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Closed system oscillations

Many chemical and biochemical reactions can be in an oscillatory regime in which the concentrations of intermediates and products vary in a regular oscillatory way in time the oscillations may be sinusoidal but usually are not. Sustained oscillations require an open system with a continuous influx of reactants in a closed system oscillations may occur initially when the sjretem is far from equilibrium, but disappear as the system approaches equilibrium. A simple example of an oscillatory reaction is the Selkov model [1]... [Pg.159]

Most chemically reacting systems tliat we encounter are not tliennodynamically controlled since reactions are often carried out under non-equilibrium conditions where flows of matter or energy prevent tire system from relaxing to equilibrium. Almost all biochemical reactions in living systems are of tliis type as are industrial processes carried out in open chemical reactors. In addition, tire transient dynamics of closed systems may occur on long time scales and resemble tire sustained behaviour of systems in non-equilibrium conditions. A reacting system may behave in unusual ways tliere may be more tlian one stable steady state, tire system may oscillate, sometimes witli a complicated pattern of oscillations, or even show chaotic variations of chemical concentrations. [Pg.3054]

A reaction at steady state is not in equilibrium. Nor is it a closed system, as it is continuously fed by fresh reactants, which keep the entropy lower than it would be at equilibrium. In this case the deviation from equilibrium is described by the rate of entropy increase, dS/dt, also referred to as entropy production. It can be shown that a reaction at steady state possesses a minimum rate of entropy production, and, when perturbed, it will return to this state, which is dictated by the rate at which reactants are fed to the system [R.A. van Santen and J.W. Niemantsverdriet, Chemical Kinetics and Catalysis (1995), Plenum, New York]. Hence, steady states settle for the smallest deviation from equilibrium possible under the given conditions. Steady state reactions in industry satisfy these conditions and are operated in a regime where linear non-equilibrium thermodynamics holds. Nonlinear non-equilibrium thermodynamics, however, represents a regime where explosions and uncontrolled oscillations may arise. Obviously, industry wants to avoid such situations ... [Pg.69]

Oscillations are familiar phenomena in mechanical systems and in electric circuits. Noyes and Field discussed the possibilities for concentration oscillations in closed systems and illustrated the principles by means of Oregonator model consists of the following five steps ... [Pg.120]

One particular pattern of behaviour which can be shown by systems far from equilibrium and with which we will be much concerned is that of oscillations. Some preliminary comments about the thermodynamics of oscillatory processes can be made and are particularly important. In closed systems, the only concentrations which vary in an oscillatory way are those of the intermediates there is generally a monotonic decrease in reactant concentrations and a monotonic, but not necessarily smooth, increase in those of the products. The free energy even of oscillatory systems decreases continuously during the course of the reaction AG does not oscillate. Nor are there specific individual reactions which proceed forwards at some stages and backwards at others in fact our simplest models will comprise reactions in which the reverse reactions are neglected completely. [Pg.2]

In closed system studies of the BZ reaction, three principal modes of homogeneous oscillations have been identified (1) low-frequency, large amplitude, highly nonlinear (i.e., nonharmonic) relaxation oscillations... [Pg.205]

Fig. 3. Experimental traces of bromide ion concentration in closed system studies of the Belousov-Zhabotinski reaction, showing (a) quasiharmonic (i.e., sinusoidal) oscillations, (A>) and (c) increasingly nonlinear oscillations, and ( Fig. 3. Experimental traces of bromide ion concentration in closed system studies of the Belousov-Zhabotinski reaction, showing (a) quasiharmonic (i.e., sinusoidal) oscillations, (A>) and (c) increasingly nonlinear oscillations, and (</) relaxation oscillations. The vertical bars at left represent equal concentration ranges.
The principle of detailed equilibrium accounts for the specific features of closed systems. For kinetic equations derived in terms of the law of mass/ surface action, it can be proved that (1) in such systems a positive equilibrium point is unique and stable [22-25] and (2) a non-steady-state behaviour of the closed system near this positive point of equilibrium is very simple. In this case even damped oscillations cannot take place, i.e. the positive point is a stable node [11, 26-28]. [Pg.112]

In conclusion of the discussion of reaction dynamics in closed systems, it can be suggested that the principal problems here have been solved closed systems "have been closed . The case is different for open systems. Progress in their study has been extensive. A large number of publications are devoted to the analysis of various dynamic peculiarities (multiplicity of steady states, self-oscillations, stochastic self-oscillations) in various open systems. It can hardly be said that most problems here are completely clear. [Pg.140]

Fig. 5.30. Representative trains of oscillatory glow for CO + O2 mixtures in a closed system (a) chloropicrin-treated reactor with p = 33 Torr, = 841 K giving a total of 94 oscillations over 3 hr (b) and (c) light emission and reactant consumption in a clean reactor with p = 22 Torr and T, = 900 K. (Reprinted with permission from reference [60], Royal Society... Fig. 5.30. Representative trains of oscillatory glow for CO + O2 mixtures in a closed system (a) chloropicrin-treated reactor with p = 33 Torr, = 841 K giving a total of 94 oscillations over 3 hr (b) and (c) light emission and reactant consumption in a clean reactor with p = 22 Torr and T, = 900 K. (Reprinted with permission from reference [60], Royal Society...
Because a closed system must eventually reach equilibrium, closed systems can sustain oscillating chemical reactions for only a limited time. Sustained oscillating reactions require an open system with a constant influx of reactants, energy and removal of products. [Pg.690]

The ultimate characteristics of a process control system are obtained readily by closing the loop through a proportional controller, and increasing the gain on the controller to the minimum proportional gain at which the system oscillates steadily. Johnson and Bay (J4) describe tests of both the ultimate gain approach and the reaction curve approach applied to pneumatic analog systems. [Pg.75]

R. J. Field, Experimental and mechanistic characterization of bromate-ion-driven chemical oscillations and traveling waves in closed systems, in Field and Burger (ref. Gl), Chapter 2. [Pg.460]

Oscillations of concentrations of some intermediates in the BZ reaction occur in a rather wide range of initial concentrations of the reagents. The reaction may be carried out in a closed system, for example in a graduated cylinder provided with a stirrer, or in an open system — in a flow reactor with stirring. [Pg.223]

Using proportional control only and with the feedback loop closed, introduce a set point change and vary the proportional gain until the system oscillates continuously. The frequency of continuous oscillation is the crossover frequency, cuC0. LetM be the amplitude ratio of the system s response at the crossover frequency. [Pg.543]

Gray P, Kay S R and Scott S K Oscillations of simple exothermic reactions in closed systems Proc. R. Soc. Land. A 416 321-41... [Pg.1118]

Experimental evidence for the vibrational structure of XHX transition states has been provided by photoelectron spectroscopy of XHX- anions with X = Cl, Br, and I (134,160-163). This technique, by inducing photodetachment of an electron from the XHX" anions, probes the Franck-Condon region, which is believed for these systems to include geometries in the vicinity of the transition state region for the neutral systems. Spectral bands have been interpreted as evidence for trapped-state resonances associated with asymmetric stretch-excited levels of the transition state (160-163), and they are in general agreement with synthetic photoelectron spectra calculated from the scattering computations of Schatz (17-19). In recent experimental spectra (158,162), more closely spaced oscillations have been observed these are apparently related to rotational thresholds as described by Schatz. [Pg.367]

The system used in the Landolt clock reaction, IOj/SOl , when treated with [Fe(CN)6] , shows oscillations in a CSTR. A modification of the mechanism proposed previously resolves a number of problems. A slightly different system, I03/HS03/S20i produces a small number of high-amplitude pH oscillations (up to 2 units of pH) over a narrow range of conditions in a closed system. ... [Pg.97]

Discussions in this Report will be inincipally concerned with work published since 1965. We exclude such heterograieous reactions as the combustion of carbon or the catalytic oxidation of ammonia and such intoisdy localized ignitions as diose due to sparks, hot wires, friction, ot shock. Attrition is chiefly directed to gaseous reactions in closed systems but a survey of recent relevant work on umteady bdiaviour (ignition, extinction, and oscillations) in open systrans is also included. [Pg.332]

Oscillatory States in the CSTR limit Cycles.— The nature of the diemically open system makes it an ideal vehicle for studying reactions which odiibit chemical oscillations. The continuous supply of reactants diminates damping from reactant depletion inevitable in closed systems and permits the experimental establishment of true limit-cycle behaviour. However, not all oscillations in the CSTR need be kinetically interesting in their origin (e.g. the periodic variations in temperature and concentrations in reactors run with feedback control More importantly from the combustion researcher s viewpoint, oscillations may arise between multiple stable steady states of any normal exothermic reaction because of restric-... [Pg.379]

This might be so when it becomes unexceptional to make measurements in the transient or incubation phase of a unimolecular reaction. In general, the transient phase of a relaxation in a closed system may contain overshoots [76.P3] or damped oscillations [81.S2] of certain populations the number of such oscillations is, however, ilnite if the eigenvalues of the relaxation matrix are real... [Pg.26]

Noyes, R, M, (1976). "Oscillations in chemical systems. XII. Applicability to closed systems of models with two and three variables,"... [Pg.125]


See other pages where Closed system oscillations is mentioned: [Pg.302]    [Pg.302]    [Pg.1096]    [Pg.299]    [Pg.2]    [Pg.15]    [Pg.111]    [Pg.111]    [Pg.220]    [Pg.205]    [Pg.206]    [Pg.518]    [Pg.84]    [Pg.98]    [Pg.11]    [Pg.656]    [Pg.390]    [Pg.102]    [Pg.18]    [Pg.389]    [Pg.7]    [Pg.1096]    [Pg.389]    [Pg.137]    [Pg.83]    [Pg.133]   
See also in sourсe #XX -- [ Pg.159 ]




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