J . Phys. Chem. 1984, 88, 4135-4137 Ib). If then the absolute values of the rate constants in K3 were increased, 4 ( 1 / 2 ) H 2 could be greatly improved a t 30 min (Table IC). It was however observed that in many c a s e the 4 600 nm; (M) deflecting mirror. Laser, a, b, c, d, S, M,, M,, and R are the same as in part a except that M 2is set at 440 nm for fluorescence measurements (If). the cell. This layer was thought to be maintained by the evaporative convection taking place in open-cell DMA/CHC13 solutions. In the present article, we report the results of a series of experiments on the DMA/CHC13 system. In these experiments, a He/Ne laser is used to probe the convective motion taking place in both pure chloroform and irradiated DMA/CHC13 open-cell systems. These results strongly suggest that the origin of the fluorescence oscillations is physical rather than chemical; Le., the DMA fluorescence would act as a probe for a time-dependent convective regime and not as a stimulus for a chemical instability. This new interpretation was first set forth by Epstein et al. in their study of the role of hydrodynamic motion in the DMA/CHCl, system and other photochemical oscillators.2 Our conclusions therefore support their findings and interpretation.
Experimental Section A schematic representation of the apparatus used in a first series of experiments is shown in Figure la. As in paper 1, the sample under study was contained in an unstoppered 1 X 1 X 4.5 cm Spectrosil fluorescence cell. The cuvette was positioned in the cell holder of an Aminco-Bowman spectrofluorimeter. In order to monitor the convective motion, the beam from a He/Ne laser (A,, = 632.8 nm, 1 mW) was aligned so that it passes through the sample at the same height but at right angles to the UV light beam coming from the Aminco xenon source. The intensity of the transmitted laser beam was monitored by detector D. The principle behind the use of a laser beam to probe the convective motion is that a ray of light passing through a fluid undergoes an angular deflection directly proportional to the refractive index gradient at each point along its path.' As a result, these deflection change the intensity of the light reaching the Aminco-Bowman detector through pinhole slit d. If time-dependent convection is taking place within the bulk sample, then it must be accompanied by corresponding time-dependent changes in the local refractive index along the laser path. Time-dependent convective motion can therefore be revealed and investigated by monitoring the (2) Epstein, I. R.; Morgan, M.; Steel, C.; Valdes-Aguilera, 0. J . Phys. Chem. 1983,87, 3955. (3) Berg, J. C.; Acrivos, A.; Boudart, M. Adu. Chem. Eng. 1966, 6, 61.
transmitted laser light intensity (I,) as a function of time. A schematic diagram of the apparatus used in a second series of experiments is shown in Figure lb. In this configuration, the UV and laser light beams are arranged in such a way that they both pass through the same volume element of the DMA/CHCl, solution. The key component here is the band-pass filter F (A,, = 260 nm; band-pass = 15 nm). This filter is transparent to the 260-nm fluorescence excitation beam but acts as a reflector to the incoming laser beam that enters the solution from the opposite side of the cell. In order to isolate the transmitted laser light signal, the optics guiding the laser beam out of the Aminco were aligned such that the incoming and outcoming beams are not superimposable. This slight misalignment allowed us to pick out the outcoming beam at point M and deflect it to a radiometer/photometer detector (EG&G Model 450-1). The fluorescence and transmitted light intensities were then recorded simultaneously as a function of time on a two-channel strip-chart recorder.
Results Experiments Using Pure Chloroform. In a first series of experiments, we probed the convection motion in pure CHCl,, Le., not containing any DMA. Figure 2 shows some of the traces of the transmitted laser light intensity obtained by using the Figure l a arrangement. For most runs, the traces of I, oscillations were found to be chaotic. In some cases however, periodicity was observed as seen as Figure 2. The I , oscillations were found to be very sensitive to the volume of chloroform used, Le., to the depth of the fluid column. At -4 cm', oscillations were violent, pulselike, and of shorter period ( ~ 5 - 1 0s, e.g. Figure 2C). At = 3 cm3, they were much less violent and of generally longer period. Below -1 cm3, no oscillations were observed, the transmitted light intensity remaining stable at its initial value. Also, the oscillatory behavior was not found to depend much on the position at which the convection motion was probed along the X axis; Le., if a 10-s-period oscillation was observed near the edge of the cell, then an oscillation of similar period was (most of the time) observed at the center of the cell, or at any of the intermediate positions. In order to visualize this time-dependent phenomenon, the cell containing the chloroform sample was illuminated with the enlarged beam ( ~ 5 - c m diameter) from the He/Ne laser. The outcoming beam was then magnified and projected onto a viewing screen. An image showing refractive index variations along the light path as dark zones against a lighter background was thereby obtained. Our observations can be summarized as follows. As already pointed out in paper 1, the convective motion is basically roll-like. The number of rolls as well as their shape were, however, found to change with time, a feature that the local scattering technique used in previous work' had failed to reveal. Within the top layer of chloroform, the evaporation-induced convection gives rise to what appears to be a chaotic or turbulent fluid motion. Within the bottom layer of fluid, however, the convection motion is much more quiet and regular. Streams of cooler fluid can be seen to emerge, more or less periodically, from the upper layer and slowly plunge into the liquid. Upon reaching the bottom of the cell, these streams collapse and give rise to a low-amplitude (reactior) wave that can be seen
The Journal of Physical Chemistry, Vol. 88, No. 18. 1984 4137
Oscillatory Fluorescence in Irradiated Solutions 1
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Figure 3. Parallel traces of the fluorescence intensity (I,) and the transmitted laser light intensity ( I t ) for DMA/CHC13 solutions. Experimental configuration as in Figure lb. DMA concentrations: 4 X M for all traces. Volumes of solution: (A, B) 3 and (C) 4.0 cm3.
climbing along the cell walls. The amplitude of this fluid wave was estimated to be of the order of 1-2 mm. It might be added here that a phenomenon very similar to these plunging streams was observed more than 20 years ago by Spangenberg and Rowland in their study of evaporative convection in deep tanks of water.4 Experiments with DMA/CHC13 Solutions. In a second series of experiments, the convection motion was probed in DMA/CHC13 solutions. The concentrations used were the same as those for which periodic fluorescence oscillations have been reported,' Le., -4 X M. The experiments described above for pure chloroform were repeated for DMA/CHC13 solutions, under the same experimental conditions. As might have been expected, the convective behavior of diluted DMA/CHC13 solutions was found to be absolutely identical with the one observed and already described above for pure chloroform. We also checked for a possible influence of the fluorescence excitation beam on the convective motion. Using the arrangement described in Figure la, we repeatedly turned on and off the 260-nm fluorescence excitation beam and looked for any effect on the trace of Z, as a function of time. No such effect was observed. Special attention was paid to the volume of solution in the vicinity of the front face of the cell. Since most of the absorption at 260 nm takes place within the first millimeter of solution = 1.85 X lo5 L. mol-'-cm-'), this was thought to be the region where this effect would be more pronounced. Here again, no such effect was observed. In order to better understand the correlation between the periodic convective motion and the fluorescence oscillations, the apparatus described in Figure l b was used. To a good approximation, this arrangement monitors two variables that are both dependent, in a different way however, on the properties of the same transversed volume of solution. Typical dual traces obtained in those experiments are shown in Figure 3. Figure 3, A and B, shows traces in which some segments do reveal the existence of a correlation between the two oscillatory signals. In general, it was found that the shorter the period of the convective motion, the less likely it was to observe fluorscence oscillations of a similar period. In other words, when the convection motion is chaotic, the fluorescence behavior is chaotic as well and no correlation is observed between the two. This was typically the case for the larger volumes of solution (e.g., -4 cm3, e.g., Figure 3C). With smaller volumes (-3 cm3), both phenomena were found to be much more often in phase (e.g., Figure 3, A and B). With still (4) Spangenberg, W. G.; Rowland, W. R. Phys. Fluids 1961, 4 , 743.
smaller volumes ( E 1 cm3), no oscillations in either signal were observed.
Discussion The results presented above suggest that the origin of the fluorescence oscillations in irradiated DMA/CHCl, solutions is hydrodynamic rather than chemical as previously assumed.' In other words, the driving force for the fluorescence oscillations would be a time-dependent hydrodynamic motion and not a photochemical reaction. This conclusion is supported by the two following sets of experimental results: (1) Oscillations in the refractive index along the laser light path occur in the absence of DMA, Le., in pure chloroform. (2) A fairly good correlation is observed between the period (and sometimes phase) of the fluorescence and hydrodynamic oscillations. It is to be noted that the hydrodynamic oscillations are themselves very unlikely to be photochemically induced since chloroform is totally transparent to the 632.8-nm laser light used in our experiments. The theory of evaporative convection has been the subject of some interest in the past years.5 In evaporating fluids, one is concerned with the hydrodynamic stability of a system subject to a negative temperature gradient, Le., cooled from above. From a formal point of view, this problem is not believed to differ significantly from the classical Benard problem, Le., convection in a fluid heated from below. For the Benard systems, the existence of periodic regimes is well documented for shallow layers of fluids.6 Unfortunately, the problem of periodic convection in deep layers of fluids has received very little attention. The only observations of stable oscillatory modes in such systems seems to be due to Olsen and Rosenberger in their study of convective instabilities in columns of gas heated from below.7 In a recent paper on photochemical oscillations, Epstein et al. have considered the problem of determining the value of the Rayleigh number RT beyond which a time-dependent convective motion could take place in deep layers of fluid.* It was suggested that an approximate expression for this number can be written as R, pR,, where R, 200 and p is a number which depends on the Prandtl number of the fluid. Using this approach, one finds for chloroform RT 12R, = 24OOs2 The Rayleigh number for a 3-cm-high (1-cm diameter) column of chloroform is readily calculated to be R = 1.84 X 105AT,*where AT is the temperature gradient between the top and bottom of the liquid layer. As pointed out by Epstein et al., the magnitude of the temperature gradient (-0.015 oCcm-') necessary to sustain a time-dependent convective regime is therefore very small. It is in fact very likely that the surface cooling taking place in evaporating solutions of DMA/CHC13 provides a temperature gradient that is more than sufficient to produce a Rayleigh number larger than the necessary 2400.9
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Acknowledgment. We thank F. Bertrand for assistance with several of the experiments. This work was supported by CRAD Grant No. 3610-644: F4120. M. G. acknowledges a scientific and technical grant from the European Communities Committee. Registry No. CHCl,, 67-66-3; DMA, 781-43-1. (5) Quinn, G. P.; Saville, S. A. Lett. Heat Mass Transfer. 1976, 3, 309. See also ref 3. (6) Normand, C.; Pomeau, Y . ;Velarde, M. G. Rev. Mod. Phys. 1977.49, 581 and references therein. (7) Olson, J. M.; Rosenberger, F. J . Fluid. Mech. 1979, 92, 609. (8) For chloroform, one has p (kinematic viscosity) = 4 X IOw3 cmz.s-', C, (specific heat) = 0.226 cabg-'; p (density) = 1.489 gcm-', K (thermal conductivity) = 2.46 X cal.s-'an-'.K-', a (expansivity) = 1.107 X K-' (values taken from: Perry, J. H., Chilton, C. H., Eds. "Chemical Engineers Handbook"; McGraw-Hill, New York, 1973). The Prandtl number (P)is defined as P = p C , p / ~ . Using the values above, one gets P = 5.5 for chloroform. The Rayleigh number is defined as R = gap2Cpa4AT/(rrth), where g is the gravitational constant, AT the difference in temperature between the top and bottom of the column of fluid, h the height of the column, and a its diameter. For a column of chloroform 1 cm in diameter and 3 cm in height, one finds R = 1.841 X 105AT. (9) Spangenberg and Rowland4 have measured the temperature depression of an evaporatively cooled surface film of water at various depths within the layer. Typically, the temperature depression at 1.O mm below the surface was found to be as large as 0.2 OC, 1 min after the start of the free evaporation process; see also: Ewing, G.; McAlister, E. D. Science 1959, 131, 1376.
