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J Phys. Chem. 1989, 93, 6530-6533
Spatial Temperature Oscillations during Hydrogen Oxidation on a Nickel Foil Lance Lobban+and Dan Luss* Department of Chemical Engineering, University of Houston, Houston, Texas 77204-4792 (Received: March 13, 1989)
Temperature waves were observed on the surface of a nickel disk on which oxidation was carried out. The temperature front moved at a velocity of about 1 cm/s and had a width of about 1 cm. Complex dynamic local temperatures of overall reaction rate may be due to interaction among temperature waves triggered at different positions rather than an exotic reaction mechanism.
Introduction The coupling of chemical reactions and transport processes is known to lead in some cases to the formation of spatially organized structures of the reactive compounds. The discovery of the Belousov-Zhabotinski' reaction generated significant interest in chemical structures and waves and led to the finding of patterns in several homogeneous Theoretical studies5-*predict that propagating waves and dissipative structures should be observed also on heterogeneous catalytic surfaces. These spatial or spatiotemporal structures may mask measurements that assume a uniform synchronized reaction over the whole surface. Davis9 pointed out over 50 years ago that the structure and surface temperature of electrically heated catalytic wires may be nonuniform. BarelkoIo found moving temperature waves and standing waves on electrically heated catalytic wires. Ertl's research observed waves of surface structure during the oxidation of carbon monoxide on a platinum crystal. Schmitz and co-workers13,14 noted temperature patterns during stationary and oscillatory states on unheated catalytic pellets and foils. Kaul and WolfIs observed a lag in the thermal oscillations measured by separated thermocouples during the oxidation of CO on a supported Pt catalyst. Spatial or spatiotemporal structures may mask kinetic data obtained on heterogeneous catalysts and interpreted under the assumption that a uniform synchronized state exists on the surface. Moreover, such structures may cause the appearance of complex or even chaotic behavior of the overall reaction rate. There is a clear need for a quantitative characterization of the spatiotemporal structures on these surfaces in order to understand their evolution and impact. We report here measurements of surface temperature waves and nonuniform states during the exothermic oxidation of hydrogen on a nickel foil. Experimental System and Procedure The experiments were conducted in a cylindrical 7.62-cm-i.d. by 3.8-cm-high quartz reactor (Figure 1). The reactor top was a 0.32-cm-thick sapphire window (Union Carbide Crystals Division). The catalyst was a 3.81-cm circular nickel disk, 0.013 cm thick (Mathey-Bishop 99.5% purity) held parallel to the sapphire window by four fine wire thermocouples (0.025 cm) looped through small holes in the periphery of the foil. A fifth thermocouple was placed under the catalytic disk near its center. The reactor was fed with a mixture of hydrogen, oxygen, and nitrogen. The individual gases were metered by mass-flow controllers and mixed in a tube packed with glass beads. The mixture entered the reactor through four evenly spaced radial inlet ports and exited through four other similar ports positioned 1.3 cm below the inlet ports and shifted aside by 45". Tracer experiments showed that the mixing by the inlet jets caused the residence time distribution in the reactor to be very close to that of a continuously stirred tank reactor. The oxygen concentration of the effluent was measured by a Beckman oxygen analyzer. The reactants were heated by electrical heating tapes wrapped around the feed lines. The reactor was placed inside an oven to control its temperature. -___Present address: Department of Chemical Engineering, University of Oklahoma, Forman, OK 73019.
l l _ _ l l _ _ l _ _
The infrared radiation emitted from the catalyst was measured by a thermal imager (AGEMA Thermovision 780). Spatial resolution was about 0.6 mm2, while the thermal resolution was 0.4-1 "C depending on the temperature and range setting. The imager scans the surface 25 times per second, producing a thermal image of 100 columns and either 64 or 128 lines. The data can be digitized and recorded on a magnetic tape at the rate of one image every 1.2 s. The images can also be translated into 10-color images, displayed on monitors, and recorded on a VCR. The IR radiation of the reactor, which is reflected from the catalyst surface, distorts the thermal images. To remove these distortions, the reflected IR radiation was recorded first at the specific feed temperature in the absence of a chemical reaction. This image was subtracted from that recorded at the same feed temperature (and hence the same oven temperature) under reaction conditions. Additional details about the data processing are reported by Lobban.16 The catalyst activation consisted of repeated oxidation-reduction steps at 450 OC as described by Kurtanjek et ai." The experiments were conducted using fixed hydrogen and nitrogen flow rates and inlet gas temperature. The oxygen feed concentration was increased in small steps. Experimental Results
The oxidation of hydrogen over the nickel foil was carried out for oxygen feed concentration (Cf) in the range of 0-6.00 vol % and feed temperatures ( T f )from 170 to 271 'C, The experiments revealed that four regions with qualitatively different observable dynamic features existed in the (CrTf) plane (Figure 2). In the region denoted by U, a unique stationary state exists. In region 0, a unique oscillatory state was observed. In region (U, O ) , both a stationary state and an oscillatory state existed and the initial conditions determined which one was reached. In region (M, 0), two stationary states existed, as well as one oscillatory state
( I ) Zaikin, A . N.; Zhabotinski, A. M. Nature 1970, 225, 535. (2) Muller, S. C.; Plesser, T.; Hess, B. Naturwissenschaffen 1986, 73, 165. (3) Nosticzius, W.; Horsthemke, W.; McCormick, N. L.; Swinney, H. L.; Tam, W . Y . Nature 1987, 329, 581. (4) Tam, W. Y . ; Horsthemke, W.; Noszticzius, Z.; Swinney, H. L. J . Chem. Phys. 1988, 88. 3395. (5) Pismen, L. Chem. Eng. Sci. 1980, 35, 1950. (6) Sheintuch, M.; Pismen, L. Chem. Eng. Sci. 1981, 36, 893. (7) Schmitz, R.; Tsotsis, T. Chem, Eng. Sci. 1983, 38, 1421. (8) Bykov, V . ; Gorban, A.; Kamenshehikov, L.; Yablonskii, G. Kinet. Cutal. 1983, 24, 520. (9) Davis, W. Philos. Mag. 1935, 19, 309. (IO) Barelko, V. V.; Kurochka, I. I.; Merzhanou, A. G.; Shkadinskii, K. G. Chem. Eng. Sci. 1978, 33, 805. ( 1 1 ) Cox, M. P.; Ertl, G.; Imbihl, R. Phys. Reu. Left. 1985, 54, 1725. (12) Imbihl, R.; Cox, M. P.; Ertl, G. J . Chem. Phys. 1986, 84, 3519. (13) Schmitz, R. A.; D'Netto, G.A,; Razon, L. F.; Brown, J. R. In Chemical Instobilties; Nicolis, G . , Baras, F., Eds.; Reidel: Dordrecht, 1984;
p 33. (14) (15) (16) (17)
Pawlicki, P.; Schmitz, R. A. Chem. Eng. Prog. 1987, 83(2), 40. Kaul, D. J.; Wolf, E. E. J . Coral. 1985, 93, 321. Lobban, L. L. Ph.D. Dissertation, University of Houston, 1987. Kurtanjek, Z.; Sheintuch, M.; Luss, D. J . Cafal. 1980, 66, 1 I .
0022-365418912093-6530$01.50/0 0 1989 American Chemical Society
The Journal of Physical Chemistry, Vol. 93, No. 17, 1989 6531
Hydrogen Oxidation on a Nickel Foil
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Figure 4. Thermal images of the nickel foil recorded during the interval to to t l in Figure 3. Image labels refer to time elapsed since I,-,. Temperature ranges corresponding to each type of shading are shown below the images.
Figure 1. Side and top views of the Pyrex reactor and nickel catalyst. The top view is the thermal imager view of the catalyst.
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2 3 4 0 2 (% v.) Figure 2. Bifurcation map describing regions with qualitatively different dynamic behavior. U refers to a unique stationary state; 0, unique oscillatory state; U, 0, stationary and oscillatory state; M, 0, multiple stationary and single oscillatory state. Open and closed circles refer to a soft and hard bifurcation to oscillatory state, respectively. Open squares refer to an ignition to a stationary state, and closed squares refer to an extinction or hard bifurcation.
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Figure 3. Oscillations recorded in the effluent oxygen concentration for a feed temperature of 245 “C and a feed oxygen concentration of 4.46%. Thermal images recorded between to and t l are shown in Figure 4. Thermal images recorded between t2 and t3 are shown in Figure 7.
surrounding one of the stationary states. The amplitude of the oscillation in the effluent oxygen concentration increased with an increase in Cf. The typical shape of the oscillatory signal was a sharp spike (a rapid decrease and subsequent increase in the reaction rate) followed by a period in which a very slow or an unobservable change in the effluent concentration occurred (Figure 3). During that period, the reaction rate was high (low effluent oxygen concentration). For oxygen concentrations larger than 3 vol 5% the extinction led to oxidation of the surface, requiring reactivation at high temperatures. To avoid this difficulty, the bifurcation map was constructed only for Cf smaller than 3 vol % O2 A detailed analysis of the transitions (bifurcations) between
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Figure 5. AT images calculated from images recorded during the interval to to t l in Figure 3. Image labels refer to time elapsed since to. White pixels signify a positive temperature change, and black pixels signify a negative or no temperature change.
the four regions is presented elsewhere.16 The thermal imager showed that for Cf smaller than 1 vol % the catalyst temperature was essentially uniform for both stationary and oscillatory states. However, for C, larger than 1% vol spatial temperature variations exceeding 5 O C were obsehred for both stationary and oscillatory states. This nonuniformity increased in magnitude with increasing C,. Figure 4 is a black and white version of the color thermal images observed during the spike shown in Figure 3 between to and t , . (The time labels in Figure 4 show the time elapsed from to.) The qualitative features of these images are typical of oscillations observed over a wide range of feed temperatures and concentrations. The image for time 0 in Figure 4 describes the nearly unchanging nonuniform temperature distribution observed for about 75 s between two consecutive spikes. At this time the reaction rate starts to decrease for about 24 s, increasing the effluent oxygen concentration (Figure 3). The temperature increases in the next 40 s and remains then essentially unchanged until the next oscillation starts. It is difficult to determine by a visual examination of the thermal images if they describe the propagation of a temperature wave or a cooling or heating of a surface that had initially a nonuniform temperature distribution. To discriminate between these two possibilities, we prepared maps of the rate of temperature change on the surface by calculating at each point AT/At from consecutive images. (These will be referred to as “AT images” for convenience). Black and white AT images corresponding to Figure 4 are shown in Figure 5. Points at which A T / A t is positive are white, while the others are black. The images show that initially the cooling starts from a small region at the left top of the disk and slowly propagates across the disk. After 9.3 s the temperature is decreasing at all points. The AT images from 12.7 to 32.5 s show a gradual uniform transition from cooling (black dots) to heating (white dots). In some cases, the heating on the cooled side began before the cooling wave had propagated across the whole disk.
6532 The Journal of Physical Chemistry, Vol 93, No. 17, 1989
Lobban and Luss
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' ' ' ' ' 1 2 3 Position on the cross section
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Figure 6. Plot of values of A T / A t along a cross section of the nickel foil. The cross section runs perpendicular to the front. The path of the cross section is indicated on the small inset figure. 2.
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341-351 351-361 361-371 371-381 381-391 391-401 401-411 Figure 7. Thermal images of the nickel foil recorded during the interval t2 to f3 in Figure 3. Image labels refer to time elapsed since t2. The thermal images show the cooling being initiated at a location different from that of the images in Figure 4.
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Figure 9. A T images recorded during the double peak oscillations shown in Figure 8. The A T images reveal oxidation triggered at alternatng edge locations. 3241
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Figure 10. Oscillations for a feed temperature of 244 O C and a feed
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Figure 8. Double peak oscillations recorded in the temperature measured by the support thermocouple at the left-hand edge of the catalyst for a feed temperature of 219 O C and a feed oxygen concentration of 5.05%.
The AT images show that in many cases the cooling front has the shape of a moving chord. Figure 6 describes A T / A t along a diameter perpendicular to the chord for five different times. At t = 7 s the front is approximately at the center of the disk and is rather steep, with a width of about 1 cm. The front velocity is about 0.4 cm/s. The thermal images showed that the cooling did not always start from the same location on the disk. Figure 7 shows thermal images measured between t2 and t3 in Figure 3, with time labels denoting time elapsed from t2. These images show an initial cooling location different from that in Figure 4. However, the front width and velocity are similar to those obtained between to and tl. Our experiments showed that there was no clear dependence of the front velocity or width on the feed temperature or concentration. The front velocity varied from 0.2 to 0.7 cm/s and the front width from 0.8 to 1.5 cm. During the oscillatory states the cooling front always was initiated at the edge of the catalyst, but that position was not always the same for consecutive oscillations. Double peak oscillations in the effluent oxygen concentration and local temperature were observed in some experiments using
concentration of 1.80%. (a) Oscillations in the local temperature measured at two different locations on the catalyst. TI is the support thermocouple near the top of the catalyt, and T4 is the thermocouple positioned near the center of the catalyst. (b) Oscillations in the effluent oxygen concentration.
a high oxygen concentration (larger than 4 vol %). Figure 8 describes such a temperature oscillation as measured by a thermocouple placed at the left edge of the disk. The corresponding AT images (Figure 9) show that the complex oscillatory local behavior is due to surface cooling initiated at two alternating locations. The experiments revealed that local traces of the temperature made at different points can be qualitatively different due to the spatial nonuniform behavior. For example, Figure 10b describes the regular oscillation in the observed O2effluent concentration for a feed concentration of 1.80 vol % and feed temperature of 224 OC. Figure loa shows that the temperature trace measured next to the point at which the oscillations are initiated (TI) is rather different from that measured near the center of the foil (T4). The signal T4 shows the brief increase in temperature caused by the increased gas-phase O2 concentration before the cooling front arrives.
Discussion The rapid oscillatory cooling and heating of the nickel surface is probably caused by successive oxidation and reduction of the surface. The activity of the oxidized surface is lower than that of the reduced nickel. Thus, oxidation reduces the reaction rate and leads to cooling and oxidation of nearby sites, which is observed as a cooling front. This oxidation-reduction mechanism
J . Phys. Chem. 1989, 93, 6533-6539 has been suggested p r e v i o ~ s l y ' as ~ ~the ' ~ cause of the rate oscillations. The experiments show that spatial nonuniformities have an important impact on the observed features of local temperatures or overall reaction rate, especially during oscillatory behavior. In some cases propagating reaction fronts lead to simple observed local or overall oscillatory behavior. However, when successive fronts are triggered at different positions, the interaction among the fronts may lead to complex local behavior, such as double peak or more complex oscillations. Thus, dynamic bifurcation between oscillatory behavior of qualitatively different complexity may be due to the spatial nonuniformities and the existence of different triggering positions rather than an exotic reaction mechanism. Hence, spacial care must be exercised in any attempt to determine kinetics using observed bifurcation diagrams or maps of regions having qualitatively different dynamic overall reaction rate. We (18) Lindstrom, T. H.; Tsotsis, T. T. Surf. Sci. 1985, 150, 487.
6533
conjecture that many of the observed chaotic oscillations in the overall reaction rate of catalytic system^'^*^^ are due to the interaction among several reaction fronts and not to an intrinsic chaotic feature of the kinetic mechanism. The experiments indicate that color thermal images are not a sensitive detector of thermal waves, since a uniform heating of a nonuniform surface leads to similar images. The analysis of AT images enables a more accurate detection of thermal fronts and of their main features such as velocity and width. Acknowledgment. We are thankful to the NSF, the Welch Foundation, and the Texas Advance Research Program for support of this research. Registry No. H1,1333-74-0; Ni, 7440-02-0. (19) Razon, L. F.; Chang, S. H.; Schmitz, R. A. Chem. Eng. Sci. 1986, 41, 1561. (20) Sheintuch, M.; Schmidt, J. J. Phys. Chem. 1988, 92, 3404.
Thermogravltatlonal Thermal Diffusion in Electrolyte Solutions. 1. Steady State Frederick H. Horne*vt and Yuan Xu Department of Chemistry, Michigan State University, East Lansing, Michigan 48824 (Received: September 7, 1988)
The full set of nonequilibrium thermodynamic and hydrodyn'amic differential equations is solved for the steady state of thermogravitational thermal diffusion of aqueous solutions of uni-univalent salts, with particular attention to sodium and potassium chloride solutions. Results agree with previous work on nonelectrolyte solutions except that (1) the experimental Soret coefficient in the Hittorf frame differs from the nonelectrolyte coefficient by the thermal expansivity coefficient, and (2) for small temperature gradients or large column length the composition dependence of the overall density (the "forgotten effect") may be important for calculating the value of the Soret coefficient from experimental data.
1. Introduction Interest in thermogravitational thermal diffusion (TGTD) in electrolyte solutions has accelerated in recent years due principally to three developments: (1) increased and more efficient use of TGTD as a means of separating liquid solution components;' (2) improved approaches to the long-sought but so far elusive goal of an explicit usable molecular theory of coupled mass and heat flows in mixtures;2 and (3) the published reports of Gaeta, Perna, Scala, and B e l l ~ c c iwhose ,~ TGTD experiments appear to imply unusual phase-transition behavior in dilute aqueous sodium chloride and potassium chloride solutions. Petit, Renner, and Lin," using a pure thermal diffusion technique, and Naokata and Kimie,4busing a TGTD technique, did not find the behavior suggested by Gaeta et al. Since Gaeta et al. and other TGTD experimentalists have used for their experimental calculations only very approximate equations, developed long ago for gas mixture^,^ and since the Gaeta et al. results are so intriguing, it seemed appropriate to obtain accurate time-dependent equations for TGTD in electrolyte solutions. The results may be readily adapted to nonelectrolyte liquid mixtures and to gas mixtures. In this paper we present the full set of steady-state differential equations and their solutions for the usual TGTD boundary conditions. The results agree in form with those found previously for binary liquid mixtures,6 but the approach to solving the equations here is new. Moreover, specialization to electrolyte solutions leads to a final formula that involves the corrected Soret coefficient u*,' which differs somewhat from the Soret coefficient u of Gaeta et al. 'Present address (to which reprint requests should be sent): College of Science, Oregon State University, Corvallis, OR 9733 1-4608.
The steady-state results serve as both guide and target in obtaining the time-dependent results to be reported in paper 11. Reservoir effects, which can be of great significance in time-dependent experiments, will be treated in paper 111.
2. Transport Equations For a continuous, isotropic, binary mixture at steady state, the equation of conservation of mass is, for each component v.civi = 0
(2.1 )
where ci is the molar density of component i and vi is its local velocity. The barycentric velocity v is the mass-fraction sum of the component velocities (1) Navarro, J. L.; Nadariaga, J. A.; Saviron, J. M. Phys. SOC.Jpn. 1983, 52, 478. (2) (a) Wolynes, P. G. Annu. Reu. Phys. Chem. 1980, 31, 345. (b) Kahana, P. y.;Lin, J. L. J. Chem. Phys. 1982, 74, 2995. (c) Mauzerall, D.; Ballard, S. G. Annu. Rev. Phys. Chem. 1982, 33, 377. (d) Calef, D. F.; Deutch, J. M. Annu. Rev. Phys. Chem. 1983,34,493. ( e ) Fries, P. H.; Patey, G. N. J. Chem. Phys. 1984, 80, 6253. (3) Gaeta, F. S.; Perna, G.; Scala, G.; Bellucci, F. J. Phys. Chem. 1982, 86, 2967. (4) (a) Petit, C. J.; Renner, K. E.; Lin, J. L. J. Phys. Chem. 1984,88,2435. (b) Naokata, T.; Kimie, N. Bull. Chem. SOC.Jpn. 1984, 57, 349. (5) (a) Furry, W. H.; Jones, R. C.; Onsager, L. Phys. Reu. 1939,55, 1083. (b) Tyrell, H. J. V. Diffusion and Heat Flow in Liquids; Butterworths: London, 1961. (c) Alexander, H. F. Z . Phys. Chem. 1954, 203, 212. (6) (a) Horne, F. H.; Bearman, R. J. J. Chem. Phys. 1962,37,2842. (b) Horne, F. H.; Bearman, R. J. J. Chem. Phys. 1967,46,4128. (c) Horne, F. H.; Bearman, R. J . J. Chem. Phys. 1968,49, 2457. (7) (a) deGroot, S. R. L Effet Soret; North-Holland, Amsterdam, 1945. (b) Haase, R. Thermodynamics of Irreversible Process; Addison-Wesley: Reading, MA, 1969.
0022-365418912093-6533$01.50/0 0 1989 American Chemical Society
