Aperiodic flow

Figure A3.14.7. Example oscillatory time series for CO + O2 reaction in a flow reactor corresponding to different P-T locations in figure A3,14,6 (a) period-1 (b) period-2 (c) period-4 (d) aperiodic (chaotic) trace (e) period-5 (1) period-3.

One phenomenon that is drawing increasing attention, not only from chemists, but from mathematicians and physicists as well, has been dubbed chemical chaos", the existence of sustained aperiodic oscillation of species concentrations in a flow sys-... 

Alan Mutch, of the University of Manitoba, argues that both blood flow and ventilation are delivered in a fractal manner in both space and time in a healthy body. However, during critical illness, conventional life support devices deliver respiratory gases by mechanical ventilation or blood by cardiopulmonary bypass pump in a monotonously periodic fashion. This periodic driving overrides the natural aperiodic operation of the body. Mutch [107] speculates that these devices result in the loss of normal fractal transmission and consequently ... 

The non-dimensional parameter a = UT/L of the sine-flow that controls the extent of chaotic advection can be interpreted as a ratio of two characteristic timescales. One of them is the typical advection time over the characteristic lengthscale of the velocity field L/U. This is a property of the instantaneous velocity field and would be the same for a steady flow. Therefore it can not characterize the dynamics of chaotic mixing. For a time-periodic velocity field another timescale is the period of the flow. In the case of an aperiodic time-dependent flow an analogous timescale can be defined as... 

Simple periodic chemical oscillation may now be said to be reasonably well understood. More complex behavior can arise when a single oscillator is pushed into new realms or when it is coupled either to other oscillators or to external influences. Some chemical oscillators that are simply periodic under one set of conditions can exhibit complex, multi-peaked, periodic or even aperiodic, chaotic (14) behavior at other concentrations and flow rates in an open reactor. Some examples of chaotic oscillations in the chlorite-thiosulfate system are shown in Figure 4. Coupling two or more reactions together can result in the... 

Figure 4. Chaotic oscillation in the potential of a Pt redox electrode in the chlorite-thiosulfate reaction in a flow reactor. Note the aperiodic alternation between large and small amplitude peaks. Input concentrations, [ClOfJo = 5 x 10 M, [S203 ]o = 3 X 10 M, pH = 4, residence time in reactor = a) 6.8 min, b) 10.5 min, c) 23.6 min. Reproduced from Orbdn et al. (14). Copyright 1982 American Chemical Society.

The primary conclusion is that in the unlikely event that the tie rods vibrate in resonance with maximum possible excitation the stresses and deflections in the tie rods will be sufficiently small that there is no possibility of fatigue failure. In the actual case, the tie rods are not expected to be in resonance with the exciting force because the maximum local cross flow velocity will probably be less than 7 ft s. Furthermore, at high Reynolds numbers, there are experimental indications that the exciting forces will be aperiodic and that the combination of parallel and cross flow will decrease the stability of the flow... 

Quantification of mixing in aperiodic chaotic flows. Chaos, SdUtons, Fractals, 4, 869. 

Hsiao, K.-T. and Advani, S. G., A method to predict microscopic temperature distribution inside aperiodic unit cell of non-isothermal flow in porous media . Journal of Porous Media, 5, 69-86, 2002. 

Figure 8.9 Phase diagram of the chlorite-thiosulfate system in the [S203 ]q — ko plane with [C102]o = 5 X 10 MandpH4. SIMPLE and simple denote pure large-and pure small-amplitude oscillations, respectively. l iV denotes 1 multipeak oscillations. Vertical segments I show flow rate at which new 1 iV state appears. Filled-in boxes denote regions in which basic states are mixed to form aperiodic states. V, Low-potential steady state (SSI) A, high-potential steady state (SSII) o, bistability (SSI/SSII). (Reprinted with permission from Orban, M. Epstein, I. R. 1982. Complex Periodic and Aperiodic Oscillation in the Chlorite-Thiosulfate Reaction, J. Phys. Chem. 86, 3907-3910. 1982 American Chemical Society.)...

The spatially homogeneous stable state of a system that may be destabilized by a differential flow may be a stable fixed point or a periodic or aperiodic attractor. We consider here primarily the destabilization of homogeneous stable steady states, and in less detail, of homogeneous limit cycle oscillations. 

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