J. Phys. Chem. 1987, 91, 2487-2489
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Condensation of Supersaturated Water Vapor at Low Temperatures in a Shock Tube F. Peters Lehrstuhl fur Stromungslehre, Universitat Essen, 0-4300 Essen, FRG (Received: June 17, 1986)
The onset of condensation by homogeneous nucleation of water vapor in the supersaturated state was measured in the isentropic expansion wave of two different shock tubes. Available data on condensation are extended to lower pressures by a factor of ten to 0.1 Torr at 180 K.
Introduction The shock tube was first applied to condensation research by Wegener and Lundquist.' It has since served to determine the onset of condensation of water and other substances in the supersaturated ~ t a t e . ~ For - ~ the condensation of inert gases precooled shock tubes were e m p l ~ y e d . ~ The , ~ quantitative determination of nucleation rates in shock tube experiments was demonstrated by Peterss Comparable experimental tools are cloud chambers, supersonic nozzles, and molecular beams covering cooling rates in the wide range from -1 OC/ms for cloud chambers to -lo6 OC/ms for molecular beams. Shock tubes give cooling rates of about -10 to -100 OC/ms, between those of cloud chambers and nozzles. The different experimental methods are reviewed by Wegener and W U ,Kotake ~ and Glass,lo and others. Here we confine ourselves to a brief description of the experimental technique and give results omitting a discussion of the gas dynamics which has been dealt with in the cited papers. The shock tube consists of a straight pipe divided into a highand a low-pressure section, i.e. driver and driven section, by a mylar diaphragm, as illustrated in Figure 1. The high-pressure section contains argon (99.999% purity) mixed with small mole fractions of water at a typical pressure of 750 to 1700 Torr. The lowpressure section is open to the atmosphere or partially evacuated. Both sections are at room temperature prior to the experiment. Upon breaking the diaphragm an expansion wave travels into the high-pressure section and is reflected at the end wall. This wave decreases the initial high pressure within 2 to 4 ms by as much as 70%. Figure 1 displays the pressure drop for two different observation stations A and B. The expansion wave is isentropic and the gas temperature as a function of pressure is found from T/T, = (p/pp-l)/r
(1)
with subscript 4 indicating initial states and y = cp/cv,the ratio of specific heats (y = 5 / 3 for argon). Pressure and temperature as encountered at station A or B force the water vapor into its supersaturated state. Heterogeneous nucleation may be ruled out because foreign nuclei are not available in sufficient concentrations and the tube walls remain at room temperature for the short duration of an experiment. At station A or B a laser beam is passed through the tube normal to its axis. A photomultiplier is placed to receive light scattered by the forming of water droplets. The condensation occurs spontaneously at a certain critical supersaturation giving a rapidly increasing light signal. The supersaturation is defined as the actual vapor pressure over the (1) (2) (3) (4) (5)
Wegener, P. P.; Lundquist, G. J . Appl. Phys. 1951, 22, 233. Barschdorff, D. Phys. Fluids 1975, 18, 539. Glass, I. I.; Kalra, S. P.; Sislian, J. P. AIAA J . 1977, 15, 686. Peters, F. J . Chem. Phys. 1982, 77, 4788. Wegener, P. P.; Lee, C . F. J . Aerosol Sei. 1983, 14, 29. (6) Matthew, M. W.; Steinwandel, J. J . Aerosol Sei. 1983, 14, 755 (7) Zahoransky, R. A. J . Chem. Phys. 1985,82. (8) Peters, F. Exp. Fluids 1983, I , 143. (9) Wegener, P. P.;Wu.B. J. C . Adv. Colloid Interface Sei. 1977, 7 , 235. (10) Kotake, S.; Glass, I. I . Prog. Aerospace Sei. 1981, 19, 129.
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TABLE I: Onset of Condensation of Water Vapor in Argon in the Supersaturated State As Plotted in Figure 2" Ta, K pa. Torr Torr p K , Torr Tu, K Shock Tube I1 293.0 293.0 293.9 294.6 294.9 294.9 295.1 295.2 295.7 293.7 293.7 293.7 293.9 293.9 293.7 293.8
1276.2 1349.8 1644.2 1054.4 1201.6 1348.8 1350.8 1203.6 1056.4 1658.2 922.2 701.4 922.2 1731.8 627.8 1216.6
296.5 296.5 296.5 296.5 296.5 296.5 296.5 296.5 296.5
773.0 773.0 713.0 773.0 773.0 773.0 773.0 773.0 773.0
1.99 2.11 2.51 1.17 1.33 1.50 3.00 2.67 2.35 1.84 1.02 0.78 0.51 0.96 0.35 0.68
0.92 0.98 1.26 0.46 0.55 0.64 1.46 1.29 1.07 0.88 0.41 0.27 0.15 0.39 0.11 0.24
214.6 215.5 221.2 203.3 206.5 210.4 221.1 220.9 216.2 218.1 203.2 192.5 181.7 205.0 185.9 192.9
2.10 1.62 1.44 1.10 0.81 0.46 0.32 0.26 0.17
225.8 223.0 220.7 217.2 211.6 202.4 198.0 194.6 185.0
Shock Tube I 4.06 3.3 1 3.01 2.41 1.88 1.21 0.89 0.74 0.55
" T4, p4, and p4ware the temperature, total pressure, and partial pressure of water before the expansion. TK and pKare the temperature and pressure at onset. saturation vapor pressure for a flat surface at the same temperature. The result of the experiments is the pressure measured at the instant of the increasing light signal for different water vapor pressures. From this pressure the corresponding temperature may be found from eq 1 and consequently the thermodynamic state at the onset of nucleation is determined.
Experiments The experiments were performed with two different, geometrically similar shock tubes. Shock tube I was made from glass tubing of 50 mm i.d. Observation station B was located 1.28 m upstream of the diaphragm (Figure 1). A He-Ne laser (632.8 nm) was used together with a RCA 7265 photomultiplier as the light detector. The pressure was measured at the observation station by a quartz pressure transducer (Kistler 606L). The pressure and light signal were simultaneously recorded on an oscilloscope. A stainless steel mixing tank with a magnetic stirrer was connected to the driver side of the shock tube by stainless steel tubing. First, distilled water was evaporated into the evacuated tank at a partial pressure between 10 Torr and the saturation pressure (21.7 Torr at 23.5 "C). The pressure was measured to within 3~3%. Second, argon was added while operating the stirrer. Water vapor pressures around 1 Torr could 0 1987 American Chemical Society
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The Journal of Physical Chemistry, Vol. 91, No. 10, 1987 0.5ms
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-*
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Figure 2. Onset of condensation of water vapor by homogeneous nucleation in argon in the supersaturatedstate. (A)This work Shock tube I at cooling rates of about -10 OC/ms. (0)This work: Shock tube 11 at cooling rates of about -50 OC/ms. ( 0 )Shock tube data by Wegener and Lee.s (+) Shock tube data by Barschdorff.2 The upper dashed line represents a collection of nozzle data as given by Wegener and Wu9 for cooling rates on the order of -10' OC/ms.
not be measured reliably. They were produced, therefore, by partial depletion of tank mixtures of higher initial water content and subsequent refilling with argon. While this procedure is correct in principle, adsorption of water at tank walls etc. during the dilution with argon could affect the low water pressure. A second series of experiments was made to check the results from shock tube I. Shock tube I1 was built from brass tubing of 46 mm i.d. The observation station was placed at the end wall 1 m away from the diaphragm (A in Figure 1). The pressure drop was measured by a quartz pressure transducer (Kistler 6031). The light source was an argon laser (488 nm) placed normal to the tube axis directly in front of the end wall. The end wall was a glass window through which the photomultiplier (RCA 6 199) observed the scattered light at a right angle. Pressure and light signals were recorded on an oscilloscope. Again distilled water was evaporated into an evacuated mixing tank made of brass like the shock tube. The pressure increase ranging from 2.5 to 10 Torr
was measured with an accuracy of *1.5%. In order to check the water content in the argon after mixing a part of the argon-water mixture was drained through a U-tube packed with a drying agent (silica gel). The mass increase of the tube due to the absorbed water was measured on an analytical balance and, consequently, the partial pressure of the water in the tank could be determined. It was found that this partial pressure was as much as 5% smaller than the initially measured partial pressure. In turn the actual partial pressure of water in the argon might scatter by +1.5% and -5% about the measured value.
Results and Discussion The results for shock tubes I and I1 are given in Table I and in Figure 2 . The figure shows the equilibrium vapor pressure of water over liquid and solid. The sample isentrope computed from eq 1 connects the initial conditions ( T4,p4w)with the detected onset conditions ( TK, pKw).The results of both shock tubes agree within a scatter of *4 O C . The agreement validates the difficult determination of the low partial pressures of water vapor. Due to the above-mentioned adsorption on tank walls etc. the pressure at onset may be high by 5%. The expansion pressure p and the total initial pressure p4 are known with higher accuracy. Figure 3 shows two recordings of pressure and light signal of shock tube 11. Signals a (top) correspond to a higher water content than signals b (bottom). We see that the light signals stay constant after the steep onset rise. This indicates that condensation is terminated because equilibrium is established between the condensed phase and the depleted vapor. Light signal b comes close to the detection limit of the optical system which is reached for the onset pressure of 0.1 Torr. Our results extend the shock tube data obtained by Barschdorfp and Wegener and Lee4 to appreciably lower pressures and tem-
J. Phys. Chem. 1987, 91, 2489-2492 peratures and corresponding larger values of supersaturation. For comparison the upper dashed line indicates a collection of nozzle data taken from Wegener and W U . ~They show higher supersaturation because of higher cooling rates in the order of -103 OC/ms compared to our shock tube cooling rates between -10 and -50 OC/ms. It appears that the results shown here represent the lowest pressures and temperatures at which the homogeneous conden-
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sation of water vapor in a carrier gas has been observed. Acknowledgment. The work with shock tube I was carried out at Yale University, Applied Mechanics, in Prof. p. p. Wegener’s laboratory, and was supported in Part by NASA Grant No. NAG-2-15 to Yale University. The work with shock tube I1 was in Part supported by the University of Essen. Registry No. H20, 7732-18-5.
Homogeneous Nucleation of Mercury Vapor J. Martens, H. Uchtmann, and F. Hensel* Institute of Physical Chemistry, University of Marburg, 0-3550 Marburg, FRG (Received: June 17, 1986)
We report the first experimental determination of the critical supersaturation for the homogeneous nucleation of mercury in the temperature range 260 to 400 K. The measurements were made in an upward thermal diffusion cloud chamber. The results demonstrate that none of the current theories for homogeneous nucleation satisfactorily predict the observed critical supersaturations. The measured values are about 3 orders of magnitude lower than the values predicted by the conventional Becker-Doring-Zeldovitch theory.
Introduction The study of the condensation of a supersaturated vapor to its liquid state by homogeneous nucleation has attracted interest for more than 50 years. It is the subject of numerous theoretical and experimental papers and various review articles.’-“ Most of the investigations have been devoted to the study of molecular liquids. Attempts to quantify the basic physics of the nucleation process for supersaturated metal vapors have received less attention? This is essentially due to the fact that according to the classical nucleation t h e o ~ it’ is extremely difficult to get metals to nucleate. The nucleation expression of the classical theory is J = A(pm/kT)2(2u/~m)1/2v,exp(-AG*/kT)
(1)
where J is the number of critical size clusters formed per cm3, and AG* is the Gibbs free energy for formation of the critical size . critical radius r* is given by cluster, AG* = 4 ~ r * ~ ( u / 3 )The the Gibbs-Thompson-Helmholtz equation r* = 2uv,/kT In S. The saturation ratio S is defined as pv/pm;pv is the partial pressure of the condensable vapor; T i s the temperature; p m is the vaporliquid equilibrium pressure at the same T; k is Boltzmann’s constant; u is the surface tension; m is the mass of a single vapor molecule; v, is the volume of the condensable molecule in the condensed phase; and A is a correction factor used to match theory to experiment. The magnitude of the nucleation rate is very sensitive to surface tension (cubic in the exponential expression). Because metals have surface tensions tens to hundreds of times higher than most molecular fluids, the classical theory requires sometimes extremely high supersaturations to lower the energy barrier to values encountered with molecular fluids. Due to the extremely high supersaturations the starting or critical radius r* for formation of a stable nucleation site in a supersaturated metal vapor (e.g. H g a t temperatures between 260 and 400 K) is unphysically small, i.e. the critical cluster sizes are in the size range Stein, G. D. Surj. Sci. 1985, 156, 44. Abraham, 0.;Kim, S.; Stein, G. D. J . Chem. Phys. 1981, 75, 402. Reiss, H.; Marvin, D. C.; Heist, R. H. J . Colloid Interface Sci. 1977, 58, 125. (4) Katz, J. L.; Scoppa, .. C. J.; Kumar, N. G.; Mirabel, P. J . Chem. Phys. 1975, 62, 448. (5) Frurip, D. J.; Bauer, S. H. J. Phys. Chem. 1977, 81, 1001. ( 6 ) Volmer, M. Kinetik der Phasenbilduna, Theodor Steinkooff Verlaa: 1
Dresden, 1939. (7) Frenkel, J. Kinetic Theory of Liquids; Dover Publications: New York, 1955.
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N = 1 to N = 10. Various investigations have criticized the classical theory because it uses the bulk surface tension to compute free energy differences between such small clusters and the bulk medium, Le., the capillarity approximation. One method of accounting for variations in free energy with cluster size is to allow the surface tension to vary with cluster size by the Tolman formula and to obtain the free parameter from coexistence-line data. However, this method has a conceptual difficulty for metals like Hg because surface tension is meaningless when clusters are too small ( N = 1 to 10) to contain interior atoms. In addition such small clusters of Hg must be expected to have a dominant nonmetallic character.* Experimental support for the existence of a size-dependent metal-insulator transition in small H g clusters comes from susceptibility measurementsg of small particles of Hg obtained by forcing the metal into cavities of the mineral Na-X zeolite. After the pressure is released some mercury leaves the porous material; the remaining metal takes the form of spherical drops containing 7-10 atoms. From the susceptibility it can be concluded that these particles are nonmetallic. In order to better understand the role of the metal-insulator transition in the homogeneous nucleation process of supersaturated metal vapors and to confirm or disprove the predictions of the classical nucleation theories we are currently investigating the experimental conditions necessary for homogeneous condensation of metal vapors. It is the purpose of the present brief paper to report the first reliable determinations of the supersaturation of Hg vapor, giving rise to the onset of nucleation (typically a nucleation rate of one drop per cubic centimeter per second) over a temperature range from 260 to 400 K. This is usually referred to as the critical supersaturation.’0 Our measurements were made in an upward thermal diffusion cloud chamber in which the diffusional process to produce supersaturation is one-dimensional and carefully computed so that the thermodynamic state is precisely known. There is no convection or turbulent transport to complicate the process. Experimental Method General descriptions of the thermal diffusion cloud chamber as well as the principles of operation and data analysis are available elsewhere and will not be reproduced in detail here.3-4J*12 There (8) Miedema, A. R.; Dorleijn, J. W. F. Phil. Mag. E 1981, 43, 251. (9) Bogonolov, V. N.; Volkonskaya, T. I.; Zadorozhnii, A. I.; Kapanadze, A. A.; Lutsenko, E. L. Sou. Phys. Solid State (Engl. Travel.) 1975, 17, 11 10. (10) Katz, J. L.; Ostermier, B. J. J . Chem. Phys. 1967, 41, 478.
0 1987 American Chemical Society
