Oscillations isothermal conditions

The mode of coupling between different parts of the surface is also of relevance for the occurrence of temporal oscillations with polycrystalline samples, even if heat conduction as the usually dominating mechanism can be ruled out. Large-amplitude oscillations have, for example, been observed with a polycrystalline Pt ribbon under isothermal conditions (143). This suggests coupling between different crystallites of the same surface orientation through the gas phase, because differently oriented... 

Heat conductance. This process will usually dominate with real catalysts near atmospheric pressure conditions, but was shown also to govern the CO + NO reaction on Pt(100). In this case sustained oscillations were observed under the influence of small ( 1 K) temperature fluctuations, but under strictly isothermal conditions these were damped. 

In an open system such as a CSTR chemical reactions can undergo self-sustained oscillations even though all external conditions such as feed rate and concentrations are held constant. The Belousov-Zhabotinskii reaction can undergo such oscillations under isothermal conditions. As has been demonstrated both by experiments [1] and by calculations 12,3] this reaction can produce a variety of oscillation types from simple relaxation oscillations to complicated multipeaked periodic oscillations. Evidence has also been given that chaotic behavior, as opposed to periodic or quasi-periodic behavior, can take place with this reaction [4-12]. In addition, it has been shown in recent theoretical studies that chaos can occur in open chemical reactors [11,13-17]. 

Emulsion polymerization is usually carried out isothermally in batch or continuous stirred-tank reactors. Temperature control is much easier than for bulk or solution polymerization because the small ( 0.5 fim) polymer particles, which are the locus of the reaction, are suspended in a continuous aqueous medium. This complex, multiphase reactor also shows multiple steady states under isothermal conditions. In industrial practice, such a reactor often shows sustained oscillations. Solid-catalyzed olefin polymerization in a slurry batch reactor is a classic example of a slurry reactor where the solid particles change size and characteristics with time during the reaction process. 

Reaction rate oscillations may be accompanied by temperature oscillations [temperature fluctuations of up to 500 K have been reported (24)] or they may be isothermal. Isothermality occurs either because the catalyst can conduct heat away much faster than the rate at which it is produced by the reaction, as is the case in UHV studies, or because isothermal conditions are forced on the system by anemometry, as described in the work of Luss and co-workers (757). Oscillation frequencies can range from more than 10 Hz (24) up to periods of several hours (217,219). Often there is evidence for several time scales in a single oscillating stem. Relatively regular high-frequency oscillations may be superimposed over relaxation oscillations (93,98), with the two types of oscillations caused by different changes on the catalyst surface. 

Experimenting with CO oxidation on a platinum screen (catalytic wire) under isothermic conditions Hugo (1972) reported observing undamped oscillations. Although these oscillations may be explained on the basis of a complicated reaction mechanism involving concentrations of the activated molecules, this is not elaborated in Hugo s paper. 

Belyaev, et al. studied the catalytic oxidation of hydrogen, and found that the reactants act on the catalyst. This effect may be regarded as feedback. Several stationary states were found for the catalytic hydrogen oxidation reactions on nickel and for the reaction of CO with H. Belyaev et al. found stable auto-oscillations of the hydrogen oxidation rate on nickel foil under isothermal conditions. See Fig. III.16. 

Keil and Wiecke (1980) investigated oscillations in the CO oxidation on Pt catalysts in a tubular reactor under isothermal conditions. At lower and higher CO contents the kinetics of the reaction could be described uniformly by a Langmuir-Hinshelwood relationship. 

All these setups work under isothermal conditions. In the MDR, a thin sheet (around 2 mm) is placed between the two dies kept at the desired temperature the lower disc oscillates and a reaction torque/pressure transducer is positioned above the upper die. It has been found that the MDR gives shorter times of cure than the ODR because of better heat transfer and higher torque values owing to the die design. The MDR is run at three temperatures to allow evaluation of the kinetic parameters of the cure reaction. Thus, the activation energy and the preexponential factor can be calculated from the fractional modulus time values obtained with this apparatus. The modulus value is assumed to vary with time following first-order kinetics, and the rate constant varies with temperature according to the Arrhenius equation. 

Jaisinghani and Ray (40) also predicted the existence of three steady states for the free-radical polymerization of methyl methacrylate under autothermal operation. As their analysis could only locate unstable limit cycles, they concluded that stable oscillations for this system were unlikely. However, they speculated that other monomer-initiator combinations could exhibit more interesting dynamic phenomena. Since at that time there had been no evidence of experimental work for this class of problems, their theoretical analysis provided the foundation for future experimental work aimed at validating the predicted phenomena. Later studies include the investigations of Balaraman et al. (43) for the continuous bulk copolymerization of styrene and acrylonitrile, and Kuchanov et al. (44) who demonstrated the existence of sustained oscillations for bulk copolymerization under non-isothermal conditions. Hamer, Akramov and Ray (45) were first to predict stable limit cycles for non-isothermal solution homopolymerization and copolymerization in a CSTR. Parameter space plots and dynamic simulations were presented for methyl methacrylate and vinyl acetate homopolymerization, as well as for their copolymerization. The copolymerization system exhibited a new bifurcation diagram observed for the first time where three Hopf bifurcations were located, leading to stable and unstable periodic branches over a small parameter range. Schmidt, Clinch and Ray (46) provided the first experimental evidence of multiple steady states for non-isothermal solution polymerization. Their... 

The clean Pt (100) and (110) surfaces are reconstructed and then construction is lifted if a critical CO coverage is reacted. Both modifications of the respective planes exhibit different sticking coefficients so that as a net result, the surface switches between the states of high and low reactivities. Thus, the rate of catalytic CO oxidation on defined Pt (100) and Pt (110) surfaces at low pressure under isothermal condition exhibits temporal oscillations which are coupled with periodic transformation of the surface structures between reconstructed and non-reconstructed phases [66],... 

It is known that under finite axial dispersion or complete back mixing and at steady-state isothermal conditions, autocatalytic reactions may exhibit oscillations, isolas, and other multiplicity features [21-24]. Cordonier et al. analyzed the forced oscillations of such systems [25]. 

A reaction system which is not occurred in an isothermal condition and able to show chemical oscillations is driven by temperature changes that have significance for chemists in order to process controls and designing a reaction. Periodicity in such chemical oscillators which is certainly evolved by thermal changes has been investigated by several researchers especially in hydrocarbon fuels and their combustion derivatives [25]. A detailed theoretical and practical validation of those oscillating combustion reactions has also been reported in chlorination of CH3CI in vapor-phase reaction [26]. 

A rate-law of the form ) may arise in enzyme reactions, or in heterogeneous catalysis obeying a Langmuir-Hinshelwood law. The oxidation of carbon monoxide at low pressures displays sustained oscillations under isothermal conditions in an open system [15], and results indicate that an important role is played by the state of the reactor surface. This, and other features of the observed behaviour, are readily correlated qualitatively with this simple, two-step model. 

One unique but normally undesirable feature of continuous emulsion polymerization carried out in a stirred tank reactor is reactor dynamics. For example, sustained oscillations (limit cycles) in the number of latex particles per unit volume of water, monomer conversion, and concentration of free surfactant have been observed in continuous emulsion polymerization systems operated at isothermal conditions [52-55], as illustrated in Figure 7.4a. Particle nucleation phenomena and gel effect are primarily responsible for the observed reactor instabilities. Several mathematical models that quantitatively predict the reaction kinetics (including the reactor dynamics) involved in continuous emulsion polymerization can be found in references 56-58. Tauer and Muller [59] developed a kinetic model for the emulsion polymerization of vinyl chloride in a continuous stirred tank reactor. The results show that the sustained oscillations depend on the rates of particle growth and coalescence. Furthermore, multiple steady states have been experienced in continuous emulsion polymerization carried out in a stirred tank reactor, and this phenomenon is attributed to the gel effect [60,61]. All these factors inevitably result in severe problems of process control and product quality. 

Fig. 18. Work-function change of the Pt(llO) surface vs. CO pressure and T at constant oxygen pressure of 5.2-10 " Torr. Vertical bars indicate the maximum amplitude of oscillations obtained at the respective temperature. Temporal oscillations in the catalytic CO oxidation on Pt(llO) under isothermal conditions in a flow reactor were detected and recorded by means of work function measurements between 440 and 590 K and in a pressure range between about 10 and 10 Torr. A large variety of oscillation forms, including well-defined transitions from periodic to irregular oscillations, was found, depending on the choice of partial pressures and temperature. FEED studies demonstrated that the oscillations occur near the completion of the CO induced 1x2 and 1x1 structural transformation of the surface. Slight variation of the parameters led to period doubling and transition to irregular behavior. From [86E].

The author has therefore tried to measure the thermal reaction power as well as the change in pressure due to CO2 produced in the bench scale calorimeter TKR under virtually isothermal conditions. The level of the pH-value, prerequisite for the start of oscillations, is produced by an injection of strong concentrated sulphuric acid into the batch, which is already brought to the set temperature of the reaction. The unavoidable stroke of heat due to the abruptly released large amount of heat of dilution cannot be compensated completely, even despite having pre-chilled sulphuric acid and electric heating power p2 temporarily reduced to zero (Fig. 5.15). The result is a large jump in temperature within the reaction mixture, so that the set temperature respectively the equilibrium of control is achieved relatively late. 

The steady-state design equations (i.e., Equations (14.1)-(14.3) with the accumulation terms zero) can be solved to find one or more steady states. However, the solution provides no direct information about stability. On the other hand, if a transient solution reaches a steady state, then that steady state is stable and physically achievable from the initial composition used in the calculations. If the same steady state is found for all possible initial compositions, then that steady state is unique and globally stable. This is the usual case for isothermal reactions in a CSTR. Example 14.2 and Problem 14.6 show that isothermal systems can have multiple steady states or may never achieve a steady state, but the chemistry of these examples is contrived. Multiple steady states are more common in nonisothermal reactors, although at least one steady state is usually stable. Systems with stable steady states may oscillate or be chaotic for some initial conditions. Example 14.9 gives an experimentally verified example. 

Self-sustained Oscillations. Under certain conditions, isothermal limit cycles in gaseous concentrations over catalysts are observed. These are probably caused by interaction of steps on the surface. Sometimes heat and mass transfer effects intervene, leading to temperature oscillations also. Since this subject has recently been reviewed (42, 43) only a few recent papers will be mentioned here. 

Cutlip and Kenney (44) have observed isothermal limit cycles in the oxidation of CO over 0.5% Pt/Al203 in a gradientless reactor only in the presence of added 1-butene. Without butene there were no oscillations although regions of multiple steady states exist. Dwyer (22) has followed the surface CO infrared adsorption band and found that it was in phase with the gas-phase concentration. Kurtanjek et al. (45) have studied hydrogen oxidation over Ni and have also taken the logical step of following the surface concentration. Contact potential difference was used to follow the oxidation state of the nickel surface. Under some conditions, oscillations were observed on the surface when none were detected in the gas phase. Recently, Sheintuch (46) has made additional studies of CO oxidation over Pt foil. 

To explain the role of transport, simulations have been also performed in an isothermal PSR. Oscillatory instabilities were again found [8]. These facts indicate that oscillations are radical induced. However, without the heat of reactions, no self-sustained oscillations are found for these conditions. The heat of reactions is a prerequisite at these conditions to pull the HB point outside the multiplic-... 

Sinusoidal oscillations of the continuous phase cause levitation or countergravity motion much more readily for gas bubbles, due to changes in bubble volume which cause a steady component in the pressure gradient drag term (Jl, J2). If the fluid motion is given by Eq. (11-49), the pressure in the vicinity of the bubble also varies sinusoidally. For normal experimental conditions, the resulting volume oscillations are isothermal (P2), and given by (Jl) ... 

We have now seen how local stability analysis can give us useful information about any given state in terms of the experimental conditions (i.e. in terms of the parameters p and ku for the present isothermal autocatalytic model). The methods are powerful and for low-dimensional systems their application is not difficult. In particular we can recognize the range of conditions over which damped oscillatory behaviour or even sustained oscillations might be observed. The Hopf bifurcation condition, in terms of the eigenvalues k2 and k2, enabled us to locate the onset or death of oscillatory behaviour. Some comments have been made about the stability and growth of the oscillations, but the details of this part of the analysis will have to wait until the next chapter. 

A simple Langmuir-Hinshelwood model explains quantitatively the steady-state behavior (4) but it fails to explain the oscillatory phenomena that were observed. The origin of the limit cycles is not clear. Rate oscillations have not been reported previously for silver catalyzed oxidations. Oxidation of ethylene, propylene and ethylene oxide on the same silver surface and under the same temperature, space velocity and air-fuel ratio conditions did not give rise to oscillations. It thus appears that the oscillations are related specifically to the nature of chemisorbed propylene oxide. This is also supported by the lack of any correlation between the limits of oscillatory behavior and the surface oxygen activity as opposed to the isothermal oscillations of the platinum catalyzed ethylene oxidation where the SEP measurements showed that periodic phenomena occur only between specific values of the surface oxygen activity (6,9). 

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