Stirring and Mixing Effects

Rate Law, dx/dt X Constant Smooth Gradient Step Funetion 

Chemical engineers have devoted much attention to the issue of mixing in flow rcaetors because of the industrial importance of reactions that occur in CSTRs. 

They have learned a great deal, and readers seeking a more thorough treatment than we are about to provide should seek it in the chemical engineering literature (Curl, 1963 Villermaux, 1983 Zwietering, 1984 Ulbrecht and Pearson, 1985). Here, we give a brief summary of some of the most important features of the mixing process in a CSTR. 

One of the clearest demonstrations of how difficult it is to obtain perfect mixing in a CSTR is found in the studies of Menzinger and Dutt (1990) on the chlorite-iodide reaction. These authors placed a platinum microelectrode at different distances from the central stirring rod in their cylindrical flow reactor. In one experiment, at a stirring rate of 880 rpm, consistent with many well-stirred CSTR experiments, they observed a difference in electrode potential of about 50 mV when the electrode was moved radially from a position at the axis to a position 12 mm away in the radial direction. This difference corresponds to a 

The studies of Menzinger and coworkers described above were inspired by a pioneering set of experiments by Roux, De Kepper, and Boissonade (Roux et al., 1983a) on the chlorite-iodide reaction in a flow reactor, in which they measured, at several different stirring rates, the hysteresis curve as a function of flow 

---

Only the BZ reaction has played a more central role in the development of nonlinear chemical dynamics than the chlorite-iodide reaction (De Kepper et al., 1990). This latter system displays oscillations, bistability, stirring and mixing effects, and spatial pattern formation. With the addition of malonic acid, it provides the reaction system used in the first experimental demonstration of Turing patterns (Chapter 14). Efforts were made in the late 1980s to model the reaction (Epstein and Kustin, 1985 Citri and Epstein, 1987 Rabai and Beck, 1987), but each of these attempts focused on a different subset of the experimental data, and none was totally successful. Since each model contains a different set of reactions fitted to a different set of data, individual rate constants vary widely among the different models. For example, the rate constant for the reaction between HOCl and HOI has been given as zero (Citri and Epstein, 1987), 2 x10 s (Rabai... 

Dutt, A. K. Menzinger, M. 1990. Stirring and Mixing Effects on Chemical Instabilities Bistability of the BrOJ/Br /Ce System, J. Phys. Chem. 94, 4867-4870. 

Reactors are mostly not isothermal, as heat is consumed or released, and perfect mixing or a perfect heat exchange with the surrounding is impossible. However, some reactors are almost isothermal, such as, for example, a well-mixed continuous stirred tank reactor (CSTR). In a batchwise operated stirred tank or in a plug-flow reactor (PFR), isothermal conditions with regard to reaction or residence time (axial position), respectively, are hard to realize. However, the assumption of an isothermal system is helpful for a first examination of reactor types as it simplifies the equations and we can focus on concentration and mixing effects only. Thus, here, we inspect isothermal reactors. Thermal effects are considered in Section 4.10.3. 

A lake mixes on some time scale so it might be modeled as a stirred reactor for times longer than the mixing time, and it is a tubular reactor for shorter times. Most lakes turn over seasonally because of the density rrtirtimum of water at 4°C so they are mixed on at least a 1 year time scale. Small lakes are mixed effectively by wind on shorter time scales. Deep lakes exhibit an upper layer that turns over and mixes and a lower layer that does not. The inlets to a lake are aU the rivers that flow into it and also water coming from rainfall, and the outlets are aU the rivers that flow out of it and evaporatiorr... 

However with stirring and coalescence and breakup, both effects tend to mix the contents of the bubbles or drops, and this situation should be handled using the CSTR mass balance equation. As you might expect, for a real drop or bubble reactor the residence time distribution might not be given accurately by either of these limits, and it might be necessary to measure the RDT to correctly describe the flow pattern in the discontinuous phase. 

---