Hydrodynamic draining parameter

Just as the Gaussian chain is the basic paradigm of the statistics of polymer solutions, so is its extension to the bead-spring model still basic to current work in the held of polymer dynamics. The two limiting cases of free draining (no hydrodynamic interaction between beads, characterized by the draining parameter A = 0) and non-free draining (dominant hydrodynamic interaction, A= CO, due to Rouse and Zimm, respectively, are sufficiently familiar that the approach is often known as the Rouse-Zimm model. ... 

Equation (57) shows the same degenerate form of relaxation times as Eq. (30). The characteristic relaxation times are derived from the exact Zimm-Kilb eigenvalues [11,81]. The matching of the experimental and theoretical dependence of the moduli on frequency has only one adjustable parameter, i.e., die hydrodynamic interaction parameter, h. The free-draining case was evaluated by Ham [79]. 

Furthermore, it is sometimes questionable to use literature data for modeling purposes, as small variations in process parameters, reactor hydrodynamics, and analytical equipment limitations could skew selectivity results. To obtain a full product spectrum from an FT process, a few analyses need to be added together to form a complete picture. This normally involves analysis of the tail gas, water, oil, and wax fractions, which need to be combined in the correct ratio (calculated from the drainings of the respective phases) to construct a true product spectrum. Reducing the number of analyses to completely describe the product spectrum is one obvious way to minimize small errors compounding into large variations in... 

Secondly, hydrodynamic interactions (depending on the d/A ratio) are weaker for rigid-chain coils than for flexible-chain coils and when their hydrodynamic parameters are considered, draining effect should be taken into account. 

As mentioned repeatedly, according to the two-parameter theory, the expansion factor as> the penetration function and the hydrodynamic expansion factors a, and at in the non-draining limit should become universal functions of a single variable z. These non-dimensional quantities are experimentally determinable without any assumption. Thus, the validity of the two-parameter theory can be tested directly by looking at whether a single curve independent of polymer rind solvent condition (solvent species and temperature) is obtciined or not when any of them is plotted against the other. Such tests were made by many authors (for example, see Ref. [2] and [119]). Here we refer to a recent one by Miyaki and Fujita [49] (and also Miyaki [44]), who used the following criteria A and B. 

A different index of the change from Zimmlike to Rouselike behavior with increasing concentration can be obtained from the limiting behavior at low frequencies. This does not involve differences in frequency dependence, since G and G" — uvs are proportional to and co respectively in this region for all theories instead, it depends on the magnitudes of the respective proportionality constants, which are Ao and vo Vs- In connection with Table 9-II, it was noted that the parameter 52/5f varies from 0.2 to 0.4 for the change from free draining to dominant hydrodynamic interaction. For finite concentrations this parameter can be identified with... 

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