Liquid Films in the Viscous Flow Region - Industrial & Engineering


The development of nonlinear waves on the surface of a horizontally rotating thin liquid film. D. J. Needham , J. H. Merkin. Journal of Fluid Mechanic...
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Liquid Films in the Viscous Flow Region .

In the case of flow of liquid films bounded by solid and essentially static air interfaces, a third type of flow called “pseudo-streamline” has been found to exist between Re 25 and Re 1500. This type of flow is characterized by the appearance of waves in the liquid film and by a much higher interfacial velocity than that predicted by streamline flow equations. However, the Reynolds number-friction factor correlation for true streamline flow is applicable in this region.

S . J. FRIEDMAN AND C. 0. MILLER Case School of Applied Science, Cleveland, Ohio

I

T H E general field of diffusional processes, including absorption, extraction, heat transfer, humidification, and distillation, the flow of thin liquid films is often encountered. Filmwise condensation in condensers and in heat exchangers and the flow of one phase in packed or wetted-wall columns involve the formation and flow of thin liquid films. I n the case of absorption where the gas film is controlling, the flow characteristics of the liquid, when given a constant area of contact, do not appreciably enter into the factors influencing the efficiency of operation. However, in the treatment of filmwise condensation or in diffusional processes, where both liquid and gas films or the liquid film alone is controlling, the flow characteristics of the film liquid have a definite bearing upon the efficiency of the operation. The more exactly the film thickness, interfacial velocity, and average velocity of the film liquid can be evaluated, the more precisely the mass transfer or heat transfer data can be analyzed. Two general types of fluid flow are well known-namely, streamline or viscous flow and turbulent flow. The case of viscous flow may be analyzed rigorously from a mathematical standpoint, if all of the variables involved can be evaluated. Turbulent flow, on the other hand, has proved t o be such a complex mechanism t h a t all correlations have been based on experimental data. I n the case of flow of fluids through circular pipes, sufficient evidence exists t o prove the mathematical theory behind the viscous flow equations, and much investigation has been carried out in the correlation of turbulent flow data. Although some work has been reported on the flow of liquid films (2, 8 , 6), and considerable data are available in the turbulent region of flow and the transition region just preceding it, the data in the viscous range, particularly of low-viscosity liquids, are sparse. The data available indicate only that the transition from streamline t o turbulent flow occurs in the region of Reynolds number 1500 and prove roughly the validity of the mathematical laws governing this type of flow. No attempt has been made, however, t o measure directly the velocity a t the liquidgas interface. Since films in viscous flow are often encountered in wetted-wall towers, packed towers, and condensers, it was thought advisable to investigate this region more thoroughly and t o prove whether mathematical treatment was strictly applicable in this region. _U

case when a stationary air core is used, the relation between film thickness and flow rate may be represented by

It is also true that the velocity, v, in the film a t any distance, x, from the wall is represented by the equation

From this equation it is evident t h a t a parabolic velocity distribution is t o be expected in the liquid film. If such is the case and if the velocity at the interface is postulated t o be the maximum velocity (i. e., if no tractive force is exerted at the liquid-gas interface as would be expected with a stationary air core), Equation 1reduces t o (3)

and Equation 2 reduces t o (4)

Comparison of average velocity V , calculated from Equation 3, t o the interfacial or maximum velocity, U , obtained from Equation 4,yields the relation

U

=

1.5V

(51

Use may be made of the plot of Reynolds number vs. the Fanning friction factor in the case of film flow as well as in the case of flow in conduits. I n the case of film flow these two quantities may be represented as follows:

Re 4Q P / P (6 ) f = 2 qm3/&2 (7) It is also evident from Equations 3, 6, and 7, t h a t in the case of viscous flow with no tractive force a t the liquid gas interface,

Previous Work Theoretical equations for the streamline flow of films down tubes are easily derivable from the definition of viscosity (3). I n the case of wetted-wall towers where no bouyant effect is exerted by the nare fluid on the wall fluid, as is essentially the

f = 24/Re (8) Considerable work has been done by investigators on the film thickness of liquids in film flow bounded on one side by a 885

886

INDUSTRIAL AND ENGINEERING CHEMISTRY

liquid-solid interface and on the other by a liquid-gas interface. Hopf (4) and Schoklitsch (6) studied the flow of water along an inclined plane; Chwang ( 2 ) investigated the flow of water and oil on a flat glass plate; Claassen (1) examined the flow of water down the outside of a steel t u b e ; Willey a n d Cooper ( 2 ) studied the flow of dilute sulfuric acid solutions inside of glass tubes; and Warden (2) investigated the flow of water down glass and brass tubes. The data of Warden (2) and Willey and Cooper ( 2 ) are perhaps best of those cited. These d a t a were well correlated b y Cooper, Drew, FIGURE1. DIAGRAM OF APPAand McAdams (2) in RATUS a plot of Reynolds number vs. friction factor. Fallah, Hunter, and Nash (3) recorrelated these data together with measurements of their own for the flow of water inside glass tubes in somewhat the same manner. In all of the above cases, with the exception of Hopf (4),Schoklitsch (6), and Chwang ( 2 ) who studied t h e flow on flat surfaces, the average film thickness was measured by stopping the flow of the liquid and measuring the amount of liquid on the tube when the flow stopped. From these investigations i t was concluded t h a t the change from Viscous t o turbulent flow occurred a t about Re 1500 since for all values of Re below 1500 the plot o f f us. Re fell along the line f = 24/Re. This result, in light of the preceding theory, would tend t o indicate t h a t a parabolic velocity gradient existed through the a m when viscous flow existed and that the velocitv at the liquid-gas interface was a maximum at a value of U =

indicate a change in the type of flow a t Re 8 when film thickness was actually measured. The investigation described here offers a n explanation of the results of Kirkbride by postulating a pseudo-critical flow point a t Re 20-30 for the flow of liquids bounded b y a solid and essentially static air interfaces. A t this point waves begin to form in the fluid film, and the velocity distribution within the film changes.

Experimental Procedure The apparatus setup is shown in Figure 1. The tube down which the li uid flowed was; a d o o t Pyrex tube, B, sealed at onej”end and ground perfectly plane and perpendicular to the axis of the tube at the other end. Extreme care was exercised in the grinding of this tube so that no variation of flow characteristics would occur around the periphery. B o t h a 1.00-inch and a 0.626-inch tube were utilized to make certain that the phenomenon occurring was not a function of the tube diameter. This tube was mounted on two turnbuckle FIGWRE 2. MODIFICATIONS OF APPAsupports by means RATUS of which the tube could be made Derfectly vertical, as was found t o be necessary. The top of this tube was jacketed with a 2-inch Pyrex tube, A , about 12 inches long, properly supported and connected to t h e main tube at the bottom by a rubber stopper, E , sealed with a Bakelite varnish. The inlet liquid line entered at the bottom of this jacket which acted as a calming section, and the liquid flowed upward in the jacket, over the edge of the inner tube and down its inside surface. The liquid was supplied from a 5-gallon constanthead reservoir carboy, D,placed about 3 feet above the top of the main tube. The liquid flowed by gravity out of the carboy into

1.5 V . However, when Kirkbride ( 5 ) measured the film thickness with a micrometer arrangement of water and hydrocarbon oils flowing down the outside of a vertical tube, he found that ripples which started to occur a t Re 8 tended to make his results deviate positively from theoretical film thicknesses. These same waves were noted b y Fallah, Hunter, and ”ash (3) in their investigation at even their lowest flow rates (Re about 200). No attempt has been made to explain these apparently anomalous results of Kirkbride (6) which seemed to

Vol. 33, No. 7

THICKNESS ws. PLOW RATE FIGUE~: 3. FILM

July, 1941

INDUSTRIAL AND ENGINEERING CHEMISTRY

887

the jacket through glass tubing into which a rotameter, C, was connected. The liquid was removed from the bottom of the tube into a suitable receiver by a glass line, F , sealed into the bottom of the main tube. No attempt was made to jacket the tube since the effect of temperature on the density and viscosity of the fluids studied was well known, and the proper value of these quantities could be used on runs made at various temperatures. The liquids studied were water, kerosene, toluene, and a light paraffin oil. The physical characteristics of water and toluene were obtained from the International Critical Tables, while those of kerosene and the paraffin oil were determined in the laboratoryat 20°, 25', and 30" C. and interpolated for temperatures within this range. The densities were determined in 50-ml. calibrated pycnometers and viscosities with a modified Ostwald viscometer. Values for the densities ando viscosities of the liquids studied are given for 20 , 25', and 30" C. in Table I. The rotameter was calibrated for each $of the liquids studied. In order to measure the maximum velocity within the liquid film as it traveled down the side of the glass tube, the apparatus was modified as shown in Figure 2A. A dro ping funnel, G, was mounted L A S S TUEE directly above the tuie, and attached to the dropOM QLASS TUBE ping funnel was a small length of 7-mm. tubing, INOM Q L A S S T U E E one end of which was drawn to a fine curved I N I - I N C H Q L A S S TUBE capillary point, H . The end of the curved ca il lary tubing was allowed to contact the fluid firm: and the whole was supported so that it could be iotated 360' about the vertical axis. Marker J R E Y N O L D S NUMBER - Re was placed 1.5 feet below the top of the main tube, and another marker, K , was placed exactly 2 feet below the first one. By filling the droppin funnel FIGURE 4. FRICTION CHARTUSINGAVERAGE PROPERTIES with a suitable dye solution and turning t t e stopcock of the funnel rapidly, a small drop of colored fluid could be inserted into the moving film, and the velocity of the color downward between the two markers nite time interval (the time necessary to make the velocity could be clocked. determinations). The outlet temperature of the liquid was measBefore a run was started, the tube was thoroughly cleaned ured so that correct values of density and viscosity could be used with chromic acid solution and washed with water; and in the in the calculations. runs using toluene, kerosene, and paraffin oil, it was also washed To determine the average fdm thickness, the dropping funnel with alcohol followed by carbon tetrachloride. Finally all lines arrangement was removed from the a paratus and was replaced, and the tube were filled completely with the liquid being studied. as shown in Figure 2B, by a sealed 6-root piece of 16-mm. Pyrex To start a run, the inlet liquid stopcocks were opened before the tubing, L,clamped concentrically within the 1-inch tube. T h e outlet sto cock so that the tube wall was always covered b outlet water line was fixed a t a definite height and a scale, M , liquid. I f this was not done, channeling frequently occurrei was placed behind the two tubes so that liquid levels below the especially with water as the liquid. to of the tube could be easily measured. $he apparatus was cleaned and the flow rate set in the manner previously described, particular care being taken that the liquid flowed only down the outside tube and did not channel TABLE I. DENSITIESAND VISCOSITIES between the two concentric tubes. The outlet liquid line was so --Density, Grams/Cc.--Viscosity, Centipoisesarranged as to obtain a minimum reading of the 11 uid level under Material 20' C. 25' C. 30' C. 20' C. 26' C. 30' C. dynamic conditions on the scale. When this lev3 had reached a Water 0.9982 0.9971 0.9957 1.005 0.8937 0.8007 constant value, the hei h t on the scale was noted. After a suitLubeoil 0.8781 0.8750 0.8718 32.73 26.08 20.41 able time interval the flow of liquid in and out of the tube was Kerosene 0.7836 0.7800 0.7764 1.003 0.930 0.867 stopped simultaneously and the tube was allowed to drain 5 minToluene 0.8657 0.8610 0.8564 0.5903 0,5547 0.6229 utes. The increase in height of the liquid m the tube was then read from the scale. Then the volume, B, of liquid on the tube wall when flow was stopped, exclusive of that amount which adThe outlet liquid line was then clamped so that a 6-inch column heres to the wall under static conditions, can be represented by of liquid remained in the bottom of the tube and the desired flow rate, as indicated by the calibrated rotameter, was then set by B = ?r (R2 - rz) AH adjustment of the inlet stopcock. A suitable dye solution was placed in the dropping funnel, and the stopcock of the funnel To obtain the volume of li uid which adhered to the tube was turned once rapidly. A stop watch was started when the under static conditions, a simiyar piece of 1-inch Pyrex tubing, first trace of dye reached the upper marker and stopped when the mounted vertically wa8 allowed to undergo the same cleansing first trace of dye reached the lower marker 2 feet below. By obprocess, then was killed with the liquid being studied, emptied, serving the time of fall, the maximum velocity within the film and allowed t o drain for 5 minutes. The inside of this tube was a t that particular point on the periphery could be calculated. wiped dry with tared pieces of cotton toweling, and the increase However, if the tube was out of alignment with the vertical as in weight of the toweling was taken as the amount of liquid adlittle as 0.10 inch in 5 feet, the velocity a t various points on the hering to the tube. Five determinations were made and the periphery differed as much as 100-200 per cent, depending upon average value was taken. From this the amount of liquid adthe flow rate. Consequently, a traverse around the inside of the hering per unit length of 1-inch tubing could be easily calculated. tube was made which consisted of three separate velocity deterIt was found that the empirical equation, minations in each of the four quadrants. The average of the twelve determinations was then taken as the maximum velocity C = 1.16 ( p / p ) l / * a t the given flow rate. This traverse served to indicate that the tube was in a vertical position and also yielded a correct mean would represent the data within 5 per cent for liquids adhering value for velocity. Runs in which the velocities in the various to a &foot piece of 1-ingh tubing after 5 minutes of drainage. quadrants differed by more than 25 per cent were discarded. It is possible that this equation would hold for glass tubes of The average volume flow rate of the liquid was determined by other dimensions if the liquid adhered in an unbroken film over measuring the amount of liquid passing down the tube in a defithe entire surface of the tube.

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INDUSTRIAL AND ENGINEERING CHEMISTRY

888

By adding the volume of liquid clinging t o the tube wall to the volume found by increase in the liquid level in the tube, the total volume of liquid on the tube wall could be ascertained. Knowing the height and the periphery of the tube over which the liquid film flowed, the average film thickness could then be calculated. The volume flow rate was measured by the amount of liquid obtained in the outlet receiver over a definite time interval, and from this the average velocity of the film could be calculated. The outlet liquid temperature was measured so that correct values of densities and viscosities would be used.

Viscous Flow Data The data obtained for average film thickness, average velocity, and maximum velocity of the four liquids are listed in Tables I1 and 111. The results for the average value of film thickness are shown in Figure 3. Included are some of the data of Warden (a), Willey and Cooper @),and Fallah, Hunter, and Kash (3). All of the points plotted lie in the flow region where the Reynolds number is less than 1000, so that viscous flow is to be expected. From this ilm graph it is apparent that the average f thickness of the liquids follows closely the viscous flow Equation 8 which resolves into log 7?2 = '/s log 62 ( d P ) - l / 3 1% ( 9 / 3 ) when transposed into logarithmic coordinates. Within the limits of experimental error, the points lie on this line and thus show that the data obtained are in agreement with those of other investigators when the average film thickness is used for values of Reynolds number less than 1000. T o show more conclusively the agreement of these data with the accepted equations of viscous flow, the Reynolds number was plotted against the friction factor as shown in Figure 4. The experimental points fall along the line f = Re/24, which is the theoretical equation for viscous flow. This agreement is excellent up to Re 500, which was the highest rate of flow studied. Data of other investigators in this region are also included. The results plotted in Figures 3 and 4 bear out the work of Cooper, Drew, and McAdams (a), and show that, when average properties of the film are utilized to evaluate the Fanning friction factor, turbulence does not begin until a value of Re > 1000 is reached. Wave motion began to appear in the film at very low flow rates for water, kerosene, and toluene, but did not appear in the oil film until very high flow rates were reached. Owing to the high viscosity of the oil, the flow rate necessary to produce the characteristic ripples was very fast, and under these conditions i t was impossible to measure average film thickness or maximum velocity with the present apparatus; hence, only qualitative observations could be made. The appearance and disappearance of the wave motion within the film seemed to occur a t a fixed flow rate for a given liquid, yet the data could be correlated by the equation

Q

= p9m3/3p

Vol. 33, No. 7

TABLE11. AVERAGEFILM THICKNESS AND Temp.,

c.

Vol. Flow R a t e Q, Cc. /Cm./ Sec.

Film Thickness ;M Cm. 2 1 0 2

Av. Velocity V,

Cm./Sec.

(TYPICAL DAT.~)

X'ELOCITY

ir/p

x

102

Reynolds No. Re, 4Qp/~

Friction Factor f , 2 ~ni3//Q~

Water inside a 1.00-Inch Glass Tube 27.8 27.0 25.0 25.0 25.0 25.0 24.2 25.3 23.0 26.0 25.5 25.0 25.5 25.2 25.2

0.123 0.184 O.OS73 0.0595 0.106 0.242 0.306 0.175 0.368 0.0095 0,0229 1.105 0.450 0.857 0.625

23.2 23.0 24.6 24.6 24.6 24.5 24.5 24.2 24.0 24.0 24.0 24.0

0.1670 0.1442 0.306 0.0068 0.282 0.209 0.1792 0.229 0.254 0.1025 0.0634 0.345

1.51 1.70 1.29 1.11 1.47 1.98 2.01 1.69 2.26 0.589 0.822 3.24 2.27 2.82 2.50

8.12 10.82 6.80 5.38 7.25 12.25 15.28 10.30 16.28 1.61 2.79 34.1 19.80 32.1 25.0

0.843 0.857 0.897 0.897 0.897 0.897 0.913 0.891 0.938 0.877 0.887 0.896 0.886 0.893 0.893

58.2 85.8 39.0 26.5 47.5 108.0 134.0 78.3 157.0 4.3 10.3 494.0 203 384 280

0.449 0.284 0.548 0.752 0.547 0.259 0.169 0.314 0.168 6.35 2.07 0.0549 0.114 0.0602 0.0787

Oil inside a 1.00-Inch Glass Tube 5.60 5.32 6.72 1.76 6.37 5.90 5.80 6.17 6.37 4.68 3.92 6.96

2.98 2.71 4.55 0.388 4.42 3.53 3.20 3.72 3.98 2.19 1.630 4.95

32.4 32.7 30.35 30.35 30.35 30.5 30.5 31.0 31.2 31.2 31.2 31.2

2.05 1.888 4.03 0.900 3.71 2.74 2.35 2.96 3.25 1.314 0.799 4.42

11.93 14.23 6.56 22.8 6.38 10.82 10.73 8.76 7.86 19.30 29.8 5.56

OF MAXIMUM VELOCITYTO AVERAGE TABLE111. COMPARISON VELOCITY(TYPICAL DATA)

Temp.,

C.

VOl. Flox Rate Q, Cc./Cm./ Sec.

Max. Velocity

Reynolds

U,

lo2

U(P/P)

VWP)

NO. R8.

(Calcd.)

U/V

Water down a 1.00-Inch Glass Tube 0.918 0.1412 0.0755 15.4 0.1700 0.918 0.0805 16.5 0.201 24.1 0.907 0.0893 0.0980 0.0630 10.5 0.928 0.0722 0.903 0.0488 8.00 0.0777 0.597 0.0510 8.70 0.1047 0.907 0.0637 11.6 0.1487 10.4 0.903 0.0755 0.0802 0.0527 9.02 0.888 0.0328 0.0458 0.888 5.16 0.1823 0.0843 20.5 0.888 0.1522 0.0637 0.840 18.1 0.1363 0.284 0.840 33.8 0.1050 0.0653 12.6 0.840 0.1913 0.0863 0.857 22.3 0.0770 0.0547 0.897 8.58 0.252 0.1308 0.897 30.3 0.0770 0.1452 0.893 16.2 0.250 0.1147 0.899 28.1 0.203 0,0990 22.8 0.889

1.87 2.11 2.25 1.56 1.42 1.53 1.64 1.97 1.52 1.40 2.16 1.82 2.08 1.62 2.22 1.41 2.08 1.89 2.18 2.05

55.0 60.5 72.8 41.0 29.4 30.0 42.8 51.8 34.1 16.8 69.5 76.2 158.0 52.6 77.2 35.7 134.2 59.6 105.6

2.10 2.09 1.76 1.37 2.08 2.03 1.74 1.68 1.38 1.55 1.50 1.27 1.75 2.32 1.99 1.70 1.63 2.23 2.17 2.01

85.8 68.9 53.1 27.8 99.0 69.2 55.3 26.6 35.2 37.0 26.0 17.0 55.9 72.3 58.9 39.5 27.4 86.3 78.1 56.4

1.54 1.58 1.64 1.50 1.56 1.60 1.57 1.56 1.55

3.14 2.14 5.01 1.48 3.48 4.60 4.50 3.77 2.48

Cm./Seo.

24.0 24.0 24.5 23.5 24.7 25.0 24.5 24.7 25.5 25.5 25.5 28.0 28.0 28.0 27.0 25.0 25.0 25.2 25.4 25.4

0.1263 0.1388 0.1648 0.0950 0.0664 0.0672 0.0968 0.1283 0.0755 0.0372 0.1543 0.1603 0.331 0.1107 0.1653 0.0800 0.300 0.1332 0.242 0.1952

23.9 23.9 24.2 24.5 26.6 26.6 26.6 24.2 23.8 23.8 24.0 24.0 24.0 22.6 22.6 22.6 22.6 22.6 22.6 22.6

0.1972 0.1583 0.1213 0.0632 0.2138 0.1495 0.1295 0.0608 0.0810 0.0828 0,0597 0.0390 0.1282 0.1713 0.1395 0.0937 0.0648 0.2043 0.1350 0.1337

23.3 19.7 14.2 7.07 24.9 19.1 14.1 8.60 8.50 9.70 7.72 4.82 14.6 23.2 17.3 11.5 8.53 25.1 22.7 17.1

22.8 24.0 25.0 25.0 24.6 24.4 24.5 24.0 23.6

0.258 0.1668 0.373 0.1100 0.264 0.352 0.343 0.294 0.1968

6.18 4.83 8.77 3.55 6.53 8.13 7.88 7.00 5.28

P/P

X

4Qp/,,

88.0

Water down a 0.626-Inch Glass Tube 0.919 0.919 0.915 0.907 0.865 0.863 0.865 0.915 0.922 0.922 0.917 0.917 0.917 0.948 0.948 0.948 0,948 0.948 0.948 0.948

0.214 0.181 0.130 0.0640 0.215 0.165 0.122 0.0787 0.0782 0,0892 0.0713 0.0443 0.134 0.218 0.161 0.109 0.808 0.238 0.216 0.162

0.1017 0.0853 0.0740 0.0457 0.1033 0.0812

0.0700 0.0467 0.0567 0.0575 0.0462 0.0348 0.0767 0.0942 0.0825 0.0638 0.0497 0.1067 0.0995 0.0803

Oil down a 1.00-Inch Glass Tube 32.9 31.2 29.8 29.8 30.35 30.6 30.5 31.2 31.75

2.03 1.508 2.61 1.058 1.987 2.49 2.41 2.19 1.678

1.325 0.955 1,592 0.703 1.275 1.558 1.533 1.398 1.080

INDUSTRIAL AND ENGINEERING CHEMISTRY

July, 1941

TABLE 11. AVERAGE FILMTHICKNESS AND VELOCITY (TYPICALDATA) (Cont’d.) Vol. Flow Film Temp., QC

Rate Q Co./Cm:/ Sec.

Thickness Av. M, Velocity V, Cm. X 10% Cm./Sec.

p/p

X 102

Reynolds No. Re, 4Qp/p

Friction Factor f 2

sd/Q;

Kerosene inside a 1.00-Inch Glass Tube 24.6 24.5 24.1 24.1 24.8 24.8 24.6 24.3 23.8 23.8 23.8 23.8 23.7 23.9 23.8

0.316 0.279 0.1995 0.1452 0.0818 0.0485 0.0256 0.0188 0.395 0.460 0.845 1.063 1.265 0.922 1.813

24.7 24.2 23.6 24.3 23.8 23.8 23.8 24.0 24.0 24.0 24.0

0.224 0.450 0.1517 0.0432 0.0076 0.0135 0.0234 0.0466 0.0578 0.0812 0.1592

2.27 2.11 1.874 1.648 1.456 1.270 1.001 0.895 2.43 2.57 3.33 3.56 3.76 3.36 4.62

1.198 1. I 9 9 1.205 1.205 1.193 1.193 1 I198 1.202 1.209 1.209 1.209 1.209 1.212 1.208 1.209

13.88 13.22 10.45 8.82 6.62 3.82 2.56 2.10 16.30 17.90 25.4 29.9 33.6 27.4 42.8

105.0 93.2 65.0 48.2 27.4 16.3 8.53 6.25 130.9 152.1 280 352 418 305.5 600

0.231 0.238 0.338 0.417 0.905 1.710 3.02 3.99 0.180 0.158 0.101 0.0780 0.0652 0.0876 0.0580

138. 277. 92.6 26.6 4.65 8.25 14.3 28.5 35.4 49.7 87.2

0.166 0.873 0.233 1.00 5.03 3.06 1.83 0.922 0.752 0.445 0.258

Toluene inside a 1.00-Inch Glass Tube 0.647 0.650 0.655 0.649 0.653 0.653 0.653 0.652 0.652 0.652 0.652

13.87 21.6 10.87 4.40 1.44 2.06 2.93 4.67 5.52 7.10 10.28

1.618 2.080 1.398 0.983 0.529 0.656 0.798 1.006 1.OB8 1.142 1.387

OF MAXIMUM VELOCITY TO AVERAGE TABLE111. COMPARISON VELOCITY (TYPICAL DATA)(Cont’d.)

Temp., C.

Vol. Flow Rate Q Cc./Cm:/ Sea.

24.7 24.7 25.0 25.2 25.2 22.7 22.6 22.7 22.8 23.0 23.4

0.242 0.206 0.1700 0.392 0.457 0.292 0.287 0.230 0.1943 0.1103 0.1767

23.8 24.2 24.0 23.8 24.0 24.0 24.2 24.2 22.6 23.8 22.6 24.6 24.1 24.6 24.6 24.6 24.8 24.8 24.2 24.0

0.1170 0.1732 0.0645 0.0378 0.1118 0.0837 0.0533 0 0426 0.0321 0.0952 0.0758 0.0975 0.1575 0.1810 0.238 0.800 0.1358 0.1905 0.271 0.1283

23.2 23.6 23.6 23.6 23.6 23.6 23.6 23.6 22.8 22.7 23.0 22.8 22.8 22.8 22.7 22.7 22.8 22.8 22.8 22.8

0.0703 0.0576 0.1192 0.1033 0.1727 0.0367 0.0434 0.0610 0.226 0.1583 0.0968 0.0692 0.0501 0.0221 0.0932 0.1412 0.1158 0.1547 0.0747 0.0822

Max. Velocity

U,

Cm./Sec.

p/p

X 102

U(p/p)

V(M/P)

(Calcd.)

U/v

Reynolds No. Rs, ~QP/s

Oil down a 1.00-Inch Glass Tube (Cont’d.) 6.08 5.48 4.80 8.73 9.93 6.63 6.51 5.78 5.15 3.18 6.04

30.2 30.2 29.8 29.5 29.5 33.1 33.3 33.1 32.9 32.7 32.0

1.827 1.657 1.428 2.58 2.93 2.20 2.17 1.912 1.682 1.040 1.612

1.205 1.072 0.938 1.630 1.800 1.448 1.433 1.230 1.095 0.750 1.007

1.52 1.55 1.53 1.58 1.63 1.51 1.51 1.56 1.54 1.40 1.40

3.21 2.73 2.28 5.31 6.18 3.53 3.45 2.78 2.36 1.45 2.21

Kerosene down a 1.00-Inch Glass Tube 13.23 19.42 7.82 6.25 12.63 9.42 6.85 6.08 5.12 10.65 8.95 11.33 16.93 19.00 25.1 9.28 14.67 19.18 24.8 14.20

1.210 1.204 1.207 1.210 1.207 1.207 1.204 1.204 1.233 1.210 1.233 1.198 1.205 1.198 1.198 1.198 1.194 1.194 1.204 1.207

0.1600 0.234 0.0943 0.0757 0.1527 0.1138 0.0825 0.0733 0.0632 0.1288 0.1105 0.1358 0.204 0.228 0.301 0.1112 0.1753 0.228 0.299 0.1713

0.0867 0.1125 0.0582 0.0410 0.0842 0.0688 0.0513 0.0443 0.0375 0.0753 0.0657 0.0767 0.1055 0.1150 0.1280 0.1167 0.0950 0.1197 0.1508 0.980

1.85 2.08 1.62 1.35 1.82 1.65 1.61 1.66 1.64 1.71 1.68 1.77 1.94 1.98 2.18 1.67 1.85 1.92 1.98 1.75

38.7 57.5 21.4 12.5 37.1 27.1 17.7 14.2 10.4 31.5 24.6 32.6 52.3 60.5 79.3 26.7 49.6 63.9 89.9 42.5

1.68 1.83 2.05 1.86 2.17 1.59 1.54 1.67 2.03 2.08 1.91 1.74 1.62 1.85 1.73 1.96 1.88 1.90 1.62 1.74

42.8 35.2 72.9 63.2 106.6 22.4 26.5 37.3 137.0 95.8 58.9 41.9 30.4 13.4 56.4 85.5 70.2 93.7 45.2 49.8

Toluene down a 0.626 -Inch Glass Tube 10.52 10.00 18.23 15.89 24.2 6.23 7.08 9.52 27.6 22.4 14.63 10.72 8.07 5.38 13.12 19.55 16.38 20.1 10.57 11.93

0.636 0.634 0.654 0.654 0.654 0.654 0.654 0.654 0.660 0.661 0.638 0.660 0.660 0.660 0.661 0.661 0.660 0.660 0.662 0.660

0.0638 0.0656 0.1197 0.1038 0.1587 0.0408 0.0463 0.0623 0.1818 0.1477 0.0977 0.0707 0.0532 0.0355 0.0867 0.1292 0.1080 0.1327 0.0700 0.0790

0.0410 0.0358 0.0583 0.0558 0.0745 0.0267 0.0300 0.0373 0.0897 0.0708 0.0812 0.0407 0.0326 0.0192 0.0800 0.0658 0.0575 0.0697 0.0433 0.0455

889

for all flow rates, regardless of whether the film was in wave motion or not, and lay along the curvef = Re/24 on the friction factor plot. The results of the determination of the maximum velocity within the film are shown in Figure 5. The ratio of maximum velocity U t o average velocity Ti, as calculated by Equation 3, is plotted against the Reynolds number. This ratio U / V should be 1.5 over the entire viscous range, since the viscous flow Equation 3 is based on a parabolic velocity distribution through the film with the maximum velocity occurring a t the liquid-gas interface. From Figure 5 it is evident t h a t the a ratio U / V is about 1.5 for values of Reynolds number up t o 25-30. Beyond this range the ratio U/V increases above the theoretical t o values as high as 2.5. This indicates positively that the velocity distribution within the film undergoes some change when the flow rate reaches a value of approximately 25 for the Reynolds number. To show this break a little clearer, the quantity U ( p / p ) was plotted against Q ( p / p ) for the water runs in Figure 6. The dotted line is the theoretical equation for maximum velocity U in terms of flow rate Q as can be derived from Equations 4 and 5. The break occurs a t a value of Q ( p / p ) = 0.0008, which corresponds to a Reynolds number of 20-30. Similar curves were obtained for kerosene and toluene, showing breaks a t values of Q ( p / p ) corresponding to values of Re 20-30. From the method utilized in the measurement of the maximum velocity, it is probable t h a t the values obtained were slightly lower than the actual values, since some of the color of the dye was dissipated over the 2-foot traverse down the tube and thus made i t more difficult t o notice the first tinge of color as it passed. For this reason the value of U / V is probably even still farther from the theoretical value of 1.5 than Figure 5 indicates. For certain runs it appeared that a velocity slightly greater than that necessary to produce waves in the f ilmwas required to produce any noticeable variation from the theoretical value for U / V , which is probably due t o the difficulty just mentioned. It is apparent, then, t h a t a change of some sort is occurring in the flow mechanism at Re 20-30. I n the region of Re < 20 the streamline equations are obeyed both in regard t o average properties and to velocity distribution. I n the region where Re> 20-30, the following experimentally observed phenomena may be noted: 1. Waves occur in the film between Re 25 and Re 1000. 2. The observed average film thickness agrees with the theoretical equations based on uniform films and viscous motion. 3. The interfacial velocity in the region of wave motion is substantially higher than the equations for uniform films indicate.

Based on these observations, a t least two possible explanations of the flow mechanism may be suggested. One might be t h a t a thin layer next to the liquid-gas interface is moving

890

INDUSTRIAL AND ENGINEERING CHEMISTRY

Vol. 33, No. 7

this region is distinguished from the true streamline region as well as the turbulent region by applying the term “pseudostreamline” region to this range of flow.

Conclusions Because of the limitations of the method used for determining the maximum velocity, it was impracticable to study flow conditions from this standpoint for values of Re > 150. However, from the appearance of the film and the trend in Figure 5, it is probable that the value of U / V remains greater than 1.5 until true turbulence sets in. With this hypothesis it is possible to make the following conclusions REYNOLDS NUMBER - R e from this investigation: The reason for the apparent disagreement TO AVERAGE VELOCITY FIGURE 5 . R x n o OF MAXIMUM between the data of Kirkbride (6) and that of other investigators (1-4) based on a different method of measuring film thickness can be concluded to be the result of a third type of flow existing i n in a semiturbulent condition a t a much higher velocity than liquid fYms which, up to this time, has not been evaluated. the basic viscosity equation would predict. It is possible This “pseudo-streamline” type of flow, occurs in a region) that this rapidly moving layer, which would involve a much between true streamline flow and turbulent flow and exists higher shearing force than that called for in the basic equain the range 25-1500 for Reynolds number. tion might set up a wave condition in the main body of the Pseudo-streamline flow is characterized by the appearance liquid film accounting for the observed motion. However, of waves in the liquid film and a much higher gas-liquid interthe turbulence would necessarily be confined to this thin facial velocity than that predicted by the true streamline layer since general turbulence throughout the entire film flow equations. However, the average film thickness-volume would reduce the ratio U / V to less than 1.5 and would cause flow rate relation and the Reynolds number-friction factor disagreement with the viscous flow equations or a friction relation for true streamline flow are obeyed in this region. factor plot. One observation which would tend to uphold The change from streamline to pseudo-streamline flow is ai this explanation is the much more rapid thinning out of the function of the Reynolds number and is not a function of dve in this flow region than in the true streamline-flow region. Another possible explanation is that friction a t the liquid-gas interface establishes waves within the film, and that these waves flowing in streamline motion obey general differential equations for such flow for point conditions within the film. If such were the case and if the nature of the interfacial forces were known, a general mathematical solution might be possible. The high velocities obtained would then be the velocities a t the crests of the waves, which would necessarily be greater than the average interfacial velocity as calculated from streamline flow equations. However, it must be noted that Equation 8 for streamline flow of liquid films, which is the basis of correlating streamline data, is based on the following assumptions: 1. General validity of the differential equation representing the balance of forces within a differential section of the film. 2. A film of uniform thickness. 3. A parabolic velocity distribution within the film with a maximum occurring at the liquidgas interface.

l

OO

.o I

)4

.0008

.W12

.0016

.0020

.0024

,0028

ai?)

VELOCITY OF WATER FILMus. FLOW RATE FIGURE 6. MAXIMUM I n the data presented here and by other investigators, the general equations for streamline flow were followed up to Re the diameter of the tube down which the liquid is flowing if 1500. However, the observed velocity distribution and film the velocity, density, and viscosity of the surrounding metype in the region Re > 25 are not those involved in assumpdium are kept essentially constant. tions 2 and 3. Because of these facts, any attempt a t correlation of heat transfer or mass transfer data in this region by Aclmowledgment use of true streamline equations will be subject to error due to The authors wish to thank C. F. Prutton for his many the higher interfacial srelocity and nonuniformity of the film. helpful suggestions and keen interest in this problem and C. Therefore, it is believed that the terminology of true streamG. Kirkbride for his helpful criticism of the work. line flow to the region of Re 25-1500 is misleading and that

July, 1941

INDUSTRIAL AND ENGINEERING CHEMISTRY

Nomenclature

v

B = volume of liquid on tube wall C = volume of liquid clinging per sq. om. of surface f = Fanning friction factor, 2 qmS/Q2 g = acceleration of gravity, 981 cm./(sec.) (sec.) A H = increase in height of liquid level m = film thickness, cm. Q = volumetric discharge per unit of periphery, cc./cm./sec. R = inside radius of outer tube r = outside radius of inner tube Re = Reynolds number, U = velocity of liquid film at liquid-gas interface, cm./sec. B = average velocity of liquid film, cm./sec.

= =

p p

=

891

velocity in film at distance r from tube wall density of film liquid, rams/cc. absolute viscosity of fiym liquid, poises

Literature Cited (1) (2) (3) (4) (5) (6)

Claassen, Centr. Zuckerind., 26, 497 (1918). Cooper, Drew, and McAdams, IND. ENG.CHEM.,26, 428 (1934). Fallah, Hunter, and Nash, J. SOC.Chem. Ind., 53, 369T (1934). Hopf, Ann. Physik, 32, 777 (1910). Kirkbride, Trans. Am. I n s t . Chem. Engrs., 30, 170 (1933-34). Schoklitsch, Akad. Wiss. Wien, Math.-natzrrw Klasse, 129, IIA, 895 (1920).

Vapor-Phase Catalytic Oxidation of Organic Compounds Production of Benzoic Acid, Maleic Acid, and Benzaldehyde from Toluene at Atmospheric Pressure' W. GEORGE PARKS AND RALPH W. YULA Rhode Island State College, Kingston, R. I.

~_____

~

The direct vapor-phase catalytic oxidation of toluene in the presence of various solid catalysts to produce benzaldehyde and benzoic acid has been investigated. Vanadium pentoxide prepared by the decomposition of ammonium metavanadate at temperatures below 300' C. was the most satisfactory catalyst. The effect. of temperature, time of contact, air/toluene ratio and concentration of vanadium pentoxide on Alfrax, granular aluminum, and silica gel was measured. The highest yields of partial oxidation products wereobtainedwithvanadiumpentoxide supported on Alfrax at temperatures between 380' and 460' C., time of contact 0.5 second, and airjtoluene ratio above 25. Under these conditions the maximum yield of benzoic acid, maleic acid, and benzaldehyde was 34, 21, and 12 per cent, respectively. Although the mechanism for the formation of maleic acid is complex, relatively large quantities were produced. The results indicate that the most important variables controlling this reaction are temperature and method of catalyst preparation.

LTHOUGH the direct vapor-phase catalytic partial oxidation of toluene presents some difficulties, the possibility of commercial operation of sonie process is attractive because of the high ratio between raw material cost and value of the products free from chlorine and other inorganic impurities. The desirable products of toluene oxidation are mainly benzaldehyde, benzoic acid, and anthraquinone. They are obtained in proportions that depend upon catalyst, temperature, oxygen ratio, and time of contact. The formation of benzaldehyde is favored by a high temperature, mild catalyst, and short time of contact. With a high oxygen-hydrocarbon ratio and long time of contact the principal product is benzoic acid. I n the presence of vanadium oxide catalysts the oxidation reaction begins a t approximately 300' C. However, the most favorable temperature is somewhat higher, 400-450' C., where approximately 50 per cent of the toluene oxidized per pass forms benzaldehyde. Molybdenum oxide is a less active catalyst and requires a higher temperature for high per-pass yields. With a tin vanadate catalyst a t 290" C., 53 per cent of the toluene oxidized per pass forms benzoic acid (18). Anthraquinone may be formed (< 5 per cent) under certain conditions, but it is of no economic importance. A great deal of information on catalysts, construction of apparatus, and conditions for operation is to be found in the literature and in the numerous patents issued following the investigations of Gibbs (3) and Weiss and Downs (17). I n the vapor-phase oxidation of toluene by air, complete combustion occurs with cobalt and cerium oxides, while manganese, copper, nickel, chrom'um, and uranium are less active. Vanadium oxide occupies an intermediate position and produces

A

1

The first two papers in this series appeared in 1936 (16) and 1939 (14).