floating drops and li! U
A Jask containing two separate liquid phases of isopropanol. The drop, called a liquid boule, i s separated from the host liquid by a vapor film, called the shroud. T h i s i s the largest boule yet photographed-its uolume is about 780 ml. The gauze rings act as stabilizers
18
INDUSTRIAL A N D ENGINEERING CHEMISTRY
K. C. D. H I C K M A N hat small drops of water will float evanescently on
Tcalm water, has probably been known for centuries.
Drops are often seen floating downstream from waterfalls and floating in kitchen utensils, especially when hot. Organic liquids provide longer-lived drops-in extractors many drops a t a time will dance on the boiling solvent. An investigation of evaporation from quiet surfaces has led to the growth of relatively large masses of this second liquid phase, identical in composition with the liquid on which it rests. Such a drop, resting on the same liquid without merging with it, is shown in the photograph opposite. The molecular traffic between a liquid surface and its vapor, though tending toward a readily calculated maximum, is beset with anomalies which have worried both scientist and practical distiller for half a century. Buried in the literature on the evaporation coefficient are papers of mine (5) on the torpid behavior that sometimes invades liquid surfaces, a condition outside the experience of all but the vacuum technologist. I n the spring of 1961, E. D. McAlister suggested torpidity phenomena might bear on the evaporation of ocean and lakes and beckoned me to two fascinating months a t the Scripps Institution of Oceanography where, with G. Ewing ( 3 ) , he introduced me to a new realm of opportunity. Casual looking and talking suggested that torpidity as an operative factor was unlikely to be seen on terrestrial waters because of the overburden of atmosphere ; nevertheless the predisposing forces should be there, reflected perhaps in ways not yet observed; and techniques already developed might be used to search for them. These techniques had been simple-a bench by a window, a burner under a flask half filled with phlegmatic fluid, a vacuum pump, a camera, and of course, the observer. The approach was part of a philosophy for entering a new field, namely, that endeavor and knowledge can be decimalized in a succession of brackets and that no subject really need be moved to a higher bracket while a lower remains unfilled. The present call was to examine the evaporation behavior of water (and by contrast and reference, other liquids) from quiet, almost resting surfaces as seen in nature-e.g., not boiling, stirred, or squirted. The complicating factors in nature are wind, waves, and contamination; something could be learned perhaps by
eliminating these and evaporating the liquid from the top surface into its own saturated vapor by slight superheating above the boiling point. Commencing as usual with flask, heater, window, and camera, it was first learned how to superheat without ebullition, then how to retain the filling-by addition of a condenser. Drops from the condenser persistently floated on the surface of the superheated water. The snap conclusion-that this was a unique property of that unique substance, water-was soon dismissed when drops were floated on other liquids, including perfluoroheptane, manifestly different from water. The floating drop, long known but little investigated in spite of its intrinsic interest, appeared promising as a surface probe to study the evaporation coefficient. The research was thus launched in the wake of the cruising drop. Large floating masses were soon grown, affording the curious anomaly of a one-component system with two identical phases; after this, item upon item turned up. Some of these, such as relation of boule size to superheat, have been mapped with precision, while others have been examined superficially, the plan being to fill the present technique bracket before passing to more complicated means. Interim conclusions are that under critically determined conditions of superheat and electrical neutrality, most, perhaps all, liquids can be floated on themselves in considerable bulk for long periods, remaining separated only by their vapor. There is an apparent absence of chemical specificity. T o the implied question whether this flotation aids the study of the evaporation coefficient, the answer is a cautious “Yes.” The large supported mass covers the primary evaporating surface, thus adding resistance to the escape of vapor. Paradoxically, the combination of host liquid and supported mass evaporates faster than the host alone because it forms a primitive engine which accelerates the transfer of heat to the exposed surface of the floated mass. This previews what it is hoped to report later, that each liquid develops characteristic means for ventilating its surface in a thermal gradient. Background References
A condensed account ( 6 ) has been given of the sessile drops-smaller and larger masses of liquids that float on the top of the same or other miscible liquid-being examined in this laboratory. Other references are found chiefly in three groups: Rayleigh (74. 75), VOL. 5 6
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19
Figure 1. Superheat Jask containing distilled zeater. drops. Right, desuperheater in action'
Left, individual
Boys ( 2 ) , and others (76) before the turn of the century; Mahajan (70) and students (78) between 1920 and 1935 ; and Russian workers ( 4 ) , including P. S. Prokhorov ( 7 2 ) , 1935 to date. Rayleigh, who referred back to Savart (77) and Plateau ( 7 7 ) noted that drops formed by disintegration of a drop of water bounce off one another without even temporary merging though purposely electrified drops combine on contact. The Mahajan group catalogued phenomena over a wide range of liquids and circumstances and derived a formula (9) for relating the lifetime of drops to the viscosities of the drop liquid, the host liquid, and the surrounding atmosphere. Prokhorov's meticulous measurements of drop avoidance and coalescence led him to propound the rule that long separation of drops that press on one another or a supporting surface is possible only when gas is continuously generated within the area of nearest approach. There are two common means for such generation-diffusion of nonsolvent gas into the approach area which by dilution induces further evaporation and volume expansion, and vapor evolution from a liquid a t a temperature above its boiling point; drops float longest on superheated liquids. liquid Superheat
When the vapor pressure of a liquid exceeds the pressure p mm. of Hg of the vapor above the surface by a n amount A@,, distillation proceeds (7) at a rate
Q
=
583
Afjd
(M/T)'"E
(1)
where Q = grams per second per square meter of free surface and E is the fraction, unity or less, of the surface which remains free of molecular obstruction, for instance by impurity or adsorbed layer; T is the absolute temperature of the outer-outermost layer where vapor20
INDUSTRIAL A N D ENGINEERING CHEMISTRY
Figure 2.
Multihle Joating drops-ufiFer,
butanol, and lower, water
liquid exchange occurs, and T exceeds the equilibrium boiling point by an amount A t d , which corresponds to 4Jd.
The calculated distillation races of water for small pressure increases are high a t the atmospheric boiling point. When A@d = 1 mm., Q = 477 kg. 'sq. meter hr. with a "top-layer" temperature rise of only 0.06' C. Even violently boilinq water suffers a temperature rise much greater and water evaporating quietl) from its surface cannot be made to distill at this rate; and if it could, the temperature would rise by a n increment many hundreds or thousands of times the minimum Std. This extra temperature is the liquid superheat, Ats. The discrepancy can hardly be laid to the evaporation coefficient which with clean water (5) and certainly with nonaqueous, nonpolar (7) liquids remains near unity; instead it must be attributed to failure to measure correctly the temperature of the evaporating layer. A small error in measured T causes a very laryr error in atd, from which Ap, is derived for Equation 1. The limitation of distillation is thus due. as the oceanographers ( 3 ) recognize (79). to the resistance to the flo~iof heat to the surface to replace the latent heat of evaporation. A layer 0.1 to 1.O mm. thick of liquid which is stagnant 01 in laminar flow will be seen later to provide the observed diminution in rate. It is thus convenient to define an over-all or virtual"distil1ation coefficient"E which replaces the evaporation coefficient E when the bulk temperature of the liquid is used instead of the (generally unascertainable) "front row" temperature of the surface. Then, for the small temperature differences involved
T h e drop thus rests on liquid with a steep thermal
Figure 3. Quanfifalivcsuperheat vessel, with thermd laggkg. T4st is placed in a silvncd glass Dmm scrscl and wmncd by an nnular hater suitably insulated. Conforts me pm&d by still B rchmring wpor to condnun C rmd test park. A#iskzble lube D p a s i r k apposed tlmnwcaupIes F, H. Rod E mu as hop cmrnfer rehiming &Nlde i o the lown pmt of thepark by pipc M . Counter is seuered a1 N whenpodng hops me to be induced
park A
gradient below the surface which changes with convection c m n t s and the degree of superheat; exploring the subsurface is an integral part of the floating drop investigation. Apparalus for Superhooting liquid8
The requirement is to heat liquids above boiling point without subsurface ebullition. Tall vessels with steep sides are more effective than flat shallow ones. If a round flask is used, the heat should be supplied evenly to a large annular area which excludes the bottom; a flask with conical bottom serves better than a round one, and a vertical cylinder with a low density resistance winding provides high superheat without ebullition. A simple demonstration vessel is pictured in Figure 1 where a 1-liter wide-necked Pyrex tlask is seen closed by a manifold with an internal dripping lip. A slanting air-cooled condenser returns condensatethe source of the floating drops-free from air, to a movable thermometer which can adjust the height of fall to the surface, or when pushed down further can determine the bulk temperature of the liquid. A useful adjunct is the desuperheater, a glass rod with an inverted miniature test tube on the lower end. When this is pushed into the liquid, vapor generated under the open end can only escape as bubbles, initiating ebullition according to the depth and suddenness of immersion; a very dramatic C., with water. demonstration at high superheats, 4’-8’ The source of heat (not visible) is an open resistance wire coil about 3’/~ inches in diameter held underneath the Aask in a short chimney and energized by a variable transformer. A double-walled plastic cover (just) prevents condensation on the upper parts of the flask. The apparatus can be used to demonstrate superheat
in liquids with boiliig points between 70° and 150” C. Water, the lower alcohols and ketones, benzene, toluene, and chloroform and carbon tetrachloride have been examined. The glassware is first cleaned, avoiding abrasives dr bottle brushes, rinsed with concentrated hydrochloric acid, water, ammonia, much water, then dried. A new filling, half a flask-full, at first gives vigorous ebullition but after the desuperheater has been raised and lowered a few times it can be permanently raised, assuming suitable power input, to leave a liquid evaporating quietly from the surface. Distillate begins to float in individual drops at superheat temperatures above 0.1’ C. and at AI, 1O-2’ C. the drops race rapidly over the surface until they are reflected from the wetted wall or burst against one another. If the thermometer (drop applicator) is less than threequarters drop height above the surface large multiple drops are formed which, in the case of organic liquids, maywithstand the approach of smaller drops to form dusters. After apparently arbitrary intervals the individual drops, clusters or masses burst or merge directly with the supporting liquid. Drops and clusters are shown in Figure 2. Quantitdive, O v e d o w Appamtur
A crucial question is whether drop flotation is an intrinsic property of the purest liquids or is caused or aided by impurities. The experimental technique thus seeks purity as a reference point while providing facilities for adding reagents and afterward returning the liquid to a standardized “pure” state. No matter how carefully a liquid may be prepared for the start of a superheat run, it readily becomes less so, the atmosphere, pyrolysis, and the vessel itself [Mache’s (8) glass effect (73)]all contributing impurities and altering from day to day the degree of superheat noted for a fixed energy input. The progressive spoiling can be avoided and the charge maintained at its initial (or better) state of purity by constantly redistilling and continuously overflowing the surface. Figure 3 shows a test vessel which stands in a silvered vacuum flask containing a variable annular heater, a residue still taking overflow from the test vessel, a condenser returning all distillate to an adjustable applicator with drop counter in the test vessel, and opposing thermocouples to determine At8, which latter is simply the difference in temperature between the bulk liquid and the saturated vapor above. With this arrangement any light ends generated during the experiment can be rejected to the atmosphere, nonvolatiles are trapped in the residue still, and a suspension-free liquid occupies the test vessel. Because the vapor from the residue still reaches the condenser through the working flask, the thermal shielding of the upper half is not exacting, the vapor can never overheat the surface under study. Insulated thus it required only three watts to keep a charge (I/* liter) of chloroform at its boiling point, five watts for a charge of water; each additional watt created superheat and gave a measure of the quantity evaporated from a known area. The purge still can be operated over wide rates to vary independently thereturn of distillate and surface O V ~ Q W VOL 5 6
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21
At high superheats, boules are shattered by their own vibrations of the heat input selected for the test flask. At useful operating rates, with 30-60 drops of condensate returning each minute, a volume equal to the contents of the working flask (about 500 ml.) overflows every 2-4 hours. Assuming, as may be done, that there is complete mixing and exponential dilution of the incoming with the resident liquid, the concentration of a test chemical added diminishes to half in l/log 2 = 0.72 of these times. Impurities or added solutes are thus diluted to one half a t least ten times per 24-hour day; that is, to less than '/loooth in one day, one millionth in two days, and to unimportant quantities in three or four days. If the solute tends to concentrate on the surface the dilution is quickened because of overflowing. There are two useful consequences. For a given rate of overflow variation in the rate of dilution is a rough measure of the acquisition or rejection of the solute by the surface. Second, certain aspects of initial and inter-experiment cleaning can be dispensed with because the apparatus cleans itself every few days and thus allows one to explore two or three chemical additives each week. Further, effects on drop formation of any addition can be ascertained for decreasing dilutions by making measurements in a time sequence. Thermal Conditions Below the Surface
After balancing the two thermocouples in the saturated vapor the lower couple (the probe) could be moved downward to obtain a superheat profile in depth, laterally at fixed depths for across-the-flask profiles, or held stationary to record changes with time. Curiously, except for the top 0.5 mm. and the half centimeter near the flask walls, all three records were similar, showing downward fluctuations every few seconds of 0.1-0.6 maximum At,. The most useful information reported, therefore, came from a stationary probe situated 0.3-1.0 mm. below the surface at the center. Fluctuations were not observed until a critical degree of superheat was reached-At, = 0.2°-1.0' C. according to the liquid. The temperatures evidently marked the onset of the Rayleigh instability or the Langmuir tw-itching where orderly laminar streamine; of upwelling hot liquid from periphery to the center of the flask gave way to irregular exchange with slugs of heavier, cooler
liquid falling away from the surface. The degree of fluctuation, which bore no relation to the At, of onset, was most rapid with water and least with carbon tetrachloride. The measurements will be reported in detail elsewhere but examples are presented now for discussion with the flotation phenomenon. Thus chloroform required four watts input above base maintenance to give At, of 1 C., balanced by evaporation without fluctuation (the limit of the steady state) from 123 sq. cm. of surface. This is equivalent to the transfer of 77.7 cal. per square meter per second and evaporation of 1.317 grams per second from the same area. Effective thickness of the conduction layer, withk = 0.080 (eng. units) for chloroform, is 0.391 mm. The thickest quiet layer developing in carbon tetrachloride was 0.94 mm. at At, = 0.5' C.; and in water, 0.29 mm. with At, = 0.2' C. The great temperature swings beneath the water surface at higher superheats, 1'-2' C., indicated stagnant layers fluctuating between effective thicknesses of 0.136 mm. and 1.02 mm., always supposing that changes in E were not a large contributing factor. Referring again to the evaporation of chloroform at the rate of 1.317 g. m.-* sec.-l, the rate calculated from Equation 1 for At, = 1 ' C. is 7730 g.m.-2sec.-1, leading to a virtual or over-all coefficient E(the distillation factor) = 0.00017. The vapor thus leaves the surface at one six thousandths the maximum available rate and proceeds upward with trivial momentum and insignificant pressure differential. The potential pressure within the rn. hydraulic liquid is, however, 22 mm. of Hg (29.7-( head) above ambient for the 1' C. superheat, but this develops only where the surface is shielded by a superimposed resistance (for instance, the floating drop) or mechanically disturbed (as by the drop), both of which alter the temperature. Comparative data for chloroform, carbon tetrachloride, and water are given in Table I.
PROPERTIES OF T H E FLOATING DROP Type and Purity of Liquid. Distillate of any liquid yet examined will float suspended on the surface of the same liquid regardless of dissolved materials. Even surfactants, if foaming is absent, do not hinder flotation, nor do surface layers of fatt)- acids nor long chain alcohols. Conversely, intensive purification of the liquids, whether TABLE
I. VIRTUAL
Liquid
EVAPORATlON COEFFICIENTS Infiut, Watts/ Sq. M e t e r
Superheat Range, .-l-i
C.
1 I I
Eoajoration Factor, E (All X lo-:)
Water
Chloroform Carbon tetrachloride
Figure 4. Sessile drab: mnves on siqberheated liquid 22
INDUSTRIAL
A N D ENGINEERING CHEMISTRY
a
L i m i t of stability region.
77.5 I 38.75
1
1,oa 1.0"
17
Figure 5. Free floating water boule. from top and side
Boule weighing 78 grams seen
Figure 6. Vibrating water boule. Freefloating boule about Zgrams, 2' C. superheat, seen from above and below
associated, polar, or nonpolar combined with continued overflowing, has not removed the ability to float, except in two doubtful cases. Except where otherwise mentioned, the phenomena relate to liquids receiving in-test purification and prepared beforehand as follows. Organic: purchased A.R. grade, redistilled to provide a b.p. range
