur. Mines Rep. Invest., 7768 (1973). Coghill, W. H..Anderson, C. O., U.S. Bur. Mines Tech. Paper 262 (1923). Cooper, W. F., Nuttail, W. H., J. Agr. Sci., 7, 219 (1915). Elliott, T. A., Ford, D. M., J. Chem. Soc., Faraday Trans. 1, 68, 1874 (1972). Engei, 0. G., "Waterdrop Collisions with Solid Surfaces," J. Res. Mat/. Bur. Stand., 54, 281 (1955). Ford. R. E., Furmidge, C. G. L., SOC.Chem. Ind., Monograph 25, Symp. on Wetting, 417 (1967). Giffin, E., Muraszew, A., "The Atomization of Liquid Fuels," Wiley, pp 10-14, New York, N.Y., 1953. Hartley. G. S.,Brunskiil, R. T.,"Reflection of Water Drops From Surfaces," Surface Phenomena in Chemistry and Biology," p 214, F. J. Danielli, K. G. A. Pankhust and A. C. Riddleford, Ed., Pergamon Press, New York, N.Y., 1958. Lane, W. R., "Ind. Eng. Chem., 43, 1312 (1951). Levin, 2.. Hobbs, P. V., Phil. Trans. Roy. SOC.London, 269, 5 5 5 (1971). May, K. R., J. Sci. Instrum., 22, 128 (1950). Padday, J. F., Proc. Roy. Soc. London, Ser. A, 330, 561 (1972). Sun, S.N., Schwendeman, J. L., Monsanto Res. Corp., Dayton, Ohio, unpublished information, Feb 1973. Strebig, K. C., CoalMin. Process., 12, 78 (1975). Worthington, A. M., " A Study of Splashes," Macmillan, New York, N.Y., 1963.
Bikerman, J. J., lnd. Eng. Chem., 13, 443 (1941). Carnahan, R. D., "Ink Droplet Printing Devices," presented at Tappi Reprographics Conference held at Carmel, Calif., Nov 1974.
Received f o r reuieu: January 28, 1976 Accepted September 2, 1976
Fluid Mechanic Considerations in Liquid-Liquid Settlers D. C. Drown and William J. Thomson' Department of Chemical Engineering, University of Idaho, Moscow, ldaho 83843
The dynamic characteristics of horizontal liquid-liquid settlers have been studied using three fluid systems of varying properties. It was found that the settlers could be characterized by three distinct regions: the entrance region, the dispersion zone region, and the exit region. Fluid mechanic measurements included studies of the expanding jet in the entrance region, of the velocity distributions (using laser velocimetry and cine-photographs) in the dispersion zone region, and vortex flow patterns in the exit region. It was found that the velocity distributions varied considerably from plug flow and that the dispersion zone was capable of absorbing momentum from both bulk phases. Based on comparisons under different flow conditions and with static coalescence rates, it was concluded that the dynamic coalescence rates were significantly enhanced by the deceleration of the dispersion zone. Some success was obtained by attempting to describe the observed phenomena with a simplified mathematical model.
Introduction Although gravity liquid-liquid settlers have been used commercially for many years, there is surprisingly little information available upon which to base an optimum design. While suitable design criteria exist in the case of dilute dispersions such as the separation of oil from refinery process waters, the same is not true for the concentrated dispersions which are normally encountered in liquid-liquid extraction systems. There have been a few studies directed toward scale-up criteria but these have usually been specific in nature and have yielded little in the way of a basic engineering understanding of the phenomena which govern settler performance. On the other hand, there have been a great many studies connected with basic interfacial phenomena and the interactions between single coalescing drops in isolated systems. While the latter is important in order to truly understand the physio-chemical phenomena occurring in liquidliquid settling systems, these studies usually bear little resemblance to the actual environment existing in commercial liquid-liquid settling applications. Thus, the motivation for
this work was not only to study the basic phenomena occurring in continuous liquid-liquid settlers, but to concentrate specifically on the influence of fluid mechanics on settler performance. There have been three different design criteria commonly used to scale up pilot plant models to industrial use. These three criteria are the residence time method, the overflow velocity method, and the dispersion thickness method. In the residence time method the design is based on pilot plant data or past experience with similar fluids and a similar type of settler construction. Using this method, settlers have been designed with residence times of anywhere from 5 min to 5 h (Treybal, 1963; Atkinson and Freshwater, 1958; Manchanda and Woods, 1968). This method also assumes plug flow and does not take into account either the geometry of the settler or the flow patterns within the settler. T h e overflow velocity method is based on the assumption that the rate of separation is controlled by the settling rate of the dispersed drops. Design is based on a residence time sufficient to allow for the drops to travel to the interface before exiting the settler. This Ind. Eng. Chem.,Process Des. Dev., Vol: 16, No. 2, 1977
197
