Scattering hydrodynamic interaction

As in the case of the Rouse dynamics (see Sect. 3.1.1), the intermediate incoherent scattering law for dominant hydrodynamic interaction (Zimm model) can be... 

Comparing Eqs. (83), (84) and Eqs. (21), (22) it follows immediately that Rouse and Zimm relaxation result in completely different incoherent quasielastic scattering. These differences are revealed in the line shape of the dynamic structure factor or in the (3-parameter if Eq. (23) is applied, as well as in the structure and Q-dependence of the characteristic frequency. In the case of dominant hydrodynamic interaction, Q(Q) depends on the viscosity of the pure solvent, but on no molecular parameters and varies with the third power of Q, whereas with failing hydrodynamic interaction it is determined by the inverse of the friction per mean square segment length and varies with the fourth power of Q. 

From Fig. 35, where the normalized coherent scattering laws S(Q, t)/S(Q,0) are plotted as a function of 2 (Q)t for Zimm as well as for Rouse relaxation, one sees that hydrodynamic interaction results in a much faster decay of the dynamic structure factor. 

Fig. 3. The dynamic scattering function for a pair of elements (j, k) after averaging over all orientations in the pre-average approximation of the hydrodynamic interaction, and without this approximation...

As particle concentration increases, particle interactions and multiple scattering invalidate Eq. (33). The cross terms (y /) in the static and dynamic structure factors. Eq. (29), no longer cancel out, and thus they lead to more complex relationships [l 15-119] for (l>(diffusive motion of interacting particles also becomes more complex, depending on colloidal and hydrodynamic interactions among the particles and their spatial configurations. DLS measurements of particle motion can provide information about suspension microstructure and particle interactions. 

From QELS the diffusion coefficient, and hence the particle radius, can be found, provided the particles are spherical and homodlsperse and the sol is dilute. Deconvolution is difficult when one of these premises does not apply. Dilution of the sol is a prerequisite to avoid multiple scattering and any hydrodynamic interaction between the particles. A variety of apparatus is nowadays commercially available, based on one of the above-mentioned techniques, or a combination of them, so that velocity and size are both obtained. With some of these instruments size and/or velocity distributions can be derived, but the caveat must be made that these tend to be based on software progreims in which a certain type of distribution is presupposed. 

A semirigorous multiple-scattering theory of Shaqfeh and Fredrickson (1990) that accounts for multiparticle hydrodynamic interactions for slender bodies has verified Batchelor s theory and has given a slightly improved formula for str ... 

Quasi-elastic laser light scattering (also called intensity fluctuation spectroscopy, light-beating spectroscopy or photon correlation spectroscopy) is an accurate method to measure the translational diffusion coefficients of macromolecules. The diffusion coefficient is a parameter, that depends on the size and shape of the macromolecules and on the thermodynamic and hydrodynamic interaction between the macromolecules. 

The virial coefficient takes into account the direct interactions between droplets (like B) and the hydrodynamic interactions. Light scattering data in the two-phase domains are gathered in table I. 

It should be mentioned that the above results are vahd if the hydrodynamic interactions do not affect particle transport through the adsorption layer of thickness 2a. This seems justified for smaller colloid particles and proteins. However, for micrometer-sized particles placed in shearing flows, the hydrodynamic forces play a significant role due to the coupling with the repulsive electrostatic interactions. This leads to enhanced blocking effects called hydrodynamic scattering effects and discussed extensively in recent review works [7,14]. These results have been interpreted theoretically in terms of the Brownian dynamics simulations [14], which are, however, considerably more time-consuming than the RSA simulations. 

Quasi-elastic scattering by dilute, ideal, polymer solutions II effects of hydrodynamic interactions (with E. Dubois-Violette). Phvs. (N.Y.) 2, n 4, 181-198 (1967). 

This quantity is measured in dynamic light-scattering technique, and its origin lies in the hydrodynamic interactions in the solution. 

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