of radius explicitly and is not numerically suitable for flat plate cases of NGo= co .
per of White and Tallmadge (1967) are derived in Appendices 11 to 13.
Design Procedure for Film Thickness h,
Acknowledgment
The design procedure for h, is shown in Figure 10, as indicated by h, in the box in the top left-hand corner. As with A, the design procedure for h, involves the 0.3 and 3.0 criteria. I n the small cylinder region, however, the film may coalesce into droplets. The bounds of the film instability region are not accurately known, but some approximate values based on preliminary tests (White, 1965) are shown in Figure 10. Thus, film thickness is not directly meaningful in the droplet region. However, the theory has been verified by tests in the droplet region and is therefore useful for volume flow rate.
The suggestions by Chaim Gutfinger regarding evaluation of the F and Y functions were most helpful. Nomenclature = C, function, Equation 3, dimensionless D = dimensionless thickness, h(pg/u)’I2 F = F function, Equation 19, dimensionless h = thickness of film, h, or h, cm.
Restrictions and Extensions
R
In addition to the speed limit (Figure 2) and droplet restriction on h, (Figure lo), these equations are not applicable to non-Newtonian fluids. Although a wide variety of oils agree with theoretical predictions, there is some question regarding water. The water question may, however, be due to experimental technique. Glycerol and some aqueous solutions agree with the theory. Although the above theory is based on steady-state withdrawal, results are a surprisingly good approximation for predicting volumes on short objects, say 5 to 20 cm. long, if end effects have been considered. The steady-state theory should be applied with considerable caution for removal and transient withdrawal processes, unless end effects are well understood for the application studied. Further details on theory, experimental verification, fluids tested, restrictions, extensions, applications, and other references are given in the literature review of Tallmadge and Gutfinger (1967). Some tabular values of T oare available (White and Tallmadge, 1967). Details of some relevent proofs are given for the first time by Stella (1968)-the F and y power series are derived in Appendices 8 to 10 and approximations made in the theory pa-
u, u,
C,
4, h,
N N
T
= film thickness, cm. = flow thickness, Equation 9, cm. c= ~ caDillarv number. uU,,,/u G= ~ GouchLr number,’k(pg/2~)’’~
= radius of cylinder, cm.
= dimensionless thickness, h(pg/pUw)llz surface velocity at gas interface, cm./sec. cylinder withdrawal velocity, cm./sec. volume flow rate, Equation 8, cc./sec. = Y function, Equation 2, dimensionless
= =
v =
Y
GREEKLETTERS c c = viscosity, poises P = density, g./cc. u = surface tension, dynes/cm. Literature Cited
Hamming, R. W. “Numerical Methods for Scientists and Engineers,” p. 352, McGraw Hill, New York, 1962. Hildebrand, R. H., Tallmadge, J. A., A.Z.Ch.E. J . 14, 660 (1968). Stella, R. R., M. S. thesis (chemical engineering), Drexel Institute of Technology Philadelphia, Pa., June 1968. Tallmadge, J. A., Gutfinger, Chaim, Znd. Eng. Chem. 59, No. 11, 18 (1967); 60, No. 2, 74 (1968). Tallmadge, J. A,, Labine, R. A,, Wood, B. H., Znd. Eng. Chem: Fundamentals 4, 400 (1965). White, D. A., Ph.D. dissertation, Yale University, April 1965. White, D. A , , Tallmadge, J. A., A.Z.CI1.E. J . 12, 333 (1966). White, D. A., Tallmadge, J. A., A.Z.Ch.E. J . 13, 745 (1967). RECEIVED for review December 11, 1967 ACCEPTED April 29, 1968 Work supported by National Science Foundation Grant GK-1206.
EFFECT OF PLATE WETTABILITY ON DROPLET FORMATION L . G. H A Y N E S , D. M . H I M M E L B L A U , A N D R. S . S C H E C H T E R
The University of Texas, Austin, Tex. 78772 Experimental measurements of the size of drops formed through a circular orifice were made in three liquidliquid systems of varying interfacial tension. A well defined minimum in drop size was observed as a function of liquid flow rate. The magnitude of the wetting effect was large, but could not b e successfully correlated with the system parameters.
T IS
surprising that quantitative measurements delineating
I the effect of plate wettability on the formation of droplets a t
horizontal orifices have not been reported. This void is even more striking in view of the definite coupling which has been observed between mass transfer rates in liquid-liquid systems and the wettability of the packing or plates (Jackson et al., 1962; Norman et a[., 1964; Osman and Himmelblau, 1961 ; 508
l & E C PROCESS D E S I G N A N D DEVELOPMENT
Sobotik and Himmelblau, 1960). By using plates or packing with identical characteristics other than wettability in extraction columns, mass transfer can be enhanced, or reduced. The observed effects can be due only to the wettability of the column contents, as no other variable is changed. Indeed, visual observations have been reported in which a distinct qualitative variation in the drop size was observed as the system
Physical Properties of liquid-Liquid Systems
Table 1.
UAR.
System
Dvnes/Cm. at 25’ C.
A
B
Carbon tetrachloride Water Furfural
Water Benzene n-Heptane
45
35 7.2
PLATE GLASS PORTHOLE
I Y
.,
’-I-?-
3‘ S.S.TUBING
SWAGE -LOK-UNION
TO PUMP
Figure 1.
- PB,
G./MI. at 25” C.
PYREX TEE
I1
PA
Orifice plate arrangement
wettability was changed. Moreover, Buchanan (1952) observed the formation of single droplets and concluded that the growth of droplets and drop volume are functions of wetting. However, none of the aforementioned work has directly treated the effect of the adjacent surface on drop formation. I n view of the possible importance of wettability on drop formation in many areas of engineering practice, some recent work carried out in our laboratory is of interest. These d a t a indicate the magnitude of the wettability effect and the relative importance of the variables involved. Experimental Apparatus
Figure 1 depicts the experimental apparatus. The glass tee was filled with the heavier fluid and the less dense fluid was pumped through the bottom plate into the orifice, which was mounted on a stainless steel cylinder as shown. The pump was of the syringe type, capable of delivering a calibrated and steady flow of liquid. The average drop size reported here was determined by counting the drop frequency and dividing the frequency into the known flow rate. The orifice was mounted so that photographs could be taken through a piece of flat glass mounted as shown in Figure 1. Photographs were taken both when a droplet formed
0.587 0.123 0.482
Solubility
Solubilitv
of A in B, G./700 G.
of B in A , G./700 G.
e’, cm.UAB
0.08
...
12.8
...
0.82 8.8
3.44 65.6
0.91
(dynamic state), and when the droplet was rendered stationary by stopping the flow of less dense liquid. Photographs of the stationary state were used to determine the contact angle. Three liquid-liquid systems were studied: benzene-water, water-carbon tetrachloride, and n-heptane-furfural. The pertinent physical properties of these systems are given in Table I, most of the values being taken from the literature (Dreisbach, 1955, 1959; Hodgman et al., 1956; Kirk and Othmer, 1951; Seidell and Linke, 1952; Weissberger, 1955), except for the interfacial tension of the furfural-n-heptane system which was obtained by experiment using the drop weight method as outlined by Adamson (1960). The systems were selected to cover a wide range of both contact angles and the grouping ( g A p / a A B ) , the latter of which varied from 3.44 to 66 cm.-2 for the liquid-liquid systems used. These two parameters were considered important because their values determine the equilibrium shape of a droplet of a given volume adhering to a flat plate (Staicopolus, 1962). Three orifice plates surfaces were tested-constructed of Teflon, brass, and aluminum-all being 2.25 inches in diameter, I/z inch thick, and having a n orifice diameter of inch. Each plate was first sanded with fine emery paper, all the scratches running in the same direction. Then the orifices were polished using a rotating cloth wheel. Red rouge was used to remove most of the scratches, and the red rouge was then removed from the wheel by applying a rotating wire brush. A finer polishing compound, yellow rouge, was then applied to the wheel, and the orifice plates were polished to a mirror finish with no noticeable scratches on the surface around the orifice. The Teflon plate could be polished as readily as the brass or aluminum plates, although more care had to be taken in applying the plate to the rotating wheel because of the heat buildup. Experimental Results
Figures 2, 3, and 4 show the droplet volume plotted as a function of flow rate for each liquid-liquid system studied. There is a well-defined trend in which increasing droplet volumes were found to correspond to increasing contact angles. Since the contact angle is the angle between the orifice plate and a tangent to the liquid-liquid surface constructed at the three-phase boundary (the angle being measured through the external liquid phase), this observed trend is not entirely unexpected. Fluids exhibiting larger contact angles tend to spread along the surface of the orifice plate before growing into sizable droplets which, under the action of gravity, break away from the orifice plate. Fluids with very small contact angles appear to grow out of the orifice itself without spreading along the surface of the plate. Consequently, fluids having the larger contact angles create droplets from a “base of fluid” which is much larger than the orifice, giving rise to much larger droplets than is possible for fluids which form into droplets solely from the orifice hole. The base of fluid remains on the surface of the orifice plate after a droplet breaks away and the next droplet begins to grow from this base. VOL. 7
NO. 4
OCTOBER 1 9 6 8
509
-
3 w
s
A
-
$ 0.15 -
+ ALUMINUM
A BRASS
0.00 0.0
.TEFLON
0.8
1.6 2.4 3.2 FLOW RATE (ML. PER MIN.)
4.0
Figure 4. Droplet volume as function of flow rate and contact angle for water-carbon tetrachloride system
0.01:
0.0IO
TEFLON
A BRASS
c:
2
ALUMINUM 0.00t
c
w
--
8=llS0
4
d >
L 8
O.OOE
8 =91.8'
4
a
0.004
n
0.002
0.000 0.0
0.1
0.2 0.3 0.4 FLOW RATE (ML. PER MIN.)
0.5
Figure 3. Droplet volume as function of flow rate and contact angle for n-heptane-furfural system
Although the trend is not unexpected, the magnitude of the wetting effect on droplet size is in some cases surprisingly large -for example, the droplet volumes of the benzene-water system decrease by a factor of 10 when the aluminum orifice plate is substituted for Teflon. Smaller magnitudes were observed for the other two systems. Attempts have been made to correlate these data, but without success. The correlations relating to droplet formation which are most often cited, those of Hayworth and Trebal (1950), Null and Johnson (1958), and Scheele and Meister (1968), pertain solely to growth a t nonwetted nozzles and cannot apply to the formation of droplets on wetted or partially wetted horizontal orifices, since neither of these correlations includes the contact angle as a parameter. I n the case of drops forming 510
I&EC P R O C E S S D E S I G N A N D D E V E L O P M E N T
on horizontal thin-walled nozzles it is not surprising that the results are almost independent of the contact angle. Indeed, the drop volume method of computing the interfacial or surface tension does not contain the contact angle as a parameter. The Harkins and Brown correction factors (Harkins and Brown, 1919) make no allowance for contact angle. If the external phase preferentially wets the material used to construct the nozzle, the inside diameter of the nozzle is used as the characteristic dimension. If not, the outside diameter is taken as characteristic. For sessile drops and bubbles, Jakob (1936) has given a relationship between the maximum size of a bubble and the contact angle. His correlation does not, however, provide a means of determining that fraction of the unstable mass which will actually break away from the supporting plate. I t is the prediction of this quantity that is of interest, and has not yet been published, but the results reported here indicate that any successful correlation will be complex. I n addition to the large effect of the contact angle on the size of the droplet, a second interesting result of this study was the existence of a minimum in the droplet volume as the flow rate was increased. A similar observation was reported by Maier (1927) in a study of bubble formation. This minimum is to be contrasted with the two maxima found by Xu11 and Johnson in their investigation of nozzles. Maier gives a qualitative explanation for the existence of a minimum, but does not treat the phenomenon quantitatively. The contact angles reported here were measured by arresting the flow of fluid, photographing a stationary drop, and measuring the contact angle from the photographs. Several photographs were taken during each run and the measurements repeated. A hysteresis effect could exist in contact angle measurements, depending on whether the three-phase intersection is advancing or receding, and all our measurements were of receding angles, since the drop was formed and then reduced very slightly in size before photographing. The angles reported here are averages and the technique of measurement incorporates some error. The variability of the water-carbon tetrachloride system, which was the largest deviation noted, ranged from 69.5' to 60.1". We claim an accuracy of 8y0 in the reported angles.
Conclusions
T h e contact angle plays a n important role in governing the size of droplets formed a t a horizontal orifice, and existing correlations for nozzles are entirely inadequate as a means of predicting the droplet volumes for wetted or partially wetted orifices. Because smaller drop sizes result in higher over-all rates of mass transfer this study confirms the advantages of maintaining nonwetting conditions in sieve trays and orifices in liquid-liquid extractors. Nomenclature
g
acceleration of gravity density of liquid phase designated by subscripted variable Ap = density difference between liquid phases uAB = interfacial tension between liquid phases = =
p
literature Cited
Adamson, A . W., “Physical Chemistry of Surfaces,” p. 25, Interscience, New York, 1960. Buchanan, R. H., Australian J . Appl. Sci. 3, 233 (1952). Dreisbach, R. R., Advan. Chem. Ser., No. 15, 11 (1955).
Dreisbach, R. R., Advan. Chem. Ser., No. 22, 24, 197 (1959). 41, 499 (1919). Harkins, W. D., Brown, F. E., J . Am. Chem. SOC. Hayworth, C. B., Trebal, R. E., Znd. Eng. Chem. 42, 1174 (1950). Hodgman, C. D., Weast, R. C., Selby, S. M., eds., “Handbook of Chemistry and Physics,” 38th ed., Chemical Rubber Publishing Co., Cleveland, Ohio, 1956. Jackson, M. L., Holman, K. L., Grove, D. S., A.Z.Ch.E. J . 8, 659 (1962). Jakob, J., Mech. Engr. 58, 643 (1936). Kirk, R. E., Othmer, D. F., eds., “Encyclopedia of Chemical Technology,” Vol. 6 , p. 996, Interscience Encyclopedia, New York, 1951. Maier, C. G., U. S. Bur. Mines, Bull. 260 (1927). Norman, W. S., Cakalog, T., Fresco, A. Z . , Sutcliffe, D. H., Trans. Znst. Chem. Engrs. (London) 42, 61 (1964). N u l l , H . R . , H . F . Johnson, A.Z.Ch.E. J . 4 , 2 7 3 (1958). Osman, F., Himmelblau, D. M., J . Chem. Eng. Data 6 , 551 (1961). Scheele, G. F., Meister, B. J., A.Z.Ch.E. J . 14, 9(1968). Seidell, A , , Linke, W.F., “Solubilities of Inorganic and Organic Compounds,” 3rd ed., Suppl., p. 1091, Van Nostrand, New York, 1952. Sobotik, R. H., Himmelblau, D. M., A.Z.Ch.E. J . 6 (No. 4), 619 (1960). Staicopolus, D. N., J . Colloid Sci. 17, 439 (1962). Weissberger, A,, “Technique of Organic Chemistry,” Vol. VII, “Organic Solvents,” 2nd ed., Interscience, New York, 1955. RECEIVED for review January 18, 1968 ACCEPTED April 22, 1968
CATALYTIC CRACKING OF ACETIC ACID T O ACETIC ANHYDRIDE N A R A Y A N A N P A D M A N A B H A N , P . K. D E S H P A N D E , A N D N . R . K U L O O R Department of Chemical Engineering, Indian Institute of Science, Bangalore- 12, India
Catalytic cracking of acetic acid using triethyl phosphate and silica gel catalysts was investigated. The desired reaction leading to ketene i s accompanied b y side reactions: two parallel with respect to acetic acid decomposition and the consecutive ketene decomposition reactions. Effect of temperature, catalyst concentration, space velocity, and pressure was studied in detail. Triethyl phosphate was found to be a much better catalyst than silica gel. The optimum yield of ketene was obtained at 750’ C., 100 mm. of Hg pressure, and apparent contact time of 5.687 X 1 0-4 hour.
anhydride is extensively used in the cellulose acetate industry. I t also finds application in the manufacture of aspirin, phenacetin, and other drugs, perfumery chemicals, dye intermediates, flavor bases, explosives, and plastics. T h e “ketene process,” using acetone or acetic acid as the raw material, is widely used for the manufacture of acetic anhydride. Acetic acid is a by-product of acetylation in the cellulose acetate industry and, since about 75% of the acetic anhydride produced is used in this process, acetic acid has a n edge over acetone as a raw material. Available data on the kinetics of the catalytic cracking of acetic acid are very meager and hence the present investigation was made. CETIC
A
Chemistry of Process
The gross reaction of the formation of acetic anhydride from acetic acid 2CH3COOH * (CH&O)20 H2O (1)
+
is a two-step process and proceeds via ketene. CH3COOH CH3COOH
+
CH2:CO
+ CH2:CO
+ H2O
(2)
(CH3CO)zO
(3) I n addition to Reaction 2, acetic acid and ketene decompose according to the following reactions: CH&OOH VOL 7
-+
+
CHI
+ COz
NO. 4 O C T O B E R 1 9 6 8
(4) 511
