Viscosity quasi

In most cases of quasi-viscosity there is an upper limit of r, above which fj becomes independent of it again. This is shown, in the flow diagram of Fig. 12, borrowed from Philippoff where D and r are plotted on a logarithmic scale. Thus, at very small stresses one can speak of a viscosity coefficient (Vo), but at very high stresses one finds another coefficient 0/co). Between these two the region of quasi- viscosity or structural viscosity is encountered. The appearance of a constant value for be due... 

One speaks of quasi-Viscosity, when rj changes with increasii shearing-stress r. 

Fig. 3. Quasi-viscosity of selenium glass in the transformation interval ( ioo tieans at a shearing stress of...

Figure 9.28(a) Effect of surfactant concentration on the liberation of sodium salicylate, (b) Quasi-viscosity of sodium salicylate ointments dependence on surfactant concentration. (c) Wettability of preparations dependence on surfactant concentration. From Voight [72]. 

According to the structure of this equation the quantity cp indicates the influence of the filler on yield stress, and t r on Newtonian (more exactly, quasi-Newtonian due to yield stress) viscosity. Both these dependences Y(cp) andr r(cp) were discussed above. Non-Newtonian behavior of the dispersion medium in (10) is reflected through characteristic time of relaxation X, i.e. in the absence of a filler the flow curve of a melt is described by the formula ... 

These data show clearly that that the intrinsic behavior in pure metals is visco-elastic with the velocity proportional to the applied stress (Newtonian viscosity). Although there is a large literature that speaks of a quasi-static Peierls-Nabarro stress, this is a fiction, probably resulting from studying of insufficiently pure metals. 

The more incisive calculation of Springett, et al., (1968) allows the trapped electron wave function to penetrate into the liquid a little, which results in a somewhat modified criterion often quoted as 47r/)y/V02< 0.047 for the stability of the trapped electron. It should be noted that this criterion is also approximate. It predicts correctly the stability of quasi-free electrons in LRGs and the stability of trapped electrons in liquid 3He, 4He, H2, and D2, but not so correctly the stability of delocalized electrons in liquid hydrocarbons (Jortner, 1970). The computed cavity radii are 1.7 nm in 4He at 3 K, 1.1 nm in H2 at 19 K, and 0.75 nm in Ne at 25 K (Davis and Brown, 1975). The calculated cavity radius in liquid He agrees well with the experimental value obtained from mobility measurements using the Stokes equation p = eMriRr], with perfect slip condition, where TJ is liquid viscosity (see Jortner, 1970). Stokes equation is based on fluid dynamics. It predicts the constancy of the product Jit rj, which apparently holds for liquid He but is not expected to be true in general. 

The dynamic surface tension of a monolayer may be defined as the response of a film in an initial state of static quasi-equilibrium to a sudden change in surface area. If the area of the film-covered interface is altered at a rapid rate, the monolayer may not readjust to its original conformation quickly enough to maintain the quasi-equilibrium surface pressure. It is for this reason that properly reported II/A isotherms for most monolayers are repeated at several compression/expansion rates. The reasons for this lag in equilibration time are complex combinations of shear and dilational viscosities, elasticity, and isothermal compressibility (Manheimer and Schechter, 1970 Margoni, 1871 Lucassen-Reynders et al., 1974). Furthermore, consideration of dynamic surface tension in insoluble monolayers assumes that the monolayer is indeed insoluble and stable throughout the perturbation if not, a myriad of contributions from monolayer collapse to monomer dissolution may complicate the situation further. Although theoretical models of dynamic surface tension effects have been presented, there have been very few attempts at experimental investigation of these time-dependent phenomena in spread monolayer films. 

Figure 5.5 The dynamic viscosity for a quasi-hard sphere dispersion from the data of Mellema et al.13 The frequency has been normalised to the diffusion time for two different particle radii. The volume fraction is

There are not a great number of studies on the viscoelastic behaviour of quasi-hard spheres. The studies of Mellema and coworkers13 shown in Figure 5.5 indicate the real and imaginary parts of the viscosity in a high-frequency oscillation experiment. Their data can be normalised to a characteristic time based on the diffusion coefficient given above. 

Figure 6.6 The limiting high shear viscosity for quasi-hard sphere for PMMA particles in dodecane. (The particle has a different effective radii, HK3 = 419nm, HK4 = 281 nm, HK5 = 184 nm, HK7 = 120nm, HK8 = 162 nm.) The solid line is given by the Krieger equation (6.6) for a packing of (pm( oo) = 0.605...

To determine the shape of ribosomal proteins in solution, ultracentrifugation, digital densimetry, viscosity, gel filtration, quasi-elastic light scattering, and small-angle X-ray or neutron scattering have all been used. With each technique it is possible to obtain a physical characteristic of the protein. Combining these techniques should allow the size and shape of the protein to be characterized quite well. However, the values determined in various laboratories for the same ribosomal proteins differ considerably. To help understand some of the reasons we will initially discuss each method briefly as it relates to proteins and then review the size and shape of the ribosomal proteins that have been so characterized. 

Selected entries from Methods in Enzymology [vol, page(s)] Anisotropy effects, 261, 427-430 determination by dynamic laser light scattering (quasi-elastic light scattering), 261, 432-433 determination for nucleic acids by NMR [accuracy, 261, 432-433 algorithms, 261, 11-13, 425, 430 carbon-13 relaxation, 261, 11-12, 422-426, 431, 434-435 cross-relaxation rates, 261,419-422, 435 error sources, 261, 430-432 phosphorus-31 relaxation, 261, 426-427, 431 proton relaxation, 261,51,418-422 relaxation matrix calculations, 261,12] deuterium solvent viscosity effects, 261,433 effect... 

When the Pecet number, the measure of the relative importance of advection to diffusion, is small, which is the case for high viscosity magmas, the temporal derivation of concentration and the advection term in Eq. (13.31) may be ignored, and quasi-static approximation may be developed. In this case, Eq. (13.31) reduces to... 

Recently Sato et al. [144,145] have extended the viscosity equation, Eq. (74), to multicomponent solution containing stiff-chain polymer species with different lengths. They showed a favorable comparison of the extended theory with the viscosity data for the quasi-ternary xanthan solutions presented in Fig. 21. 

A useful quasi-quantitative technique allowing determination of the degree of association of such polymers was reported by Professor Morton(15). The viscosity of concentrated solutions of high molecular weight polymers is proportional to a power of their weight average molecular weight, M, viz.,... 

R. A. Marcus I used the words saddle-point avoidance, incidentally, to conform with current terminology in the literature. More generally, one could have said, instead, avoidance of the usual (quasi-equilibrium) transition-state region (i.e., the most probable region if viscosity effects were absent). 

The discotic phases can show also a complex polymorphism. Nematic and cholesteric-like, low viscosity phases have been reported recently. In these, the director vector is perpendicular to the plane of alignment of the flat molecules56) in contrast to the normal nematics and cholesterics where it is parallel to the molecular axis. Most frequently, however, discotics form columnar arrangements as shown in Fig. 10. The order within the columns may change from liquid to quasi-crystalline. The columns are then packed in hexagonal or tetragonal coordination, but are free to slide in the direction parallel to their axes S7). The viscosity of these more ordered discotics is considerably higher than the nematic discotics. 

Note that the above study is performed for a simple system. There exists a large body of literature on the study of diffusion in complex quasi-two-dimensional systems—for example, a collodial suspension. In these systems the diffusion can have a finite value even at long time. Schofield, Marcus, and Rice [17] have recently carried out a mode coupling theory analysis of a quasi-two-dimensional colloids. In this work, equations for the dynamics of the memory functions were derived and solved self-consistently. An important aspect of this work is a detailed calculation of wavenumber- and frequency-dependent viscosity. It was found that the functional form of the dynamics of the suspension is determined principally by the binary collisions, although the mode coupling part has significant effect on the longtime diffusion. 

In building mathematical models of product formation in a mold it is possible to treat a polymeric material as motionless (or quasi-solid), because the viscosity grows very rapidly with the formation of a linear or network polymer thus, hydrodynamic phenomena can be neglected. In this situation, the polymerization process itself becomes the most important factor, and it is worth noting that the process occurs in nonisothermal conditions. 

Two additional parameters are the angular position of the point at which the film thickness is maximum, 0rot, and the ratio of the maximum thickness of the film to its mean thickness e. The zone of large Re and small Fr is shaded in Fig. 4.22 in the right bottom. The existence of circular closed flow lines proves to be impossible hence, a stable solution of the hydrodynamic problem is also impossible. The zone of quasi-solid rotation A is marked in the top left comer film flow is absent here and 1 < e < 1.01. This zone is reached either at Fr = const by decreasing Re (due to an increase in viscosity) or at Re = const by increasing Fr (through an increase in to). Two transient zones are marked with the numbers 1 and 2 in the lower unstable zone of Fig. 4.22. In zone 1, the... 

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