J. Phys. Chem. 1996, 100, 16209-16212
16209
Double-Diffusive Convection in Traveling Waves in the Iodate-Sulfite System Explained John A. Pojman,*,† Andrea Komlo´ si,‡ and Istvan P. Nagy†,‡ Department of Chemistry and Biochemistry, UniVersity of Southern Mississippi, Hattiesburg, Mississippi 39406-5043, and Department of Physical Chemistry, Kossuth Lajos UniVersity, Debrecen, Hungary H-4010 ReceiVed: May 14, 1996; In Final Form: July 18, 1996X
Keresztessy et al. investigated traveling fronts of the oxidation of sulfite by iodate and determined that the isothermal density changes (∆Fc) and enthalpy were both negative. According to the Pojman-Epstein model, only simple convection should occur in this case unless two species have significantly different diffusion coefficients. In fact, curved descending fronts with velocities greater than the ascending ones and “fingering” were observed. We have found that the diffusion coefficient of sulfuric acid is sufficiently larger than those of the other species to cause double-diffusive convection. We confirmed this by performing experiments with layers of solutions composed of components of the reactive system. Thus, the Pojman-Epstein model is upheld.
Introduction Many autocatalytic reactions in solution can sustain a localized reaction front that propagates throughout an unstirred medium.1 As a front propagates, concentration and thermal gradients are formed that alter the density of the solution, often causing convection.2-10 Pojman and Epstein11 have classified the types of convection that can occur in traveling fronts. If the reaction is exothermic (∆H < 0) and the products’ solution is less dense than the reactants’ (∆Vrxn > 0), then simple convection can occur, depending on the constraints of the container geometry. If the signs are the same, then multicomponent (double-diffusive) convection may occur, even though the overall density gradient may appear to be stable. In a descending front, double-diffusive convection manifests itself as “salt fingers”, so-called because of their discovery in ocean layer mixing. Numerous systems have been found to exhibit double-diffusive convection.2,6,8-10,12-15 In a study of fronts in the iodide-nitric acid reaction, Nagy et al. extended the Pojman-Epstein model to include the case in which ∆Fc is negative but with two chemical species having significantly different diffusion coefficients.13 The triiodidestarch complex had a much smaller diffusion coefficient than other species. Keresztessy et al. recently studied fronts in the iodate-sulfite system and found apparently anomalous behavior.14 The ∆Fc is negative in this system, and according to the Pojman-Epstein model, only simple convection should have occurred. In fact, curved descending fronts with velocities greater than the ascending ones and “fingering” were observed. Representative front shapes are shown in Figure 1. Keresztessy et al. considered three possible explanations for this apparently anomalous behavior:14 (1) Convection caused by temperature differences in tubes above the front, caused by the mild heat release, is the cause of the anisotropy. This cannot explain the appearance of fingering in large tubes nor the curved shape of the descending fronts in small tubes. Moreover, the ∆T is very close to the iodatearsenous acid system, which does follow the model.3,16 (2) The Pojman-Epstein analysis is flawed because it is based on a static system of two layers and not upon a moving density * To whom correspondence should be addressed. † University of Southern Mississippi. ‡ Kossuth Lajos University. X Abstract published in AdVance ACS Abstracts, September 1, 1996.
S0022-3654(96)01391-3 CCC: $12.00
Figure 1. Diameter dependence of the wave shapes in the iodatesulfite system. Arrows indicate direction of propagation. [KIO3]0 ) 0.01 M, [Na2SO3]0 ) 0.015 M, [NaHSO3]0 ) 0.016 M, and [bromophenol blue]0 ) 0.32 w/v %.
gradient with chemical reaction. Vasquez et al. studied the onset of convection for reaction fronts and found that neglecting the velocity of the front did not significantly affect the stability.5 However, systems that are susceptible to double-diffusive convection are not well understood. For example, the original analysis did not predict the curvature of descending fronts in the iodide-nitric acid system.13 (3) There are species in the product solution that have significantly different diffusion coefficients from reactant species. It is possible, but rather unlikely, that high molecular weight sulfur species are produced, which have smaller diffusion coefficients than the ionic reactants. Turner determined that a factor of 3 difference in diffusion coefficients is all that is required for a double-diffusive instability.17 However, no precipitation of colloidal sulfur was observed, and the reacted solutions did not exhibit the Tyndall effect. We set out to explore whether the diffusion coefficient of any of the species was significantly different, either inherently or in the presence of other species. (The presence of other species is known to affect the diffusion coefficient of some species.18) We show that explanation 3 is correct although not with polymeric sulfur species. Sulfuric acid, a product in the reaction, has a significantly larger diffusion coefficient than the reactants. Using two overlying solutions in a special cell to mimic chemical fronts, we demonstrate that the layers of solution with apparently stable density gradients can exhibit © 1996 American Chemical Society
16210 J. Phys. Chem., Vol. 100, No. 40, 1996
Pojman et al.
Figure 2. Reactor used for model systems to investigate the fluid motion under unreactive conditions.
Figure 3. Densities (g cm-3) are indicated in parentheses: (a) top, 0.006 M Na2SO3 (0.997 82); bottom, 0.01 M KIO3 (0.998 98). (b) top, 0.03 M KIO3 (0.997 80); bottom, 0.006 M Na2SO3 (0.997 82). (c) top, 0.003 M Na2SO3 (0.997 73); bottom, 0.0051 M Na2SO4 (0.997 82). (d) top, 0.0051 M Na2SO4 (0.997 815); bottom, 0.003 M Na2SO4 (0.997 82) 30 min after removal of membrane.
double-diffusive convection if sulfuric acid is present. We also performed light scattering to show that no high molecular weight species are present.
Figure 4. Densities (g cm-3) are indicated in parentheses: (a) top, 0.003 M KIO3 (0.997 80); bottom, 0.0075 M H2SO4 (0.997 81). (b) top, 0.0075 M H2SO4 (0.997 81); bottom, 0.01 M KIO3 (0.998 98).
Experimental Section Chemicals and Apparatus. Solutions were prepared with analytical grade chemicals that were used as received: Na2SO3, KIO3, and Na2SO4 from REANAL, H2SO4 from Acidum Gmk (Debrecen, Hungary), bromophenol blue from Aldrich, and deionized water. To study the stability of fluid layers, we used the cell shown in Figure 2 and described by Pota et al.19 and used by Nagy and Pojman.13 The cell is made of Plexiglas with a 1 × 1 cm square hole, between two chambers. An impermeable membrane is placed between the chambers. To bring the two solutions into contact with each other, the membrane is pulled out. The concentration of the solutions was adjusted so that the bottom layer was always more dense than the upper layer. Thus, each experiment had an apparently stable density gradient. Bromophenol blue (0.32 w/v %) was present in both layers. Densities were measured with a 25 cm3 pycnometer at 25.0 ( 0.1 °C.
Imaging. Images were captured by a system that consisted of an IBM 80-486 compatible PC, an LFS-AT 8 bit black and white frame grabber board (LEUTRON AG, Switzerland), and an SDT 4500 monochrome CCD solid state camera (Steiner Datatechnik GmbH, Germany) and the necessary optics (25 mm focal length TOKINA lenses, Japan). The light scattering was performed in batch mode using a DAWN DSP-F laser photometer (Wyatt Technology Corp.) with a 5 mW linearly polarized He-Ne laser. (The 1/e2 diameter of the Gaussian beam profile is 0.39 mm.) Results and Discussion Light scattering analysis of a reacted solution did not indicate any signal above the background, indicating no high molecular weight species are present. Components of the iodate-sulfite system were prepared as solutions and put into the test cell. Various combinations of species were prepared to test whether cross-diffusion effects
Double-Diffusive Convection in Traveling Waves
J. Phys. Chem., Vol. 100, No. 40, 1996 16211
Figure 6. (a) Mechanism for double-diffusive convection in the fingering regime. (b) Mechanism for double-diffusive convection in the diffusive regime.
Figure 5. Densities (g cm-3) are indicated in parentheses: (a) top, 0.0051 M Na2SO4 (0.997 815); bottom, 0.009 M H2SO4 (0.997 83); (b) top, 0.0075 M H2SO4 (0.997 81); bottom, 0.0051 M Na2SO4 (0.997 815).
could sufficiently affect the diffusion coefficients and cause a double-diffusive instability. A less dense solution was always on top before the membrane was removed. By changing the upper and lower solutions, the gradients caused in ascending and descending fronts could be mimicked. Figure 3 shows the results for Na2SO3 and KIO3; no convection was observed. Figure 4a represents a configuration like an ascending front; iodate is overlying sulfuric acid. Double-diffusive convection clearly occurs. The reverse arrangement (Figure 4b) is also unstable. Solutions of Na2SO4 and H2SO4 are unstable (Figure 5). Figure 5 makes it clear that it is the H+ that makes the large difference in diffusivity because the only difference between the solutions is the cation, i.e., it is not the sulfate ion that causes the instability. The only pairs of solutions to exhibit double-diffusive convection were those with sulfuric acid as one of the two. If the sulfuric acid was either the top or bottom layer, convection and fingering were observed. Because of the high mobility of H+, sulfuric acid has a large diffusion coefficient (2.9 × 10-5
cm2/s) compared to other species such as Na2SO4 (0.9 × 10-5 cm2/s).18 Thus, the larger diffusion coefficient of sulfuric acid is the cause of the instability, in the same way that layers of salt and sugar solutions are unstable. Turner showed that one species must have a diffusion coefficient at least 3 times as large as the other species, which is consistent with the reported value of sulfuric acid.20 Figure 6 shows a model of the sulfuric acid/iodate layers. Figure 6a models the fingering regime of double-diffusive convection, with conditions analogous to those in an ascending front. A parcel of sulfuric acid solution enters the iodate solution above. Sulfuric acid diffuses out more rapidly than the iodate can diffuse in, causing the parcel to become less dense than the surrounding region. It rises. A parcel of iodate solution enters the lower region where the sulfuric acid diffuses in more rapidly than the iodate can diffuse out. The more dense parcel sinks. In Figure 6b the case of a descending front is shown. If a small parcel of the sulfuric acid solution enters the lower section, because the acid can diffuse out faster than the iodate can diffuse in, the parcel is left with a lower density than the surrounding medium. The buoyant force pushes it up. If a small parcel of iodate solution enters the upper solution, sulfuric acid will diffuse in faster than the iodate can diffuse out of the parcel. The parcel will be more dense than its surroundings and sink. This leads to weak convection as shown in Figure 4b, which is called the diffusive regime of double-diffusive convection. Conclusions The apparently anomalous convection observed in the iodatesulfite system has been explained in terms of the PojmanEpstein model. Sulfuric acid, a product of the reaction, has a sufficiently larger diffusion coefficient than other species to cause the observed double-diffusive instability. Model experiments with layers of solutions exhibited double-diffusive convection when sulfuric acid was one of the components. Acknowledgment. This work was supported by the U.S.Hungarian Science and Technology Joint Fund (Grant J. F. No.
16212 J. Phys. Chem., Vol. 100, No. 40, 1996 247/92a), the National Scientific Research Fund of Hungary (OTKA Grants F-4024, F016166, and T19254), and the Ministry of Education of the Hungarian Government (MKM Grant 9/94). We thank William West for assistance with the light scattering measurements. References and Notes (1) Ross, J.; Mu¨ller, S. C.; Vidal, C. Science 1988, 240, 460-465. (2) Pojman, J. A.; Epstein, I. R.; Nagy, I. J. Phys. Chem. 1991, 95, 1306-1311. (3) Pojman, J. A.; Epstein, I. R.; McManus, T.; Showalter, K. J. Phys. Chem. 1991, 95, 1299-1306. (4) Tzalmona, A.; Armstrong, R. L.; Menzinger, M.; Cross, A.; Lemaire, C. Chem. Phys. Lett. 1992, 188, 457-461. (5) Vasquez, D. A.; Edwards, B. F.; Wilder, J. W. Phys. ReV. A 1991, 43, 6694-6699. (6) Pojman, J. A.; Craven, R.; Khan, A.; West, W. J. Phys. Chem. 1992, 96, 7466-7472. (7) Miike, H.; Mu¨ller, S. C.; Hess, B. In CooperatiVe Dynamics in Physical Systems; 1989; pp 328-329. (8) Nagypa´l, I.; Bazsa, G.; Epstein, I. R. J. Am. Chem. Soc. 1986, 108, 3635-3640.
Pojman et al. (9) Bazsa, G.; Epstein, I. R. J. Phys. Chem. 1985, 89, 3050-3053. (10) Hauser, M. J. B.; Simoyi, R. H. Phys. Lett. A 1994, 191, 31-38. (11) Pojman, J. A.; Epstein, I. R. J. Phys. Chem. 1990, 94, 4966-4972. (12) Nagy, I. P.; Pojman, J. A. J. Phys. Chem. 1993, 97, 3443-3449. (13) Nagy, I. P.; Keresztessy, A.; Pojman, J. A.; Bazsa, G.; Noszticzius, Z. J. Phys. Chem. 1994, 98, 6030-6037. (14) Keresztessy, A.; Nagy, I. P.; Bazsa, G.; Pojman, J. A. J. Phys. Chem. 1995, 99, 5379-5384. (15) Chinake, C. R.; Simoyi, R. H. J. Phys. Chem. 1994, 98, 40124019. (16) Masere, J.; Vasquez, D. A.; Edwards, B. F.; Wilder, J. W.; Showalter, K. J. Phys. Chem. 1994, 98, 6505-6508. (17) Turner, J. S. Annu. ReV. Fluid Mech. 1985, 7, 11-44. (18) Cussler, E. L. Diffusion: Mass Transfer in Fluid Systems; Cambridge: London, 1984. (19) Pota, G.; Bazsa, G.; Beck, M. T. Acta Chim. Acad. Hung. 1982, 110, 227. (20) Turner, J. S. Buoyancy Effects in Fluids; Cambridge University Press: Cambridge, 1979.
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