Oscillations in batch systems

Autocatalysis can cause sustained oscillations in batch systems. This idea originally met with skepticism. Some chemists believed that sustained oscillations would violate the second law of thermodynamics, but this is not true. Oscillating batch systems certainly exist, although they must have some external energy source or else the oscillations will eventually subside. An important example of an oscillating system is the circadian rhythm in animals. A simple model of a chemical oscillator, called the Lotka-Volterra reaction, has the assumed mechanism ... 

Chemically coupled oscillation in batch reactor involving the use of two or more organic substrates in case of B-Z oscillator and Briggs-Rauscher [58] have been studied. Both systems exhibited a bust of oscillations, characteristic of one substrate followed by a quiescent period and then a bust of oscillations characteristic of the other substrate. 

The reaction involving chlorite and iodide ions in the presence of malonic acid, the CIMA reaction, is another that supports oscillatory behaviour in a batch system (the chlorite-iodide reaction being a classic clock system the CIMA system also shows reaction-diffusion wave behaviour similar to the BZ reaction, see section A3.14.4). The initial reactants, chlorite and iodide are rapidly consumed, producing CIO2 and I2 which subsequently play the role of reactants . If the system is assembled from these species initially, we have the CDIMA reaction. The chemistry of this oscillator is driven by the following overall processes, with the empirical rate laws as given ... 

This reaction can oscillate in a well-mixed system. In a quiescent system, diffusion-limited spatial patterns can develop, but these violate the assumption of perfect mixing that is made in this chapter. A well-known chemical oscillator that also develops complex spatial patterns is the Belousov-Zhabotinsky or BZ reaction. Flame fronts and detonations are other batch reactions that violate the assumption of perfect mixing. Their analysis requires treatment of mass or thermal diffusion or the propagation of shock waves. Such reactions are briefly touched upon in Chapter 11 but, by and large, are beyond the scope of this book. 

Example 14.2 demonstrates that sustained oscillations are possible even in an isothermal flow system. This is hardly surprising since they are possible in a batch system provided there is an energy supply. 

The formaldehyde-sulfite reaction displays non-linear dynamics it is a clock reaction with a sudden pH excursion (from ca 7 up to ll).280 The induction period in batch processes is explained by the internal buffer systems, HS03 -S03. However, flow reactors also exhibit pH oscillations and bistability. 

Some of these chlorite oscillators exhibit particularly interesting or exotic phenomena. Batch oscillations in the absence of flow may be obtained in the systems numbered 3, 10 a and 13, while the chlorite-iodide-malonic acid reaction gives rise to spatial wave patterns as well. These latter, which are strikingly similar to those observed in the BZ reaction61 are shown in Fig. 12. Addition of iodide to the original chlorite-iodate-arsenite oscillator produces a system with an extremely complex phase diagram58, shown in Fig. 13, which even contains a region of tristability, three possible stable steady-states for the same values of the constraints. 

C") Chlorite-iodine-reductant. These systems, which include systems 8 b, 9 b and 10b of Table 8 appear to be only minor variants of type C ) in which (M 9) replaces (M 8). C ") Chlorite-iodide-reductant. The only known example of this type is the chlorite-iodide-malonic acid system, which is of special interest because it supports both batch oscillations and spatial wave patterns. The slow decomposition of iodinated malonic acid species apparently provides a long lasting, indirect flux of iodide (via (M2) + (M9)) in this system. 

Table 1 shows that the maximum ethanol concentration in this test was 67.7 g/1, in the outlet of the third reactor, for a flow rate of 8.1 ml/h. In this condition, the TRS and glucose concentrations were 3.3 and 0.8 g/1, respectively. The system is stable for all flow rates. The lowest flow rate, 8.1 ml/h, was more difficult to control, which was what led to some more pronounced oscillation of the variable values in this condition. It was expected in the continuous run that similar results than the ones obtained in the batch run will be achieved. As in batch operation, the cycle time is considerably longer than the reaction time, if the continuous process had reached a similar performance than the one obtained with the batch run in the continuous operation, we could save cycle time (times to clean, to fill ant to empty the reactor). Therefore, from the industrial point of view, the continuous process would lead to higher productivities. 

The temporal oscillating patterns of certain chemical intermediates have been observed only in a stirred BZ reaction system. Similar to cerium-catalyzed BZ reaction, the oscillation is occurred between colorless and yellow color at an assured time interval. There are some other important indicators where oscillations can be monitored due to the gradual color change, either direcdy in batch reactor [37, 38] or via spectrophotometric measurements [39, 40]. The most excellent illustration of oscillations manifested in batch reactors in the form of color variation of ferroin-catalyzed BZ reaction system. On the other hand, in some other reaction systems such as the manganese-catalyzed system and the cerium-catalyzed reaction, oscillations can be observed with the help of UV-visible spectrophotometer [41] where change in color might be monitored less distinctly. 

The oscillating chemical system with catechol as organic substrate in a batch reactor under unstirred conditions with Mn (11) as catalyst was reported [162]. These aromatic substrates were especially important in the study of spatial periodicities and shown a variety of spiral and scroll behaviors. Salter and Sheppard [163] reported a dual-frequency oscillator with EAA as substrate. Its behavior was much like the MA system except that a set of high-frequency, negatively damped oscillations in both redox potential and bromide ion were superimposed on early part of the induction period. 

A batch reactor is the simplest configuration for studying a chemical reaction. A solution containing the reactants is placed in a beaker and the reaction proceeds. The reaction is often thermostated with a circulating jacket to maintain constant temperature. No chemicals enter or leave the system once the reaction begins it is a closed system. Relatively few reactions undergo oscillations in a batch reactor, the BZ reaction being one of these. Oscillations in a batch reactor are necessarily... 

The best way to study the phenomena of nonlinear chemical dynamics—oscillations, chaos, waves, and spatial patterns— is to work in an open system. These phenomena can occur in closed systems like batch reactors, but only as transients on the way to the final state of equilibrium. In a closed system, we have to study them on the run, as their properties are changing. For example, to capture periodic oscillation under conditions where the amplitude and period are truly constant, we must have a flow of reactants into the system and a flow of products out of it. 

In batch conditions, the model behaves (as does the experimental system) as a clock reaction, with an induction period followed by a sudden jump of several orders of magnitude in H and then an exponential decrease in H. Under flow conditions, bistability and oscillations are obtained. The model can easily be adapted to describe a wide variety of pH oscillators, including iodate-sulfite-thiourea (Rabai et ah, 1987), iodate-sulfite-thiosulfate (Rabai and Beck, 1988), periodate-thiosulfate (Rabai et ah, 1989a), periodate-hydroxylamine (Rabai and Epstein, 1989), and iodate-hydroxylamine (Rabai and Epstein, 1990). 

A final, and in some ways the simplest, mode of negative feedback identified by Luo and Epstein (1990) is termed flow control. In some systems, the negative feedback provided by the chemical reactions alone is insufficient to generate oscillation. These systems cannot function as batch oscillators, but can give oscillations with appropriate flows in a CSTR. An illustrative example is given by Franck (1985) ... 

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