Reactor, open spatial

Genuine Turing patterns are nonequilibrium structures and can occur only in open systems. This requirement represents the first obstacle on the way to an experimental realization of Turing patterns. Needed is an open reactor, an unstirred flow reactor, which can play the same role for spatial patterns that the CSTR plays for temporal patterns. This instrumentation problem was solved in the second half of the 1980s by the Austin group. They developed two types of open spatial reactors, the Couette reactor [433,335,456,336] and the continuously fed unstirred reactor (CFUR) [322, 432,431, 323]. The latter proved to be instrumental in the experimental realization of Turing patterns. 

The experimental observation of Turing patterns is the result of a long chain of improvements in practical methods to design both new chemical oscillating reactions and open spatial reactors. 

The development of practical methods [56] for the systematic design of new oscillating reactions in continuous stirred tank reactors (CSTR) lead to the discovery of several dozens of different isothermal oscillating systems, including the CIMA reaction [57]. This reaction is one of the very few to also exhibit transient oscillatory behavior in batch conditions. This and the fact that it does not exhibit marked excitability character like the well-known Belousov-Zhabotinsky reaction [5], lead us to select the CIMA reaction for systematic research on stationary spatial structures in open spatial reactors [14]. 

Concerning open spatial reactors, a first approach was provided by the so-called Couette flow reactor . In this quasi-one-dimensionalreactor, the transport is ensured by turbulent diffusion. Fresh reagents permanently renewed at each end allow the system to be maintained at a controlled distance from equilibrium. When operated in this reactor, the CIMA reaction lead to various spatio-temporal structures (oscillating fronts) as well as to a nontrivial stationary spatial structure (three stationary fronts) [58, 59]. However, this is... 

Fig. 1. Schematic diagrams of open spatial reactors (a) the reaction medium, a thin gel disk (b) reaction system for two-side-fed reactor and (c) reaction system for one-side-fed reactor, ((a) and (b) from [10], (c) from [20])...

In a batch system, structures can develop more rapidly than in open spatial reactors, because it is not necessary to wait until a stationary concentration gradient is established. In a closed system, zero flux boundary conditions apply, since there is no mass exchange at the boundaries. The structures. 

In the past few years, however, there has been a rebirth of interest in the formation of dissipative structures in chemically reacting and diffusing systems. This interest has been mainly sparked by the developement of open spatial reactors by groups in Texas [21-28] and in Bordeaux [29-38]. Basically, two types of open reactors are currently operating (i) the two-dimensional continuously fed unstirred reactors where the transport process is essentially natural molecular diffusion and where the feeding is either uniform (continuously fed unstirred reactor [23,24]) or from the lateral boundaries (linear [34, 35], annular [21, 22, 38] or disc [25, 36] gel reactors) and (ii) the Couette... 

De Kepper has described a fascinating pattern of waves that can be studied in a continuous couette reactor. This is an open spatial reactor that provides a good approximation of a one-dimensional diffusion system, and consists of two concentric cylinders with a narrow gap between them. The inner cylinder can rotate while the outer one is fixed. At each end of the cylinder is a chamber fitted with a stirrer into which reactants can flow in and products flow out. Variation of the rate of rotation causes changes in the... 

In Fig. 1.8 we show schematically the set-np in use in our experiment, for details please see [7]. The set-up adopted for our experiments has as central element an open gel-reactor, which allows to maintain constant non-equilibrium conditions during the measurements, see Fig. 1.8, With it, and by means of computer-based spectrophotometry [37], we aiialyze w ave activity in the BZ medium with sufficiently liigh spatial and temporal resolution. 

Since they are open systems that can exchange chemical species with their surrounding solvent, gels can also play the role of chemical reactors. In this framework, the design of open spatial gel reactors has allowed well controlled experimental studies of chemical patterns such as chemical waves or Turing structures (2). They are made of a thin film of gel in contact with one or two continuous stirred tank reactors that sustain controlled nonequilibrium conditions. 

Most of the wave experiments that we have been describing were carried out in relatively simple closed systems the one-dimensional (i.e., thin tube) and two-dimensional (i.e., Petri dish) equivalents of the beaker used in the earliest experiments on temporal (zero-dimensional) oscillations. We have seen, in Chapter 3, the enormous impact that the introduction of open flow reactors had on the study of temporal behavior. Similar considerations apply to the study of spatial waves and patterns. The patterns that we have discussed, however fascinating, can only be transiently present in a closed system like a Petri dish. As in the case of a stirred beaker, an unstirred closed system is destined by thermodynamics to reach a stable, homogeneous, unchanging state of equilibrium. In this section, we describe briefly some recent experimental advances that have made possible the study of spatial waves and patterns in open systems. 

To enhance the visibility of the oscillations and spatial structures in the CIMA reaction, starch is used as a color indicator of triiodide in most experiments. In the open spatial gel reactors developed in Bordeaux and Texas polyacrylamide gel (PAA) was used as the reaction medium to prevent convective motion. The starch is introduced into the acrylamide monomer solution before poly-... 

Chemical reactions with autocatalytic or thermal feedback can combine with the diffusive transport of molecules to create a striking set of spatial or temporal patterns. A reactor with permeable wall across which fresh reactants can diffuse in and products diffuse out is an open system and so can support multiple stationary states and sustained oscillations. The diffusion processes mean that the stationary-state concentrations will vary with position in the reactor, giving a profile , which may show distinct banding (Fig. 1.16). Similar patterns are also predicted in some circumstances in closed vessels if stirring ceases. Then the spatial dependence can develop spontaneously from an initially uniform state, but uniformity must always return eventually as the system approaches equilibrium. 

Example 4.8 Chemical reactions and reacting flows The extension of the theory of linear nonequilibrium thermodynamics to nonlinear systems can describe systems far from equilibrium, such as open chemical reactions. Some chemical reactions may include multiple stationary states, periodic and nonperiodic oscillations, chemical waves, and spatial patterns. The determination of entropy of stationary states in a continuously stirred tank reactor may provide insight into the thermodynamics of open nonlinear systems and the optimum operating conditions of multiphase combustion. These conditions may be achieved by minimizing entropy production and the lost available work, which may lead to the maximum net energy output per unit mass of the flow at the reactor exit. 

The simplest type of open system of interest in combustion is the continuous-flow well-stirred tank reactor or CSTR, which is an idealization of tank reactors used widely in industry. In essence, this is simply a tank into which reactants flow continuously at some known volumetric flow-rate and the reactant-intermediate-product mixture is efficiently stirred so that there are no spatial concentration or temperature gradients. In order to maintain a constant reaction volume, there is a matching volumetric outflow of the mixture from the CSTR so that molecules spend only a finite time in the reactor. This is known as the mean residence time t es and is determined by the volumetric flow-rates and the reactor volume. 

A batch reactor is a solid vessel or container. It may be open or closed. Reactants are usually added to the reactor simultaneously. The contents are then mixed (if necessary) to ensure no spatial variations in the concentration of the species present. The reaction then proceeds. There is no transfer of mass into or out of the reactor during this period. The concentration of reactants and products change with time thus, this is a transient or unsteady-state operation. The reaction is terminated when the desired chemical change has been achieved. The contents are then discharged and sent elsewhere, usually for further processing. 

This section contains several models whose spatiotemporal behavior we analyze later. Nontrivial dynamical behavior requires nonequilibrium conditions. Such conditions can only be sustained in open systems. Experimental studies of nonequilibrium chemical reactions typically use so-called continuous-flow stirred tank reactors (CSTRs). As the name implies, a CSTR consists of a vessel into which fresh reactants are pumped at a constant rate and material is removed at the same rate to maintain a constant volume. The reactor is stirred to achieve a spatially homogeneous system. Most chemical models account for the flow in a simplified way, using the so-called pool chemical assumption. This idealization assumes that the concentrations of the reactants do not change. Strict time independence of the reactant concentrations cannot be achieved in practice, but the pool chemical assumption is a convenient modeling tool. It captures the essential fact that the system is open and maintained at a fixed distance from equilibrium. We will discuss one model that uses CSTR equations. All other models rely on the pool chemical assumption. We will denote pool chemicals using capital letters from the start of the alphabet. A, B, etc. Species whose concentration is allowed to vary are denoted by capital letters... 

Combinatorial libraries are prepared by the (1) parallel synthesis of arrays, (2) split-pool method, (3) biological method, or (4) spatially addressable parallel synthesis [74,78-80]. Parallel synthesis is carried out by the simultaneous synthesis of an array of different compounds. Several methods are available. In the multipin method, the peptide synthesis is carried out on polyethylene rods that have attached protected amino acids [81]. The amino acid sequence of a synthesized peptide on a particular pin depends on the order in which the amino acids are added. The number of products synthesized is the same as the number of pins. Another version of parallel synthesis, known as the teabag method, uses resin-filled bags in place of pins [74]. By pooling the resin portions from the appropriate bags, followed by redistribution and further coupling with a specific amino acid, a peptide library can be synthesized. The SPOT method uses a cellulose paper membrane as a solid support, which acts as an open reactor. Respective reagent solutions are pipetted onto several spots to synthesize as many peptides as the spots chosen [74,82]. 

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 this chapter, we have considered the analytical techniques that can be used in monitoring chemical oscillations and waves, from standard spectrophotometry to spatial NMR methods. The most commonly used methods have been potentio-metric because of their low cost and ease of use. Of course, to measure something, you need a reaction in a vessel. We evaluated the types of reactors used for homogeneous reactions, of which the CSTR is the most common. Spatial phenomena can be studied in simple test tubes or Petri dishes, but careful work requires open systems using gel or membrane reactors. 

Recent studies have made it easier to design reactors with vertical tubular inserts. This arises from the observation (Gunn and Hilal, 1994, 1996, 1997) that the heat transfer coefficients for these systems are almost equal to those for the corresponding open fluidized beds of the same diameter operating with the same particles. Hence, correlations for the latter (which are readily available) can be used for vertical inserts without significant loss of accuracy. Vertical inserts have an additional advantage over horizontal inserts in horizontal inserts, unlike in the vertical orientation, there is accumulation of particles on the top of the tubes and depletion of particles at the bottom, a situation that leads to a spatial variation in heat transfer coefficient. 

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