Couette reactor

If a fluid is placed between two concentric cylinders, and the inner cylinder rotated, a complex fluid dynamical motion known as Taylor-Couette flow is established. Mass transport is then by exchange between eddy vortices which can, under some conditions, be imagmed as a substantially enlranced diflfiisivity (typically with effective diflfiision coefficients several orders of magnitude above molecular difhision coefficients) that can be altered by varying the rotation rate, and with all species having the same diffusivity. Studies of the BZ and CIMA/CDIMA systems in such a Couette reactor [45] have revealed bifiircation tlirough a complex sequence of front patterns, see figure A3.14.16. 

Figure A3.14.16. Spatiotemporal complexity in a Couette reactor space-time plots showing the variation of...

Particular attention is to be paid to closure models exploiting various types of PDFs such as beta, presumed, or full PDFs (e.g., Baldyga, 1994 Fox, 1996, 2003 Ranade, 2002). While PDFs have successfully been exploited for describing chemical reactions in turbulent flames, tubular reactors (Baldyga and Henczka, 1997), and a Taylor-Couette reactor (Marchisio and Barresi, 2003), they have never been used successfully in stirred reactors so far. 

Marchisio, D. L., Barresi, A. A. Fox, R. O. 2001a Simulation of turbulent precipitation in a semi-batch Taylor-Couette reactor using CFD. AIChE Journal 47, 664-676. 

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. 

Figure 6.14 Patterns observed in the chlorite-iodide-malonic acid reaction in a Couette reactor. The CSTR composition, flow rate, and rotation rate are held fixed, except for chlorite composition in one CSTR, whieh serves as the bifurcation parameter. In each frame, the abscissa represents the position along the reactor and the ordinate represents time. The dark color results from the presence of the starch- triiodide complex. (Adapted from Ouyang et al., 1991.)...

The Taylor-Couette reactor (TCR), sometimes referred to as a vortex flow reactor, consists of two concentric cylinders, one of which rotates. Figure 5.23. 

The Taylor-Couette reactor (see Chapter 5) is also a rotor stator mixer, but is discussed separately. Units such as the Marbond HEX-reactor demonstrate mixing plus reactions plus heat transfer in one unit, and these are also discussed in Chapter 5. 

Fig. 8 Scheme of batch plant and outlet to stirred tank reactor or TCR (Taylor-Couette reactor) [11]... 

A Taylor-Couette reactor may be used instead of the stirred tank to ensure that the bimodal distributions are not caused by the inhomogeneous input of mechanical work. Figure 19 shows the resulting fragment size distributions. The Taylor-Couette reactor generates bimodal distributions as well, albeit less distinctive for the acid-catalysed gelation. Smaller gel fragments occur (dmax cc [11]... 

The chemical system used for our study is a chlorite-iodide-malonic acid (CIMA) reaction in an acidic (sulfuric acid) aqueous solution. The CIMA reaction exhibits a rich variety of phenomena oscillations in a batch reactor or in a CSTR [26], transient target waves in a closed Petri dish [26], bistability in a CSTR [26, 27], front structures in a Couette reactor [27-30], and Turing patterns in open gel reactors [7-10]. In our two-side-fed reactor. Figure lb, components of the reaction are distributed in the two compartments in such a way that neither compartment is separately reactive. Chlorite is only in compartment A , and malonic acid is only in compartment B thus there are opposing chemical concentration gradients in the direction normal to the plane of the gel. The other chemical species are contained in equal amounts in both reservoirs, except for sulfuric acid, which is more concentrated in compartment B than in compartment A. Note that chlorite and iodide in compartment A are at a low acid concentration they would react rapidly at high acid conditions. 

Fig. 1. Schematic diagram of cross-section of a Couette reactor. Geometric characteristics Bordeaux reactor L = 33 cm, 6 = 1.27 cm, o/6 = 0.830, Volume of CSTRI = Volume of CSTR II = 26 mL Texas reactor 6 = 1.27 cm, a/b = 0.875, L variable (8 20 cm), no CSTRs at ends (from [33]).

Two different reactions have presently been studied in the Couette flow reactor, namely the variants of the Belousov-Zhabotinsky [27-30, 32] and chlorite-iodide [29-33] reactions. The BZ reaction has revealed a rich variety of steady, periodic, quasi-periodic, frequency-locked, period-doubled and chaotic spatio-temporal patterns [27, 28], well described in terms of the diffusive coupling of oscillating reactor cells, the frequency of which changes continuously along the Couette reactor as the result of the imposed spatial gradient of constraints. This experimental observation has been successfully simulated with a schematic model of the BZ kinetics [68] and the recorded bifurcation sequences of patterns resemble those obtained when coupling two nonlinear oscillators. 

In most experimental runs, the volume and feeding flows of the two CSTRs at both ends of the Couette reactor were large enough for their internal state not to be significantly influenced by the dynamics inside the Couette reactor [33]. This corresponds mathematically to imposing Dirichlet boundary conditions to our model reaction-diffusion system (3). In most of the simulations... 

For some feeding conditions, the dynamics inside the Couette reactor has been observed to introduce some feedback in the ending CSTRs [32, 33]. In such conditions the two CSTRs cannot be considered anymore as maintained in a steady state. In order to account for this phenomenon we will also consider the following set of boundary conditions ... 

Let us consider first the situation where the values of the two concentration variables of our reaction-diffusion model, u and v, are kept fixed at the two boundaries a = 0 (reduced upper-branch state) and x = 1 (oxidized lower-branch state) according to Equation (4). As long as the fronts are located far enough from the two CSTRs at both ends of the Couette reactor, this seems to be a rather good approximation of the experimental situation with asymmetric feeding [31-33] (Figure 2). Let us suppose that e is kept fixed to a (small) positive value. 

But this limit is far from (i) the current experimental conditions it would require low rotation rates of the inner cylinder of the Couette reactor for which the transport process could no longer be considered as diffusive and (ii) the resolution of current numerical simulations. In the present numerical study, we focus mainly on the early bifurcations of front patterns observed on the way to this extended system limit and discuss the existence of up to three-front pattern solutions [61,62]. 

In some experiments performed with some variants of the chlorite-iodide reaction, the oscillating front patterns have been observed to invade one of the end CSTRs [32, 33]. Henceforth the two CSTRs cannot be considered to be in a steady state during the experimental run as before. In order to account for the interplay of the dynamics inside the Couette reactor and in the CSTRs, we have performed subsequent numerical simulations [59,64] of our reaction-diffusion model (3)Avith the CSTR boundary conditions defined in Equation (5). We give here a short description of the patterns observed when considering the slow-manifold (6). The following parameters are kept fixed e = 10 , a = 0.5, uq = 2,ui = —4, Vi = f ui), i = 0,1. D = hg is our control parameter. 

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... 

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