ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT = gravitational constant, cm./sec.P = velocity head, em. of Hg K , = rate of evaporation (Priiger, 7 ) - grams/(sec.) (sq. em.) ( p - p,) L, = rate of evaporation, molecular layers/sec., a t temperature T and saturated vapor pressure p - K , , ( M ~ ) ~x. Q10-7 ‘TI = molecular weight = 18 for wat’er P = saturated vapor pressure of water, mm. of Hg, at temture T Po = pressure (vacuum), mm. of Hg, into which water evaporates with pressure p ‘ 1 = total weight of water evaporated experimentally, grams t = duration of evaporation, see. T = temperature of evaporating surface, C. liquid evaporating, gmms,/sec. e = evaporation coefficient, W E = ___9
h
w=
583p
44
e
0.0583
-
4$\ q
=
pAft
References
(1) Alty, T., Phil. M a g . , 15, 82 (1933). (2) Alty, T., and Mackay, C. .4., Proc. Rou. Snc. (London),149A, 104 (1953). (3) Baranaev, J. R., J . Phve. Chem. (U.S.S.R.), 13, 1635 (1939). (4) Doraey, N. E., “Properties of Ordinary Water Substance,” New York, Reinhold Publishing Co., 1940. ( 5 ) Fraser, R., personal communication. (6) Hickman, K., IND.ENG.CHEM.,44, 1892 (1952). (7) Priiger, W., Z . Physik, 115, 202 (1940). (8) Trevoy, D. J., IND. ENG.CEEM., 44, 1888 (1952). RECEIVED for review September 38, 1953. ACCEPTEDAIarch 1 , 1954. Communication N o . 1612 from the Kodak Research Laboratories.
K. C. D. HlCKMANl
AND
W. A. TORPEY
Research Laboratories, Eosfmon Kodak Co., Rochester, N. Y.
A
KY demonstration that a a t e r can distil a t the high calculated
rate ( 6 ) ,emphasizes its failure to do so (1. b) in everyday circumstances. Previous measurements of evaporatioii coefficients have reached only 1 to 4% of theory ( S ) , and n ater boils or bumps because it cannot emit sufficient steam from its existing surface. To suppose that there is a repressive film raises many new questions. Is it mechanical-due to gradients of heat and escaping vapor which disturb equilibrium? Is it caused by orientation or polymerization of the polar natcr molecule7 Is it a layer of chemical impurity, comparable in effect 771th a monolayer of insoluble fatty acid? Or is it a combination of all these and perhaps other factors, and if so, does one factor dominate the rest? It is difficult to understand how surface polymerization and orientation of the water substance can reduce evaporation a hundredfold or more, since all coniponents of liquid water are believed to be rapidly interconvertible. If, on the other hand, contamination is responsible, the degiee of obstruction should vary with the nature and quantity of impurity. Thus, a positive test for contamination should be variations in the vapor emission of different eamples of water, examined under identical physical conditions. A confirmatory test nould be the generation of a schizoid surface pattern, m here a freely evaporating area could be seen pushing an obstructive film to one side. This paper examines the questions of the variable emission of n ater and the torpidity of its surface (4). Vacuum Still Is Used to Demonstrate Torpidity of Water
To secure a working crater in a torpid fluid, the pressure must be low enough for vapor recoil to deprrss the surface. Water near the freezing point has a saturation pressure of 5 mm. of mercury, so that a vacuum of 3 to 4 mm. or lor~erwould be necessary for the formation of patterns. If water evaporated without obstruction, it nould freeze instantly nhen exposed to such a vacuum, and the vacuum itself could be maintained only if there waq a coextensive vapor path between the evaporator and condenser. If, on the other hand, the surface was substantially 1
Present address, 186 Palham Road, Roclicster 10 h-
1446
T
blocked, there is just the chance that water could be evposed to vacuum for an observational period before freezing and that vacuum could be maintained through a constricted vapor path, such as the neck of a flask. Apparatus. This reasoning dictated the construction of the simple pot still shown in Figure 1. Coil A , under the flask in Figure I, represents a commercial radiant heater, run a t 750 watts. Coil B, immersed in the water, consists of a few 1-cni. turns of Nichrome wire and can dissipate 5 t o 50 watts. Acting as a “torpidity tester” (41, it serves to open working craters in resistant samples of water and to maintain working areas in other samples. (All the patterns produced by this coil or by eyternal heating of the flaak could be obtained by prev, arming the water. The coil n-as a convenience, not an epaential.) A camera, C, is indicated on the right, and a Fresnel lens, D , about I5 square cm , is shown between the lamp and the flask, on the left. The flask is kept free from dew by air blasts. Operation. The apparatus was cleaned with acetone, follon ed by a large quantity of distilled water from the laboratory’s aluminum supply lines. The manometer mas charged nith mercury and sealed in position: the flask was half filled with distilled water, and vacuum was induced by a mechanical oil pump. Heaters *4 and B and the air blasts were energized, and watei soon began to distil into the trap v i t h many explosive bursts a, degassing proceeded. Trichlorethylene was placcd in the trap, and sniall pieces of dry ice were added to maintain a pressuie of S to 10 mm. in the assembly and prevent undue loss of n ater vapor to the pump. The pump oil r a s changed frequently and regenerated by blowing with air overnight. First Experiment. After half an hour, all bumping ceased and the trap was filled with dry ice. -4few minutes later, the manometer read less than 2 mm. and a crater appeared on the water, surrounded by symmetrically moving pits or “cratercts.” The photograph, Figure 2, was taken and a t once the surface froAe solid. The trap was allowed to warm up, and soon the ice began to melt in the flask, presenting a beautiful pattern of cratercts, just above the internal heater, as shoan in Figure 3. Figure 3 and the following photographs Rere taken v i t h the camera aimed a t the underside of the surface, as shown in Figure 4, because clearer pictures “ere obtained that nay. The craterets now appeared a9 humps or pimples.
I N D U S T R I A L A N D ENGINEERING CHEMISTRY
Vol. 46,No. 7
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT Torpidity Is Due to layer of Impurity on Surface of Water
Effect of Standing in Glass. The water was maintained under vacuum overnight, with the pump shut off, and the procedure was repeated the next morning, but not with the same results. A residence of 16 hours of the apparently clean, distilled water in a clean, all-glass apparatus markedly reduced the evaporative power of the surface. Craterets were induced with difficulty, and their place was taken by two or three larger craters which deepened rapidly and explosively, upheaving the contents of the flask with an alarming water hammer. On one occasion, the flask was
was unity, the surface of the water in the flask could be considered a cross section in a short pipeline of the same area conducting vapor at a eaturation pressure appropriate to T = 0’ to 2” C. to a condenser which, in the limiting case, would absorb it completely. A manometric probe placed in the stream would register pressures ranging from zero to nearly full saturation pressure, according to its orientation. If, hoRever, the passage of vapor was severely throttled, as by the neck of the flask, collisions would randomize the vapor molecules and the manometer would register an average pressure approaching the saturation pressure. Again, if the evaporation coefficient were less than unity, or only portions of the surface were fully emissive, the pressure in the flask would be diminished by a factor related to the area of the emissive surface and the effective area of vapor escape-Le., the admittance to the condenser. Thus, if
A , = area of water surface A*’ = equivalent emitting area, as defined in Equation 1 A , = effective escape area or admittance for vapor from flask t o condenser p = saturation pressure of the water po = minimum pressure observed in flask
A*‘ =
- Po
P and evaporation coefficient e = -
Figure 1. A. E.
Pot Still and Freezing Trap for Demonstrating Torpidity of Water Radiant heater Heating coil
C. D.
Camera Fresnel lens
broken and the burst of vapor to the trap was 80 violent that the acetone which was then used overflowed and caught fire (hence, the substitution of trichlorethylene). Photographs of “16-hour” distilled water are shown in Figure 5 , A-D, and with different lighting in Figure 6, A-P. The photographs were taken over a period of hours but, nevertheless, show the progression from a small crater to an explosive disintegration of the surface. The vapor freely released by the expanding walls of the growing craters could exert a pressure of a t least 7 om. of water head downward, a t the prevailing temperature, providing ample force for the phenomena observed. Torpidity of Pure Water. Any sample of water examined for more than 2 days refused to perform. When the trap was iced the pressure fell to 1 mm. or less and, after an ominous wait, a crater appeared which a t once exploded. Replacing the aged m t e r with a fresh sample from the laboratory line restored the evaporative activity. A glass still was assembled to redistil the laboratory-distilled water directly into the apparatus. As a further measure, the apparatus was washed with acid, alkali, and water and thoroughly steamed, and the condensate was rejected. T h e n the apparatus was half-filled with the double-distilled miter and put through the routine, ice formed before any crater appeared, and the manometer a t no time read below 3.5 mm., showing that the water surface was highly emissive to vapor. Craterets, Figure 5, E, and then craters, Figure 5, F , appeared momentarily before freezing. Within a few hours, the emissivity of the water fell to “normal.” Approximate Calculation of E . If the evaporation coefficient July 1954
A,’ A*
Figure 2.
Working
Crater Surrounded by Torpid Water, 5’ C.
In a typical experiment, carried out just above the freezing point, p = 5 mm., PO = 2.5 mm., A , = 17,000square cm., and A , = 4 square em.
*
As’ = ___ (5 - 2.5)
8
E
= __ 1700 =
0.0047
(3)
I n other experiments, the minimum pressure, PO, ranged from 1.0 to 3.0 mm. during crater formation, so that the coefficient varied
INDUSTRIAL AND ENGINEERING CHEMISTRY
1447
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT
Figure 3.
Craterets Emitting Vapor in Torpid Water from Melting Ice
over the range E = 0.02 to 0.001. The highest values were from nev, redistilled water and the lowest from tap xater. Wave AmpMcation. A sure sign of obstructed surface \vas the amplification ( 4 ) of Jvaves that appeared during the most rapid evaporation and lasted until freezing was complete. Originating from vibrations of the building, the prininry amplification n-as from the stretched troughs of the waves, but a secondary gain was caused by shrinkage of area as the ice fronts advanced. There rrere two broad habits of ice formation-by many small crystals appearing simultaneously or by a few crystals spreading laterally. I n the first case, illustrated in Figure 7 , A , freezing of the entire surface occurred in less than a second, preventing wave
amplification. This appeared to correspond with an open surface of relatively low torpidity. (The authors have not yet encountered a fully emissive resting surface.) Examples of ice spreading from tn-o sources are shown in Figure 7, R and C. The points of origin are in the upper and lower left quadrants in Figure 7 , C. A very striking surface of a single crystal is reproduced in Figure 7, D; the growth starts a t the right and spreads in a V-shaped pattern to the left. The last portion frozen is at the lower right. Radial twinning is observed, but the concentric ridges, which might a t first be mistaken for twinning, are due to the wave motion of the liquid. As each wave is reflected from the ice front, it is stretched in the trough, evaporates more rapidly, and so freezes. The next crest of compressed surface approaches and interrupts freezing until it, too, recedes as a trough, as Ehown in Figure 8. Finally, a small area remains where the q-ave motion is so vigorous that, in spite of increased vapor emission, the water is renewed convectivel-, and freezing is further delayed. The observer is reminded of the way the increased paddling of ducks keeps a corner of a pond open during a cold spell. Pressure Changes during Freezing. When an emissive water surface froze, the manometer reading decreased, partly because the outer layers of ice fell far below freezing, and partly because the ice vapor-pressure curve departed from the water curve. This was to be expected. The increase in manometer readings when torpid water-ordinary tap water, or 16-hour water-froze was not anticipated. The manometer dipped to 1.5 to 2.0 mm. and then, as ice appeared, rose to 3.4 to 4.0 mm., and then s1o~vly fell. The inference is that ice is far more emissive than torpid water. An alternative explanation is that torpid water supercools to a greater degree than emissive rrater before freezing. A thermocouple, introduced from the bottom of the flask to a point 0.5 to
Figure 5. Water Surfaces from Below
1448
Figure 4. Pot Still and Freezing Trap
A.
Photographing underside of liquid surface
C.
B.
Craterets turn t o craters Two craters survive A single crater expands
D.
Crater disrupts whole surface Craterets develop just before freezing of emissive water
E and F.
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
Vol. 46, No. 7
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT
Figure 7. A. E. C.
D.
Figure
6.
Craterets Develop into Exploding Crater
Ice Formed
by
Rapid Evaporation
Multiple nucleation Two points of ice origin in torpid water, showing craterets Surface shown in 5, after freezing Ice spreading from single point, showing twinning and wave pattern
1 mm. below the surface, did not corroborate this theory, since a t no time did the temperature fall below -2” C. nor was there a noticeable difference between torpid and emissive samples. On freezing, there was a momentary rise to 0” C. and theu a rapid lowering. The rise was not sufficient (by a factor of 10) to account for the rise in vapor pressure.
I n order to investigate the effect of silica the flask and trap assembly of Figure 4 were coated with a water-resistant varnish, and some of the measurements of emissivity and torpidity were repeated on fresh distilled water, 16-hour glass water, and tap water. Traces of hydrogen fluoride and sodium silicate (1 to 5000) were added, separately and together. The silicate did not decrease the vapor emissions nor did the hydrogen fluoride increase them. On the contrary, the hydrogen fluoride produced the most highly obstructed water encountered. The matter has a complexity far beyond the scope of the present exploratory survev.
Schizoid Habit and Variable Emission Suggest Obstructive layer Is Chemical Impurity
Torpidity May Not Be Retained at Elevated Temperatures
The two tests applied, schizoid habit and vaiiable emission, suggest that the obstruction is due to chemical impurity, often present in a very low concentration. The impurity is contained in Ontario water and is contributed by glassware. Mache ( 6 ) , Priiger ( 7 ) , and many others have noted that “glass water” evaporated less freely than double-distilled water, but the significance of their observations does not seem to have been apprcciated either by chemical engineers or physical chemists, who continue to treat water as though its surface were HXO. Two difficult tasks remain to be undertaken-measurement of the emission and surface habits of pure conductivity water and identification of the active impurity from glass and river water. The investigation would involve the use of nonglass apparatus, and neither quartz nor plastic would be entirely satisfactory. Analytical techniques and surface observation of a refinement far beyond the scope of the present work would be required. These experiments are reported because they demonstrate the torpidity of water as it usually occurs and again draw attention to its highly obstructed surface. The impurities that borosilicate glassware can contribute are silicon and boron (80 and 12%, as oxides), with less quantities of sodium, aluminum, magnesium, and arsenic, and disturbances of H’ and OH’ concentrations. Of these, silica, a two-dimensional mosaic of tridymite, is the most obvious suspect, since it is perhaps better suited than any other material for adsorption to a polar liquid surface.
The fact that ordinary reding water acquires heavy torpidity near the freezing 2oiiit is no indication that it wiIl retain torpidity
A to B occur over period of 3 to 5 seconds Camera level with surface
July 1954
Figure 8. W a v e Amplification Evaporation, Showing Freezing Troughs
Due in
to Rapid Successive
Troughs appear as crests
INDUSTRIAL AND ENGINEERING CHEMISTRY
1449
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT a t higher temperatures. Also, a low evaporation coefficient, E , when equilibrium is drastically disturbed, does not imply that the accommodation coefficient, a, is depressed to a like degree when vapor and liquid are in equilibiium. At 2" C., 2,500,000 complete layers of H?O should vaporize and recondense each second, for a = 1. I n terms of molecular events, and if second is allomd per event, a molecule could have an aggregate average life in the surface layer of 400,000 oscillations before evaporating. For obstructed, resting vater a t the freezing point, evaporation is depressed a hundred or more times, and the aggregate life of the molecule in the surface is, say, 2.5 X l o y events, so that, over an area 50,000 molecules square, only one molecule is leaving for the vapor at any molecular instant. .4t the boiling point, 100' C., events have accelerated 170 times and in a high pressure steam boiler, 1000 to 5000 times. An interfacial structure that could form and repair fissures under million-layer-second conditions could R ell fail to do so if the surface commotion was increased 100 to 1000 times and must necessarily terminate a t the critical point. However, common experience suggests that surface torpidity prevails a t well over
100" C., for ordinary commercial water, since steam cannot be withdrawn a t an>-practical rate a t 100" C. rrithout formation of subsurface bubbles. Whether it is a factor in high pressure boilers can scarcely be guessed because of the tremendous nucleation favored for high heat transfer, but the accumulation of silica on turbine blades is evidence that material a t least is being removed from the surface. literature Cited (I) Alty. T., Phil. Mw., 15, 82-103 (1933). ( 2 ) Alty, T., and ZIackay, C. .I., Proc. R o y . SOC.( L o n d o n ) , 149A, 104
(1935). (3) Baranaev, J. R., J . Phus. Chern. (U.S.S.R.), 13, 1635 (1939). (4) Hickman, K. C. D., IND.ESG.CHEW,44, 1892 (1952). (5) Ibid., 46, 1442 (1954) (6) hlache, H., 2. Phusik 110, 189 (1938). (7) Pruger, IT., Ibid., 115,202 (1940). RECEIVED for review September 28, 1954. ACCEPTEDMarch 1, 1964. Contribution S o . 1613 from the Kodak Research Laboratories.
Condensation of Vapors of Water and Immiscible Organic Liquids HEAT TRANSFER ON A VERTICAL TUBE MELVIN TOBIAS'
AND
ARTHUR E. STOPPEL
University of Minnesofo, Minneapolis 74, Minn.
THIS
paper is concerned with one phase of the broad subject of condensation-the rate of heat transfer in condensation on cooled vertical tubes from mixtures of vapors of water and immiscible liquids. The prime application of this process is in steam distillation. The first thorough exposition of the heat transmission process in condensation of a single component was due to Kusselt (9). He showed that the mean heat transfer coefficient for a vertical tube was given by the formula
The following assumptions were involved in the derivation of this equation : 1. The temperature difference between the surface of the film of condensate and the cooling wall is independent of position. 2. The flow of the film is laminar, and the frict onal force on a volume of condensate is in equilibrium with th ' gravitational force. 3. KO shear stress exists a t the free surface, c ch as might be caused by the motion of the vapor past the filr I 4. Effects of tube wall curvature are neglect . 5 . The velocity component of the condene .e in a direction perpendicular t o the wall is neglected. 6. The temperature gradient through the film is assumed t o be linear,
A slightly different expression was obtained by Parr ( 1 1 ) by assuming constant heat flux a t the wall instead of constant temperature. 1
Present address$ Oak Ridge National Laboratory, Oak Ridge, Tenn
1450
Considerable attention has been paid to the pioneer work of Xusselt by the small number of experimenters who have studied two-phase condensation. ill1 of them employed water as one of the components. Hazelton and Baker ( 4 ) in 1944 derived an expression for two-phase condensation on a vertical tube, using assumptions similar to those of Susselt :
where the symbols refer to properties of the component which clings to the condenser tube wall. This equation did not correlate the data, but it guided them to selection of the following empirical equation :
(3) v-hich they found satisfactory for those systems for which experimental data were available. Others have relied primarily upon einpirical relationships to treat the data because of the complexity of the process of twophase condensation. In 1933, Kirkbride ( 6 ) , working with vertical tubes, suggested the equation
(4) but, as Mueller and Baker (8)showed, this is theoretically incorrect, Kirkbride appears to have been the first to note that the temperature drop across the condensing film must be the difference between the so-called eutectoid temperature and the wall temperature, The eutectoid temperature is that tempera-
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 46, No. 7
