System, quiescent

Vanishing average molar velocity and a system quiescent relative to the average molar velocity can be presumed, as the example indicates for the mass diffusion of ideal gases at constant pressure and temperature. 

This reaction can oscillate in a well-mixed system. In a quiescent system, diffusion-limited spatial patterns can develop, but these violate the assumption of perfect mixing that is made in this chapter. A well-known chemical oscillator that also develops complex spatial patterns is the Belousov-Zhabotinsky or BZ reaction. Flame fronts and detonations are other batch reactions that violate the assumption of perfect mixing. Their analysis requires treatment of mass or thermal diffusion or the propagation of shock waves. Such reactions are briefly touched upon in Chapter 11 but, by and large, are beyond the scope of this book. 

Reactors containing electrodes of this kind are used when reactants are present in the solution in an extremely low concentration, and their rate of diffusion to a quiescent electrode (even a porous one) would be too low. An acceleration of the reaction at three-dimensional electrodes is attained owing to shorter dilfusional transport distances to the closest particles in suspension and also owing to strong turbulence in the system. 

PCBs in biological samples are usually extracted by a Soxhlet column and with a nonpolar solvent such as hexane. The sample is first mixed with sodium sulfate to remove moisture. The extraction of PCBs from sediments was tested with sonication, with two sonications interspersed at a 24-h quiescent interval, with steam distillation, or with Soxhlet extraction (Dunnivant and Elzerman 1988). Comparison of the recoveries of various PCB mixtures from dry and wet sediments by the four techniques and the extraction efficiency of four solvents showed that the best overall recoveries were obtained by Soxhlet extraction and the two sonication procedures. In comparisons of solvent systems of acetone, acetonitrile, acetone-hexane (1+1), and water-acetone-isooctane (5+1.5+1), recoveries of lower chlorinated congeners (dichloro- to tetrachloro-) were usually higher with acetonitrile and recoveries of higher chlorinated congeners (tetrachloro- to heptachloro-) extracted with acetone were superior (Dunnivant and Elzerman 1988). The completeness of extraction from a sample matrix does not seem to discriminate against specific isomers however, discrimination in the cleanup and fractionation process may occur and must be tested (Duinker et al. 1988b). 

Carrousel An unconventional aerobic treatment system for sewage and industrial effluents, providing efficient oxygenation, mixing, and quiescent flow in an elliptical aeration channel fitted with baffles. Developed in The Netherlands by DHV Raagevend Ingenieursbureau B.V., and licensed in the United Kingdom by Esmil. 

If, however, these conditions are not fulfilled, for instance if the solution contains such a high level of basic impurities that they compete effectively with the monomer for the TiCI+3 then there will be no polymerisation until the concentration of impurities has been reduced sufficiently. It seems most likely now that it is these circumstances which produce the quiescent mixtures of monomer and initiator. In order to induce a polymerisation in such quiescent systems it is necessary to produce a sufficient quantity of reactive ions. This can happen either if one waits long enough for the self-ionisation to produce sufficient initiating TiCl+3 ions, or if one adds a co-initiator which reacts with the titanium tetrachloride to generate ions in a different manner and in greater numbers. 

A rheological measurement is a useful tool for probing the microstructural properties of a sample. If we are able to perform experiments at low stresses or strains the spatial arrangement of the particles and molecules that make up the system are only slightly perturbed by the measurement. We can assume that the response is characteristic of the microstructure in quiescent conditions. Here our convective motion due to the applied deformation is less than that of Brownian diffusion. The ratio of these terms is the Peclet number and is much less than unity. In Equation (5.1) we have written the Peclet number in terms of stresses ... 

For a concentrated system this represents the ratio of the diffusive timescale of the quiescent microstructure to the convection under an applied deforming field. Note again that we are defining this in terms of the stress which is, of course, the product of the shear rate and the apparent viscosity (i.e. this includes the multibody interactions in the concentrated system). As the Peclet number exceeds unity the convection is dominating. This is achieved by increasing our stress or strain. This is the region in which our systems behave as non-linear materials, where simple combinations of Newtonian or Hookean models will never satisfactorily describe the behaviour. Part of the reason for this is that the flow field appreciably alters the microstructure and results in many-body interactions. The coupling between all these interactions becomes both philosophically and computationally very difficult. 

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