Viscosity asymptotic critical behavior

The concept of universality classes, mentioned in the previous section, can be extended so as to be applicable to the characterization of the asymptotic critical behavior of dynamic properties (Hohenberg Halperin 1977). Two systems belong to the same dynamic universality class when they have the same number and types of relevant hydro-dynamic modes. Thus the asymptotical critical behavior of the mutual mass diffusivity D 2 and of the viscosity rj of liquid mixtures near a consolute point will be the same as that of the thermal diffusivity a and the viscosity j of one-component fluids near the vapor-liquid critical point (Sengers 1985). Hence, in analogy with equation (6.16) for liquid mixtures near a consolute point it can be written... 

In the literature there have been repeated reports on an apparent mean-field-like critical behavior of such ternary systems. To our knowledge, this has first been noted by Bulavin and Oleinikova in work performed in the former Soviet Union [162], which only more recently became accessible to a greater community [163], The authors measured and analyzed refractive index data along a near-critical isotherm of the system 3-methylpyridine (3-MP) + water -I- NaCl. The shape of the refractive index isotherm is determined by the exponent <5. Bulavin and Oleinikova found the mean-field value <5 = 3 (cf. Table I). Viscosity data for the same system indicate an Ising-like exponent, but a shrinking of the asymptotic range by added NaCl [164],... 

Success in correlating both thermal conductivity and viscosity by Thodos et al. pi.32] for the heavier diatomic molecules provides a basis for establishing the heavy-molecule end of the critical-point loci as nearly horizontal asymptotic lines. For the thermal conductivity no other good tie points exist, and the critical-point locus is therefore more conjectural. It is believed that a single critical point locus will adequately include all types of molecules. At the critical point the density is lower and hence the influence of orientational effects in two-body interactions will be smaller than at the triple point. Fortunately the effect of errors in locating the helium end of this locus is minimized with respect to predicting the behavior of the thermal conductivity for H2, D2, etc. The high-temperature ends of the He, He H2, D2, A, and N2 thermal conductivity curves were, in each case, extrapolated (broken lines) to their respective reduced critical temperatures. 

Figure 4 illustrates how the Carreau-Yasuda model meets the shear viscosity data of Fig. 2. A non-linear fitting algorithm (i.e. Marquardt-Levenberg) was used to obtain the parameters given in the inset. As can be seen the fit curve provides a shear viscosity function that corresponds reasonably well with experimental data so that the high shear behavior is asymptotic to a power law and the very low shear behavior corresponds to the pseudo-Newtonian viscosity po- The characteristic time X (56.55 s) can be considered as the reverse of a critical shear rate (i.e. = Yc = 0.0177 s ) that corresponds to the intersection between the high shear power...

The excess viscosity has been determined for each datum by the use of equation (14.46) and subtracting the dilute-gas value, and the critical enhancement, A c, from the experimental value, T). For this purpose, reported by the experimentalists, rather than the value obtained from equation (14.47), has been preferred. This choice minimizes the influence of systematic errors in the individual measurements and forces the data of each author to a proper asymptotic behavior for the dilute-gas state. Furthermore, the experimental excess viscosity obtained in this fashion is independent of the choice for a dilute-gas viscosity correlation. Unfortunately, the majority of measurements on viscosity of ethane have been performed at pressures above 0.7 MPa and hence only a few authors reported a >7 value. Therefore, in order to estimate the experimental zero-density viscosity of each isotherm, again an iterative procedure had to be used (Hendl et al. 1994). The correction introduced by the extrapolation to zero density is small and in general does not exceed 0.5%. 

The equation is given in dimensionless form with p = p/p and p = 317.763 kg m Values for the coefficients Hfj are listed in Table 14.15. The critical enhancement of the viscosity of steam occurs in a r on which covers approximately 1% in absolute temperature and 30% in density relative to the critical temperature and critical density, as shown in Figure 14.21. Inside this critical r on, the equations given above are used to rq>resent the background viscosity. In the case of water substance, it has been the practice to consider the relative critical enhancement, or viscosity ratio, rather than the absolute enhancement. The asymptotic behavior of the viscosity is written (Chapter 6) in terms of the correlation length f, which characterizes the spatial... 

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