Oscillatory solution, stirred

Later Uppal et al. (1974) applied the bifurcation theory to find all the solutions including the oscillatory solutions of the Continuous Stirred Tank Reactor. The CSTR equations that they studied are simplied form of those studied by Gurel and Lapidus (1965) more specifially the exponents b2 and b3 are equal to one ... 

Oscillations can also arise from the nonlinear interactions present in population dynamics (e.g. predator-prey systems). Mixing in this context is relevant for oceanic plankton populations. Phytoplankton-zooplankton (PZ) and other more complicated plankton population models often exhibit oscillatory solutions (see e.g. Edwards and Yool (2000)). Huisman and Weissing (1999) have shown that oscillations and chaotic fluctuations generated by the plankton population dynamics can provide a mechanism for the coexistence of the huge number of plankton species competing for only a few key resources (the plankton paradox ). In this chapter we review theoretical, numerical and experimental work on unsteady (mainly oscillatory) systems in the presence of mixing and stirring. 

In this short initial communication we wish to describe a general purpose continuous-flow stirred-tank reactor (CSTR) system which incorporates a digital computer for supervisory control purposes and which has been constructed for use with radical and other polymerization processes. The performance of the system has been tested by attempting to control the MWD of the product from free-radically initiated solution polymerizations of methyl methacrylate (MMA) using oscillatory feed-forward control strategies for the reagent feeds. This reaction has been selected for study because of the ease of experimentation which it affords and because the theoretical aspects of the control of MWD in radical polymerizations has attracted much attention in the scientific literature. 

The classical problem of multiple solutions and undamped oscillations occurring in a continuous stirred-tank reactor, dealt with in the papers by Aris and Amundson (39), involved a single homogeneous exothermic reaction. Their theoretical analysis was extended in a number of subsequent theoretical papers (40, 41, 42). The present paragraph does not intend to report the theoretical work on multiplicity and oscillatory activity developed from analysis of governing equations, for a detailed review the reader is referred to the excellent text by Schmitz (3). To understand the problem of oscillations and multiplicity in a continuous stirred-tank reactor the necessary and sufficient conditions for existence of these phenomena will be presented. For a detailed development of these conditions the papers by Aris and Amundson (39) and others (40) should be consulted. 

Doedel, E.J. R.F. Heinemann. 1983. Numerical computation of periodic solution branches and oscillatory dynamics of the stirred tank reactor with A —> B C reactions. Chem. Eng. Sci. 38 1493-9. 

TSM sensors can also be used as DNA-based sensors. Okahata et al. [28] studied the use of oscillatory driven 9 or 27 MHz quartz to quantify DNA-DNA and DNA-protein interactions. They used quartz with one side specifically coated and the other side rubber cased, which was dipped into a stirred and thermostated solution of the target. Binding amounts were evaluated quantitatively as mass per unit area. Effects of probe immobilization tech-... 

When a water-miscible polymer is to be made via a suspension process, the continuous phase is a water-immiscible fluid, often a hydrocarbon. In such circumstances the adjective inverse is often used to identify the process [118]. The drop phase is often an aqueous monomer solution which contains a water-soluble initiator. Inverse processes that produce very small polymer particles are sometimes referred to as inverse emulsion polymerization but that is often a misnomer because the polymerization mechanism is not always analogous to conventional emulsion polymerization. A more accurate expression is either inverse microsuspension or inverse dispersion polymerization. Here, as with conventional suspension polymerization, the polymerization reaction occurs inside the monomer-containing drops. The drop stabilizers are initially dispersed in the continuous (nonaqueous phase). If particulate solids are used for drop stabilization, the surfaces of the small particles must be rendered hydrophobic. Inverse dispersion polymerization is used to make water-soluble polymers and copolymers from monomers such as acrylic acid, acylamide, and methacrylic acid. These polymers are used in water treatment and as thickening agents for textile applications. Beads of polysaccharides can also be made in inverse suspensions but, in those cases, the polymers are usually preformed before the suspension is created. Physical changes, rather than polymerization reactions, occur in the drops. Conventional stirred reactors are usually used for inverse suspension polymerization and the drop size distribution can be fairly wide. However, Ni et al. [119] found that good control of DSD and PSD could be achieved in the inverse-phase suspension polymerization of acrylamide by using an oscillatory baffled reactor. 

Continuous stirred tank reactor polymerization reactors can also be subject to oscillatory behavior. A nonisothermal CSTR free radical solution polymerization can exhibit damped oscillatory approach to a steady state, unstable (growing) oscillations upon disturbance, and stable (limit cycle) oscillations in which the system never reaches steady state and never goes unstable, but continues to oscillate with a fixed period and amplitude. However, these phenomena are more commonly observed in emulsion polymerization. High-volume products such as styrene-butadiene rubber (SBR) often are produced by continuous emulsion polymerization. As noted earlier, this is... 

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