Structured flows

Determination of Controlling Rate Factor The most important physical variables determining the controlhng dispersion factor are particle size and structure, flow rate, fluid- and solid-phase diffu-sivities, partition ratio, and fluid viscosity. When multiple resistances and axial dispersion can potentially affect the rate, the spreading of a concentration wave in a fixed bed can be represented approximately... 

In this paper, we report recent progress made In our laboratory In using molecular theory and computer simulation to understand the structure, flow and transport of fluids confined by planar solid walls separated by a few molecular diameters. 

Consider a structured flow system of chemicals X, which can absorb light and give products Y + Z, but in which not all the products are involved in the cycle in contrast to Fig. 3.10. 

Identification of structured flows associated with rapid polymer transport and some simple mechanistic interpretations. 

Identification of Structured Flows Associated with Rapid Polymer Transport 134... 

Comparison Between PVP Transport and Structured Flow Transport.. 136... 

In view of the highly unusual nature of these results and the lack of a routine method for transport measurements unambiguously establishing that rapid transport was indeed a real manifestation of the system, our studies on rapid polymer transport remained unreported in detail. However, in a recent article 46> we have demonstrated that rapid polymer transport actually occurs in these systems due to the formation of ordered macroscopic structures which move rapidly. This rapid transport has been shown to be not the result of bulk convection since normal diffusional kinetics was observed for solvent markers such as [l4C]sorbitol. The striking feature of this new type of transport process is that it is accompanied by ordered structured flows in the... 

The use of absorption optics with the ultracentrifuge has allowed us to monitor the rapid transport of PVP in the standard PVP/dextran system as a function of g. It was demonstrated that while the rate of the PVP transport increases with increasing g acting on the system, the rate is rather insensitive to the magnitude of the gravitational force. We found 51) that the linear time rate of the transport varies as g°19. Note, however, that although rapid PVP transport has been found at various values of g, we cannot be sure whether structured flows exist. 

On the other hand, with the inclusion of a low molecular weight stabilizer in the lower compartment, i.e. 2 mol dm-3 NaCl, the evolution of the structures or structured flows was much more uniform and regular (Fig. 13b). The structures may be stable for several days. 

We have now identified the presence of structured flows in a wide variety of ternary systems of polymer/polymer/solvent 52-53>. in all cases associated with structured flow formation there was concomitant rapid transport of the polymer as compared to its behaviour in water. Indeed, even in the presence of dextran concentration gradients structures are formed which move relatively slowly but are nevertheless highly regular. The only conditions where structures have not been observed is at dextran concentrations below C values where, incidentally, polymer transport is not rapid. (See also the low rate of transport of PVP 360 in a dextran T10 medium with a concentration of 40 kg m 3 as measured in the ultracentrifuge Fig. 9.) These studies confirm the striking correlation between this parameter and the onset of rapid polymer transport and structured flow formation. 

This will be elaborated in detail in the following section. However, it is of interest that the existence of concentration-dependent (implying a far-from-equilibrium condition) cross-diffusion terms creates a non-linear mechanism between elements of the system, i.e. the flux of one polymer depends not only on its own concentration gradient but also on that of the other polymer component. This is consistent with two of the criteria required for dissipative structure formation. Furthermore, once a density inversion is initiated, by diffusion, it will be acted upon by gravity (as the system is open ) to produce a structured flow. The continued growth, stability and maintenance of the structures once formed may depend on the lateral diffusion processes between neighbouring structures. 

Fig. 17b. Schematic diagram of possible concentration and density gradients in countercurrent structured flows (for details see text)...

Far less information is available on the mechanism of the growth and stabilisation of structured flows once the nucleation process of coupled diffusion-mediated density inversion occurs. At this stage, only speculative arguments can be offered. 

We have shown above that for component configurations characteristic of system A, where solute densities are different, structured flows and rapid polymer transport may occur. These are more or less independent of the relative mobilities of the polymers involved. 

Fig. 19. Time-dependent development of structured flows in a dextran/sorbitol system (see legend of (Fig. 18) with blue-labelled dextran initially introduced into the bottom solution. The photograph was taken 2 h after formation of the boundary layer...

Fig. 20. Structured flows developed between the bottom solution containing dextran with 6.146 x 10-2 g/g phosphate buffer at pH 6.0 and dextranase with 10 units/g phosphate buffer (= 2.63 x 10s g/g phosphate buffer) and the top solution containing dextran with 3.952 x 10-2 g/g phosphate buffer (including blue dextran). The boundary was formed 3 min after the dextranase was added to the dextran solution. The photo was taken 30 min after formation of the initial boundary531...

A comparison of the data obtained by using McDougal and Turner s treatment of the prediction of structured flow formation in the PVP-dextran system with the ternary diffusion data in Fig. 16 indicates that their theory is not compatible with our observations 36). 

Studies of interdiffusion have been extended to polymer systems. Structured flow formation was detected for these systems in zonal centrifugation experiments 66,67). If a polymer solution is layered on top of a more dense solution containing a low molecular weight solute, then interdiffusion of the salt into the polymer solution eventually gives rise to density inversion, and droplets of polymer solution will sediment. This effect has often been described as droplet sedimentation or the turnover effect 68). 

Table 2. Transport of various trace solutes in a structured flow system formed by the presence of a 5 kg m-3 PVP 360 concentration gradient in a 135 kg m-3 dextran T10 solution (adapted from Ref.so>)...

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