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The general behavior of a linear Oldroyd fluid in a n annulus can be more easily seen from Figure 2 , where oscillations in the mean velocity as a function of time for elastic values of 5 = 1 , 2 , 3 and a = 0.5, under the same pressure gradient and couette flow values as in Figure 1, are presented. As [ increases, the oscillation amplitude increases, and the longer the flow takes to reach steady state. All curves converge to t h a t of a purely viscous fluid as steady state is reached. It has also been shown (Chang, 1971) that the higher elastic fluid needs a smaller pressure drop than does the lower elastic fluid in order t o get any given value of mean velocity. This phenomenon is consistent with the fact disclosed by Platten and Schechter (1970) that polymer agents reduce the pressure drop because of their elastic behavior; i.e., the corresponding reduction in drag is related t o the elasticity of the solution.
18
e Figure 2. Mean velocity vs. time for fluids having values of = 1, 2, 3 and a = 0.5, under imposed conditions of P = 1000 and /3 = 300 Time,
0.2 see, ~vhichcorrespond to 5 between 0.07 and 0.7, were found for corresponding values of qo from 1 to 20 P, with p equal approximately to 1 g/cni3. The mean velocity as a function of time for the above values of and CY, under the influence of a positive pressure gradient, P = 1000, and with a couette flom value of p = 300, is shoirn in Figure 1. It can be seen t h a t no oscillations are apparent for c; = 0.07, as the response of the fluid is equivalent to that for a Seu-toniaii fluid. For 5 = 0.7, however, the expected oscillations due to the increased elasticity of the fluid are observed.
Ac k now ledgrnent
S. J. C. expresses his appreciation to the University of Toledo for a graduate assistantship during the period of this study. literature Cited
Chang, S. J., llaster's Thesis, University of Toledo, Toledo, Ohio, 1971.
Fain, C. L. S., Arpaci, V. S., Phys. F l u i d s 9 , 1970 (1966). Flumerfelt, R. W., Pierick, M. W., Cooper, S. L., Bird, R. B., IND. ENG.CHCM.,FUNDAM. 8, 354 (1969). Platten. J.. Schechter. R. S..Phus. FIuids 13. 832 (19iO). Schofield, R. K., Scott Blair, G." W., Proc. R'oy. Soc., Ser. A 138, io7 (1932).
Toms, B. A., Strawbridge, D. J., Trans. Faraday SOC.49, 1225 (1953).
Williams, M.C., Bird, R. B., A.I.Ch.E. J . 8 , 378 (1962). RECEIVED for review June 22, 1971 ACCEPTEDAugust 25, 1972
Kinetics of Concentrated Hydrogen Peroxide Decomposition on a Rotating Disk Slobodanka M. Joksimovic-Tjapkin
*
and Dejan Delic
Institute for Chemistry, Technology, and Xetallurgy, Belgrade, .Yjegoieva 12, and Faculty of Technology and Metallurgy, Belgrade, Karnegijeva 4, Yugoslavia
An experimental system i s described for investigating the kinetics of silver-catalyzed decomposition of concentrated hydrogen peroxide solutions. The catalyst was made in the form of a rotating disk. The model was easily extended to include rapid heterogeneous exothermic reactions. The decomposition of concentrated solutions of hydrogen peroxide at silver surfaces has been investigated as a function of bulk solution and silver surface temperatures at different speeds of disk rotation. With the increase of temperature, an abrupt transition between the region of lower to higher decomposition rate occurred, similar to the ignition of a solid fuel. It was shown that hydrogen peroxide decomposition in the region of a lower reaction rate was surface-reaction controlled. From experimental data in this region, the rate was proportional to the square root of hydrogen peroxide activity. The activation energy was 1 3.3 kcal/mole.
Silver-catalyzed decomposition of concentrated solutions of hydrogen peroxide has been investigated by many researchers. A review of earlier work by Schumb, et al. (1955)) shows that the decomposition of hydrogen peroxide is not influenced by silver ions and it \\-as established that catalysis occurs ivheii metallic silver is present in the solution. hlaggs
and Sutton (1958, 1959) have shown that above 10°C decomposition of concentrated HzOz on silver is diffusion controlled. Satterfield and Audibert (1963) investigated the influence of concentration and silver surface temperature on the rate of decomposition of Hz02a t nearly constant solution temperature (-40°C). They have shown that the rate of Ind. Eng. Chem. Fundom., Vol. 12, No. 1 , 1973
33
1
i 0 0 0 o o o o c Figure 1 . Apparatus for measuring the decomposition of concentrated hydrogen peroxide solutions
decomposition, measured by increasing H202concentrations, goes through a maximum a t about 45 wt yo H202and then decreases. The results are compared to nucleate and film boiling heat transfer. Baumgartner, et al. (1963), investigated the heterogeneous decomposition of 94 wt yo HzOz on silver a t loiv and high temperatures. They established that a t lorn temperature the decomposition rate of H202 is proportional From to the silver surface area and the mole fraction of H202. t’he rate of decomposition as a function of the bulk solution temperature, they estimat’ed an activation energy of 10.4 kcal/mole. At 18OC solution temperature in the decomposition rate of 90 wt % H202 an abrupt transition is noticed which is explained as a change in the mechanism of decomposition. Experiments a t high temperatures have shown that the decomposition rate of 90 wt H202 is a heat-transferlimited process. According to the results of the authors cited above, the rate of catalytic decomposition of concentrated hydrogen peroxide becomes diffusion limited and heattransfer limited a t rather low temperatures. The purpose of this study was to estimate the chemical reaction rate equation for the decomposition of concentrated H202 solutions 011 the surface of metallic silver. As this reaction is very rapid and highly exothermic because of the complexity of the combined chemical kinetics and mass- and heattransfer problems, in order to solve the combined problem i t is necessary to choose a geometry of the catalyst surface for which the magnitude of the diffusional effect is accurately calculable. According to Lewich (1962), the surface of a rotating disk normal to the axis of rotation is an ideal geometry for the investigation of the kinetics of the heterogeneous exothermic reactions because from th‘e point’ of view of mass and heat t,ransfer it is “uniformly accessible.” This means that for laminar flow there are no radial temperature or concentration gradients and therefore the heat- and mass-transfer coefficients are constant over the surface of the rotating disk; Le., local and average coefficients are the same. This is a big advantage for the rotat,ing disk in comparison to other geometries including the flat plate, which is t’he most popular 34
Ind. Eng. Chem. Fundam., Vol. 12, No. 1, 1973
geometry for t’he investigation of kinetics of heterogeneous reactions. The rotating disk has an additional experimental advantage over other geometries; i.e., the motion in the reacting system is induced by the rotation of a reacting surface and not by the motion of the fluid. This makes it possible to attain a reasonably loiv diffusional resistance vhhout pumping large quantities of liquids a t high velocity over the reacting surface. small reaction vessel surrounding the disk is all that is needed. The rotating disk is widely used in reacting systems involving a n electrochemical reaction. Litt and Serrad (1964) investigated the acid-base neutralization where the solid component n’as in the form of a rotating disk. Olander (1967) studied the reaction of gaseous iodine and a rotating disk of germanium in the temperature range from 280 to 460°C. He obtained a clear demarcation between the reaction-limited and diff usion-limited regions. .Is mass flux a t the surface of the rotating disk is proportional to the square root of its rotational speed, i t is possible by investigation of the effect of rotational speed of the disk on the rate of a heterogeneous process to distinguish the surfacereaction-controlled from the diff usion-controlled region. Because of this favorable property, the catalyst used in this study \\-as made in the form of a rot’ating disk. Actually, as will be seen later, the catalyst surface was ringlike. According to Lewich, the diffusional flux to the surface of a rotating disk with an inner portion which has been coated with a n inert material is A \
where T~ is the radius of the coated portion of the disk and r is the radius of the disk greater than To. In spite of the fact that the surface of a n active ring on a rotating disk is not uniformly accessible from a diffusional point of vie\v, the diffusional flux is proportional to the square
root of the angular velocity. Thus by investigating the influence of the rotational speed of the disk with active ringlike surface on the rate of a heterogeneous reaction i t is also possible to distinguish the chemical reaction-controlled region from the diff usion-controlled one. Experimental Section 01
Experiments were carried out in the system shown in Figure 1. A three-necked flask was used as the container for the Hz02 solution and placed in a water or ice-water bath to maintain the solution temperature constant during a run. The bulk solution temperature was measured by an N T C resistor thermometer imbedded in a Pyrex well, as shown in Figure 1,Using about 700 g of HZ02 solution, its concentration did not change essentially during the experiments. At the beginning of this work the silver catalyst was made in the form of a disk where the active surface was its entire underside, as is usually done in the study of electrochemical reactions. In the case of HzOzdecomposition, such a form of the silver catalyst caused formation and fixation of a gas bubble in the middle of the disk surface. The gas bubble grew during the course of the reaction and when a certain magnitude of the bubble was reached it was blown off. Thus the area of the catalyst surface in contact with the H z O ~solution was not constant during a n experiment. To prevent this problem, a circular stainless steel plate was imbedded in the middle of the underside of the disk surface. I n addition, a ringlike silver surface was placed in contact with the H202solution on the upper side of the disk in order to avoid the temperature gradient across the depth of the disk and to enable the measurement of the reaction surface temperature as closely as possible. Thus the actual reaction surface consisted of two ringlike surfaces. The silver used was of 99.9 wt yopurity. The disk was driven by a shaft entering the reaction vessel through a stainless steel mercury-sealed stopper. More detailed construction of the disk with the stopper is shown in Figure 2. The N T C miniature resistor for measuring the reaction surface temperature was imbedded between two catalytic surfaces, as shown in Figure 2. The N T C resistor is used because of the very strong exponential dependence of its resistance on temperature and its very small dimensions. One lead from the disk surface NTC resistor was electrically insulated from the assembly by a Teflon tube and a hard rubber cylinder was pressed over the drive shaft. The lead was attached to a brass ring pressed on the outside of the hard rubber cylinder. The second lead was in electrical contact with the disk and other conducting parts of the assembly, L e . , with the mass. The contact was made from the brass ring during disk rotation by means of a flexible brass strip and a graphite rod, as shown in Figure 2. As the electrical resistivity of the K T C resistor a t 0°C was 8.000 ohms and its temperature dependence was
all contact resistances could be neglected. The N T C resistor was in the usual bridge arrangement which, together with the Kipp & Zonen Type BD5 2-t recorder, represents the reaction surface temperature measuring system. I n order to decrease heat losses along the axis and noncatalytic surfaces, Teflon layers are imbedded as shown in Figure 2. Due to the high value of heat conductivity of silver, it was assumed that the reaction surface temperature was uniform. The material used was distilled 85 w t yo com-
DRIVE WHEEL AND SLIP C O N T A C T
C!
ROTATING 3lS
