Langmuir 1990,6, 991-994
991
is the thickness of the adsorbing monolayer film. In the equilibrium state (Ude = Uad), the surface concentration (rLM&,) can be indicated as follows, by using eqs 1-3:
I,O P 0.8
, E
4
5 0.6
F L m = k,d[LMAl 0.4
(4)
Since [LMA] is constant when compressing the film, by combining eq 1with eq 4 we can rewrite the net desorption rate of LMA for the compressed film with the difference between I ' L m and r L M A as follows:
0.2
0
I
2
3
Elapse t l m e [mln.l
Figure 11. Effect of counteranion of Ba2+ salt on AII/AIIt=o vs time curve at liquid paraffin BaC12 aqueous solution inter1 X 10-6; salt, 1 X 10-2 (A-D), 0 mol face: Cl~-18-crown-6, dm-3 (E). Counteranion: C1- (A), SCN- (B),Clod- (C), and Nos(DL
$,,+
face. Figure 11shows the plots of AII/AII,=o vs time for the system including various anion species, and Table I indicates the initial gradient of each curve in Figure 11. The initial gradient of the curve in the figure can be concerned with the rate constant of the desorption, Le., the net desorption rate of LMA, u, can be described as follows: u = Ude - uad Ude = kderLMA/6 uad
=
(1)
(2) (3)
where Ude and Uad indicate the rate of desorption and adsorption and kde and kad are the rate constants, respectively. r L M A is the surface concentration of LMA, and 6
u = k d e ( r L m - rLm)/6 (5) If the surface pressure is dominated only by the surface concentration, and the total surface concentration of the ligands is determined by r L M A , then the following relations can hold: dII/dt -(RT)drLm/dt = (-Rnkde(rLm - rLm)
= -kd,AII
(6)
where A l l = II - no and llo is the ll in equilibrium. Equation 6 indicates that the ratio (dII/dt)/All corresponds to -&e. By comparing the ratio with IIo in Table I, we found that the anion resulting in a low surface pressure in Figure 11is not always easy to desorb from the interface into the oil phase. This will be based on the electrostatic effect on the surface pressure and the difference between the ion-pairing state a t the oil/water interface and in the oil phase. Registry No. Ba, 7440-39-3; ((octadecyloxy)methy1)-18crown-6, 102674-28-2;diisobutyl ketone, 108-83-8.
A Stable Transitional Flow Pattern in the Surface Tension Driven Spreading of Ethanol-Water Solutions Deron A. Walterst 2353 Cambridge Blvd., Columbus, Ohio 43221 Received March 3,1989.I n Final Form: November 2, 1989 When a drop of one ethanol-water solution is placed on the surface of a different ethanol-water solution, the difference in surface tension along the drop boundary causes spreading behavior which depends sensitively on the ethanol concentrations of the two bulk phases. Within a narrow range of concentration combinations, an intricate flow pattern with azimuthal symmetry was observed through the use of schlieren photography. This phenomenon, believed to be a novel Marangoni effect, was characterized in terms of its qualitative features and the region of concentrations for which it occurred. The concentration zone was consistent with a fixed surface tension difference between the two solutions. When a drop of ethanol is placed on a water surface, a violent mixing phenomenon is observed. The drop spreads rapidly and turbulently across the surface, dissolving completely in less than 1 s. If the pure liquids t Present address: Mail Code 1-60, California Institute of Technology, Pasadena, CA 91125.
0743-7463/90/2406-0991$02.50/0
are replaced by different mixtures of ethanol and water, a wide range of flow patterns and mixing rates can be observed. These are easily identified as Marangoni effects, i.e., surface tension driven hydrodynamic flows. Extensive research has been conducted on Marangoni effects and related topics. Several such Phenomena were observed as early as 1855 by Thomson,l including both 0 1990 American Chemical Society
992 Langmuir, Vol. 6,No.5, 1990
-s
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5
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-E -m .-
"2
Turbulent
90
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n
n
70
60
50 40
30
0
a 20
g
10
0 0
10
20
50 60
30 40
70
80
90 100
Pool Concentration (volume %)
Figure 1. This map characterizes the behavior of spontaneous ethanol-water mixing at different drop and pool concentrations. The solid line represents equal drop and pool surface tensions, Le., A c = 0. Below this line, the drop sinks to the bottom of the pool and displays no surface phenomena. Above and close to the solid line, the drop floats quietly on the pool surface, emitting laminar flow streams. Above the top dashed curve, the drop floats momentarily before being turbulently dissipated by the large tension gradient across the perimeter (high Ao). Between the dashed curves, there is a transition regime in which the mixing displays some turbulence along with intermediate mixing times and flow velocities. The triangles indicate points corresponding to a mixing time of 1 8. A stable flow pattern of petals radiating from a central structure is observed in the region marked -Petal Effect Zone." the effect described above and the more familiar "tears of strong wine". Beginning with Sternling and Striven? much recent work has been dedicated to analyzing the conditions for stability at a fluid interface subject to Marangoni The cases analyzed, however, differ substantially from the ethanol-water mixing effect; while the former generally consider a single interface, the latter is characterized by the intersection of three interfaces (water-air, ethanol-air, water-ethanol). Furthermore, among several basic references that cover the scope of interfacial phen~mena,"-~ no mention is made of ethanol-water mixing. Several related effects have been studied, such as evaporation from pools'o and adsorption of alcohols from the gas phase;" once again, these are quite different from the ethanol drop/water pool system. No evidence of a detailed study of this system has been found. In an earlier study conducted by the author,'* it was found that a drop of one ethanol-water solution, when placed on the surface of a pool of another ethanol-water solution, exhibited mixing behavior that depended strongly on the ethanol concentrations of the two solutions. Figure 1 is a map of combinations of drop and pool concentrations, with each zone showing a particular type of mixing. Below the solid line, the drop is denser than the pool; it immediately sinks to the bottom (precluding any surface tension effects) and mixes by diffusion. Above the solid line, the drop floats on the pool. The pool, con~
~~~
~~
(1) Thomsan, J. Phrlos. Mag. 1855, Ser.4, 10,330. (2) Stemling, C. V.; Seriven. L. E. AIChE J 1959,5. 514. (3) Linde. H.Faradov Dtseusa. Chem. Soc. 1984.. 77.181. . (4) Irvin. B. R. Langmvir 1986.2,79. (5)Seriven. L. E.; Sternling. C. V. Nature 1960,187,186. (6)Levieh. V. G.; Krylov. V. S. Annu. Rev. Fluid Mech. 1969, I , 293. ( 7 ) Meares. P.Farodav Discuss. Chem. Soe. 1984.77.7.
(8)Devies,J. T. Turb&nee Phemmew: Academie P-:
New York.
1972; Chapters 2 and 3.
(9)Dsvies, J. T.: Rideal, E. K.Interfoeid Phenomena, 2nd ed.: Aeademic Press: New York. 1963: Chapters 4-7. (IO) Berg. J. C.: Boudart. M.: Acrivos. A. J. Fluid Meeh. 1966, 24, 711
(11) Ellis. S. R. M.; Biddulph, M. Chem. Eng. Sei. 1966,21,1107. (12) Walters, D. A. Unpublished manuscript. 1986.
Figure 2. 'l'his knife-edge schlieren photograph of the petal effect shows some of i t s characteristic features: the central structure (a ring. in this case). with its radial projectiuns: one full row of petals, with second- and third-row petals visible to the lower left: and rays at the tips of the petals, pointing radially outward. Note: Black abject at the upper right of the figure is a medicine dropper, tip diameter 2.5 mm.
-
taining less ethanol, has a higher surface tension than the drop; liquid from the drop is therefore pulled outward along the surface as it dissolves in the pool. When the two solutions are quite dissimilar, as in the upper left corner of the map, the difference between their surface tensions (Au) is high 50.3 dyn/cm for a pure ethanol drop on a pure water The spreading is therefore rapid and turbulent, producing no stable flow pattern. When the two solutions have nearly the same concentration, i.e., points near the solid line, the surface tension difference is low (&4 dyn/cm); therefore, the mixing is slow and laminar. Dissipation times-the time taken for a drop to be completely dispersed by the mixing process-range from under 0.5 s with the fastest combinations to 5 s or more for the slowest. In Figure 1, the triangles indicate points experimentally determined to have dissipation times of 1s. This was subjectively judged in the earlier study to be representative of the approximate regime of transition between turbulent and laminar mixing. The dashed curves consist of points with fixed An; the transition zone therefore corresponds to a map region with a constant Au between 4 and 9 dyn/cm. For certain combinations of drop and pool concentrations within this transition zone, an azimuthally symmetrical flow pattem resembling a ring of petals was observed in the region around the drop (see Figure 2). This phenomenon, dubbed the "petal effect", was often stable for as long as 2 s. Since this effect consisted of subtle curvatures of the liquid surface, it was only visible through a sensitive schlieren instrument. It only appeared for a narrow range of drop and pool concentrations, so narrow that 10 min of differential evaporation from a 96-cm2 pool decreased the ethanol concentration sufficiently to render the mixing too turbulent to show the petal effect. In light of the dearth of previous study in this area, the difficulty of observing the effect, and the high sensitivity to solution concentrations, it is believed that the petal effect may be a novel Marangoni effect not previously observed. The objective of the current study was to characterize the features of the petal effect and explore the boundaries of the regime in which it occurs. The effect was studied by using a modified schlieren apparatus. A collimated beam of white light passed vertically through a glass cuvette containing the pool solu(13) CRC Handbook of Chemistry and Physics, 65th ed.; Weash R. C., Astle. M. J.. Beyer, W.H..Eds.: CRC Press: Boea Raton. F1, 1985; p F-32.
Surface Tension Driuen Hydrodynamic Flows 100
Langmuir, Vol. 6, No. 5, 1990 993
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__-.
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30 40 50 60 Pool Concsntratlon (volume H )
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Figure 3. This map (an enlarged portion of the map in Figure 1) shows the region in which the petal effect was observed. The circle data points reproducibly displayed the petal effect. The plus and minus signs indicate points at which mixing was either too rapid or too slow for the pattern to form. tion. A piece of hypodermic tubing was fixed 5 mm above the pool surface; through this, a siphon delivered consistent amounts of drop solution a t regular intervals (usually about 5 s). The petal effect introduced small curvatures on the pool surface; these refracted light, introducing angular deviations in the heam. A 128-mm focal length lens was used to image the pool surface onto a film plane. This lens separated the deviated rays from the rest of the beam: undeviated rays all passed through the focal plane a t a single point, whereas refracted rays were laterally displaced from this point. A spatial filter placed in the focal plane of the lens selected which rays reached the image of the pool. A pinhole, for example, permitted undeviated light to appear in the image but cut off the refracted rays; this gave a dark image of the flow pattern on a bright field. Other spatial filters used were a knife edge (conventional schlieren) and an inverse pinhole (a dark point). This latter was most successful, producing bright images on a dark field. Nevertheless, the knife-edge schlieren had an important use; because of its asymmetry, it could be used to determine whether the feature being imaged was optically positive or negative (convex up or concave up). The image was recorded directly on 400 ASA, 35-mm film, using a Nikon N2020 camera back. A typical exposure time was 1/250 s. The shutter was triggered by hand while watching the image through the viewfinder; this presented no great problem, since the petal effect usually lasted around 2 s. The camera's continuous shooting feature was sometimes used to take a sequence of photographs of the same drop as it dissipated. The interval between shots was measured a t 0.5 s, allowing three to four shots per drop. This technique was used only two to three times per experiment; most drops were only photographed once. Seven combinations of drop and pool concentrations were used. Great care was taken in mixing the solutions accurately; all solutions were mixed immediately before use to avoid errors due to evaporation. All surfaces of the apparatus which would contact the solutions were cleaned thoroughly and rinsed with the solution which they were to contain. Due to material constraints, it was not possible to conduct the experiments in an ethanolsaturated atmosphere; therefore, once the siphon and the pool container were filled, the experiment was completed within 5 min or less, minimizing concentration changes due to evaporation. It is believed that the time scale of the petal effect is too short for evaporation to play a significant part in its dynamics.
Figure 4 . 'l'his knife-edg? srhlicren phutwraph shows the heginning
