Transport structured flows

Theory and Computer Simulation of Structure, Transport, and Flow of Fluid in Micropores... 

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. 

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. 

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. 

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. 

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>)...

Solute Molecular weight Apparent diffusion coefficient in the presence of structured flow system Enhanced diffusion transport rate" Linear transport rate (10 8 m s 1)... 

Fig. 21. Schematic representation of the molecular weight dependence of rapid transport involving structured flows as vehicles for the transport. Large molecules are retained in vertically migrating rapid flows and undergo only slight or no lateral diffusion. Small molecules, on the other hand, are not retained in rapidly moving vertical flows but diffuse laterally into a vertical flow migrating into the opposite direction...

We have discussed in Section 33.2.1 that the linear rate of the PVP transport varies as g019 in a structured flow system. 

Rapid polymer transport and associated structured flow formation are multistep processes. These processes may include 1) initial diffusion of components across the boundary 2) inversion of density, 3) convective motions occurring in regions that are unstable with respect to density, 4) birth and nucleation of structured flows, 5) development of visible structured flows, and 6) movement and maintenance of structured flows over longer periods. A clear delineation of any of these steps has not been achieved so far. Future work will be concerned with the development of systems in which these individual steps may be studied in more detail. 

Then the rate at which transport, viscous flow, diffusion, and conduction occur is controlled by either the rate at which the opportunities for escape occur or the ease with which the ion jumps into the new open structure. Of course, these statements apply only to molten salts such as sodium chloride, simple molten salts as they are called, and those for which the log D versus l/Tline is straight (Fig. 5.49). If the molten salt forms complexes (e.g., ZnCl , which is formed in NaCl-ZnClj), then it is rather different the control of transport rate in these substances will be discussed in a later section. 

Study on the rapid transport of a polymer in dextran solutions, first observed by Preston et al., is extended into two directions. They arc (1) enhancement effect on the transport rate of polyvinylpyrrolidone (PVP) by the addition of a simple salt, and (2) extension to the transport of linear polyelectrolytes. The enhancement effect was observed on the structured flow as well as on the transport rate. The enhancement effect was correlated with the densities of the solutions in the lower compartment of the diffusion cell. The correlation was improved when the rate was corrected for the differences in viscosities. We have found that effects of charges on the polymers favor the rapid transport of polyacrylates (PA) and sodium hyaluronate. Counterion condensation was manifested in the transport rate of PA. Transport rates of several salts of PA in the absence of added salt increased linearly with their partial specific volumes in water. 

Rapid transport of polyvinylpyrrolidone (PVP) in dextran solutions has been observed by Preston et al. This rapid transport was ascribed to the occurrence of a ringer - like structured flow and was characterized by the linear dependence of the transported amount on time t rather than on The molecular mechanism of the phenomenon is not yet fully... 

It is pertinent to consider separately the enhancement effect of salt on two steps the initiation step (onset of the flow) and the structured flow. The transport rates are related to the properties of the final structured flow and are contributed from the effects on both steps. The effect on the initiation step is clearly noticed since the critical PVP concentrations for the occurrence of the structured flow depended on the kind of salt. Effects of a salt on the cross diffusion constants of the two polymer components will be examined on both excluded volume and frictional effect. The effect on the excluded volume interaction between the two polymer components is expected to be small. This expectation is partly supported by the result that coil dimension of PVP was not influenced by the addition of a salt at 2 M in the cases of three salts LiCl, NaCl and CsCI, while these salts showed quite diverse effects on the trrmsport rates of PVP. Since viscosities vary with the kind and the concentration of salt, frictional coefficients are influenced by the presence of a salt. In this respect cross diffusion constants may be affected by salt through a change in viscosity of the medium. 

We have observed rapid transport of polyacrylate (PA) and hyaluronate (HA) in dextran solution matrix, which will be the first extension to linear polyelectrolytes. The whole transport process did not follow the flow rcgime(linear in t) nor diffusion(linear in t ) but a combination of the two, when ionic strengths were not high enough. In the media of low ionic strengths, diffusion of linear polyelectrolytes is very rapid due to the effect of counterion diffusion. We sometimes observed structured flows under a situation that transport rate followed diffusion law. This behavior was more clearly observed on HA than PA. Effect of charges favored the rapid transport of both polyclcctrolytcs, since (a)... 

Typically, large scale transport in flows with a finite correlation length of the velocity field is diffusive with an effective diffusion coefficient Deff (Sect. 2.2.2). Therefore the coarse grained structure of the oscillatory reaction in this flow should be similar to a onedimensional oscillatory reaction-diffusion system, i.e. propagating waves and no synchronization of the local oscillations on large scales. 

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