Backflow, hydrodynamic

The earliest and simplest approach in this direction starts from Langevin equations with solutions comprising a spectrum of relaxation modes [1-4], Special features are the incorporation of entropic forces (Rouse model, [6]) which relax fluctuations of reduced entropy, and of hydrodynamic interactions (Zimm model, [7]) which couple segmental motions via long-range backflow fields in polymer solutions, and the inclusion of topological constraints or entanglements (reptation or tube model, [8-10]) which are mutually imposed within a dense ensemble of chains. 

The problem is discussed further by Ives(24) and by Spielman and Friedlander(26). The backwashing of these beds has presented problems and several techniques have been adopted. These include a backflow of air followed by water, the flowrate of which may be high enough to give rise to fluidisation, with the maximum hydrodynamic shear occurring at a voidage of about 0.7. 

Another interesting experimental stndy of concentrated suspensions of hnman erythrocytes was performed by Znkoski and Saville. Although volume fractions as high as 75% were employed, the electrophoretic mobility changed by the factor (1 - ([)) in the whole concentration range, which was simply explained by the backflow of liquid necessary to conserve the snspension volnme. The electrostatic and hydrodynamic particle-particle interactions apparently canceled each other in these experiments. Note that the electrolyte concentration was relatively high and, contrary to the experiments of Deggelmann et al., " the EDL were thin in comparison with the particle size. 

Homeotropic to planar transition backflow and kickback effects The other two geometries used in the Freedericksz experiment are more interesting as they result in a new effect, namely, hydrodynamic flow induced by orientational deformation. This is the inverse of the more familiar property of flow alignment that has been discussed at length in previous sections. 

Marlow and Rowell (37) working with coal/water slurries and using the CVP technique have shown that, at the frequencies of their measurements (200 kHz), the effect of particle concentration can be adequately described by introducing a factor (1 — g ) into their equivalent of Eq. (1) where again, g was very close to unity. In their review article Marlow et al. (6) discuss the way the cell model of Levine and coworkers (38, 39) is introduced into the CVP theory and show that, for thin double layers, the result is that the hydrodynamic and electrostatic interactions essentially cancel one another and one is left with only the factor (1—d)) to take account of the backflow of liquid caused by the particle motion. 

To complete this Section we have to mention the hydrodynamics of a nematic liquid crystal. In the equations described above the macroscopic flow was neglected. Such an approximation is usually justified since we describe only systems with zero total momenum. However, one should bear in mind that due to the coupling between the hydrodynamic and orientational degrees of freedom there are local flows accompanying the orientational changes, the effect known as backflow [38,39]. In some cases the backflow effects can alter substantially the phenomena in question. 

The use of a steady or a periodic pressure-driven backflow in capillary zone electrophoresis increases the residence time of sample bands in the separation field. Consequently, significant improvement in resolution between the analyte peaks can be realized based on this strategy provided that the hydrodynamic dispersimi in the system is kept small. 

Unfortimately, the appUcaticm of a steady or a periodic pressure-driven backflow introduces hydrodynamic dispersion of analyte bands [3] and thereby compromises the resolving power of the CZE method. However, because such sample dispersion scales directly with the lateral dimensirms of the analysis charmel, it is possible to diminish this process by either packing CZE columns with small particles or miniaturizing their lateral dimensions. Previous studies have shown that the use of packed capillaries for CZE analyses with a pressure-driven backflow... 

Depending on the geometry, dielectric reorientations are sometimes accompanied by hydrodynamic transients, i.e., a backflow. (The reorientation caused by hydrodynamic flow is well known. ) Such back-flow transients, under certain conditions, can give rise to turbulent effects similar to dynamic scattering the latter term should be reserved specifically for the sequence domains, domain instability, and scattering, produced by conductance hydrodynamics. 

The Rouse free-draining limit is based on a local response of the monomers to external forces and ignores any long range hydrodynamic interactions. However, it is well known that the motion of each monomer creates a backflow velocity field in the solvent... 

The backflow field created by a monomer decays very slowly with distance and is the origin of the long range hydrodynamic interactions between monomers each monomer moves in the flow field created by all the others. 

The main results for the dynamics of dilute solutions reflect the importance of hydrodynamic interactions each moving monomer in the solvent creates a backflow field which decays very slowly with distance. In a semi-dilute solution, the interference between all these velocity fields induces a screening of the backflow field of a given monomer, which falls off exponentially after a characteristic distance A. This idea was originally proposed by Edwards and Freed we shall briefly summarize their theory for ideal Gaussian chains. 

Similarly, a strong influence of hydrodynamic interactions has been found on the polymer translocation dynamics through a small hole in a wall [125] or in polymer packing in a virus capsid [126,127]. Cooperative backflow effects lead to a rather sharp distribution of translocation times with a peak at relatively short times. The fluid flow field, which is created as a monomer moves through the hole, guides following monomers to move in the same direction. 

The dynamics of an isolated Kuhn segment chain in its bead-and-spring form is considered in a viscous medium without hydrodynamic backflow or excluded-volume effects. The treatment is based on the Langevin equation generalized for Brownian particles with internal degrees of freedom. A first, crude formalism of this sort was reported by Kargin and Slonimskii [45]. In-... 

In the case that hydrodynamic interactions arising from the backflow by movements of segments (or particles) are dominant over friction of each segment with a viscous fluid medium, the diffusion coefficient is often evaluated theoretically as follows. According to the mode-mode coupling theory for fluids with the Oseen tensor of hydrodynamic interactions,the diffusion coefficient is expressed in terms of the static correlation function S([Pg.307]

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