Viscosity high shear relative

Zero-shear-rate viscosity Infinite-shear-rate viscosity High shear relative viscosity Intrinsic viscosity, polymer rheology,... 

Cell models akin to those discussed in Section 8.5 have also been applied to the determination of the properties of concentrated suspensions (Happel Brenner 1983, van de Ven 1989). Although it is another method which has been used to obtaining approximate expressions for the high shear relative viscosity, we choose not to expand upon it here, instead referring the reader to the references cited. One of the difficulties is that the determination of the boundary conditions at the cell surface is somewhat arbitrary. Furthermore, expressions obtained by this approach indicate that the cell model is inappropriate for highly concentrated suspensions and is most satisfactory only at low to moderate concentrations. 

Inks. Basic raw materials for letterpress inks, such as mineral oils, soya bean oil, resins, and pigments, are essentiaHy the same as those used in web offset inks. Inks are tinctoriaHy weak, relatively fluid, and their low and high shear viscosities are low. 

Depending on the concentration, the solvent, and the shear rate of measurement, concentrated polymer solutions may give wide ranges of viscosity and appear to be Newtonian or non-Newtonian. This is illustrated in Eigure 10, where solutions of a styrene—butadiene—styrene block copolymer are Newtonian and viscous at low shear rates, but become shear thinning at high shear rates, dropping to relatively low viscosities beyond 10 (42). The... 

For scaly fillers the increase of relative viscosity with filler concentration is not as pronounced as in case of fibrous fillers [177,178]. Owing to filler orientation, the flow curves for systems with different concentrations of a fibrous and a scaly filler may merge together at high shear rates [181]. In composites with a dispersed filler the decrease of the effective viscosity of the melt with increasing strain rate is much weaker. 

Foam fluids can be used in many fracturing jobs, especially when environmental sensitivity is a concern [1669]. Foam-fluid formulations are reusable, are shear stable, and form stable foams over a wide temperature range. They exhibit high viscosities even at relatively high temperatures [209]. 

With some concentrated suspensions of solid particles, particularly those in which the liquid has a relatively low viscosity, the suspension appears to slip at the pipe wall or at the solid surfaces of a viscometer. Slip occurs because the suspension is depleted of particles in the vicinity of the solid surface. In the case of concentrated suspensions, the main reason is probably that of physical exclusion if the suspension at the solid surface were to have the same spatial distribution of particles as that in the bulk, some particles would have to overlap the wall. As a result of the lower concentration of particles in the immediate vicinity of the wall, the effective viscosity of the suspension near the wall may be significantly lower than that of the bulk and consequently this wall layer may have an extremely high shear rate. If this happens, the bulk material appears to slip on this lubricating layer of low viscosity material. 

Two main types of viscometers are suitable for the determination of the viscosity of a polymer melt The rotation viscometer (Couette viscometer, cone-plate viscometer) and the capillary viscometer or capillary extrusiometer. The latter are especially suitable for laboratory use since they are relatively easy to handle and are also applicable in the case of high shear rates. With the capillary extrusiometer the measure of fluidity is not expressed in terms of the melt viscosity q but as the amount of material extruded in a given time (10 min). The amount of ex-trudate per unit of time is called the melt index or melt flow index i (MFI). It is also necessary to specify the temperature and the shearing stress or load. Thus MFI/2 (190 °C)=9.2 g/10 min means that at 190 °C and 2 kg load, 9.2 g of poly-... 

The Vel data as a function of flow rate, Q, are shown for a 10 g/mol molecular weight polystyrene in Figure A. Both the Ubbelohde viscometric data and the membrane viscometer data are platted on the same graph for a 0.6 urn pore membrane at a low concentration of 100 ppm. The flow is Newtonian. The actual agreement of the capillary and membrane viscosities at low flow rates is always excellent when << Dj., and the concentration is extremely low. At small pore size, high concentrations, and high shear rates the flow can become non-Newtonian. The latter effects are only briefly discussed in this paper, but it is this effect that offers an oportunity to characterize the shape rather than the overall size. Even for a relatively large pore (0.6, Hi , membrane the shear rates vary from 100 s at E mi/Hr to 10 s at 200... 

Under shear flow, the minimum center-to-center separation, r, between the particles will be in the interval 2Rs < r < L i.e., at the high-shear limit r = 2R, and at quiescent conditions r = L. An analysis of the flow behavior in this case leads to the following expression for the zero shear rate (i.e., Pe < 1) limit of the relative viscosity ... 

Figure H1.1.4 A complete flow curve for a time-independent non-Newtonian fluid. r 0 and i , are the viscosities associated with the first and second Newtonian plateaus, respectively. Regions (1) and (2) correspond to viscosities relative to low shear rates induced by sedimentation and leveling, respectively. Regions (3) and (4) correspond to viscosities relative to the medium shear rates induced by pouring and pumping, respectively. Regions (5) and (6) correspond to viscosities relative to high shear rates by rubbing and spraying, respectively.

A grafted layer of polymer of thickness L increases the effective size of a colloidal particle. In general, dispersions of these particles in good solvents behave as non-Newtonian fluids with low and high shear limiting relative viscosities (fj0 and rj ), and a dimensionless critical stress (a3aJkT) that depends on the effective volume fraction = (1 + L/a)3. The viscosities diverge at volume fractions m0 < for mo < fan < 4>moo> the dispersions yield and flow as pseudoplastic solids. 

It may be helpful to express the change of viscosity of a silicone oil in a different manner. If we compare a typical silicone oil with a standard hydrocarbon oil of viscosity index 100, the two having the same viscosity at 100° F., we find that after cooling to —35° F. the silicone oil has seven times the viscosity it had, whereas the hydrocarbon oil has increased 1,800-fold in viscosity. This relative constancy of viscosity of the silicone oil makes it particularly suitable for use as a fluid in hydraulic systems for the transmission of power. Silicone oils do not react with the common metals of construction, and they are so inert that even at 300° F. they do not discolor r become acid or form sludge. They are satisfactory lubricants in hydraulic pumps and in any other device where conditions of hydrodynamic lubrication prevail. When used as lubricants, methyl silicone oils do not suffer loss of viscosity through shear breakdown under continuous load at high speed. 

The tendency of particles to deform increases with increasing volume fraction. At effective volume fractions below about 0 0.4, suspensions of squishy spheres have viscosities similar to those of harder spheres (see Fig. 6-7). But at higher 0, there are substantial differences between the two, and layer deformability becomes important. Thus, for soft spheres at high 0, the dependence of relative viscosity on shear stress no longer obeys Eq. (6-14). Mewis et al. (1989) found that an equation of Cross (1965), which contains an extra parameter, works better ... 

Figure 6.7 (a) Low-shear-rate relative viscosity fjro and (b) high-shear-rate relative viscosity tj oo versus particle volume fraction 0 for sterically stabilized PMMA spheres with a = 42 nm PMMA in decalin (V), a = 42 nm in exsol ( ), a = 237 nm in decalin (A), and a = 610 nm in decalin ( ). The small spheres are effectively softer, and thus show smaller viscosities than the large spheres at... 

A similar, and even more dramatic, viscosity enhancement was observed by Buscall et al. (1993) for dispersions of 157-nm acrylate particles in white spirit (a mixture of high-boiling hydrocarbons). These particles were stabilized by an adsorbed polymer layer, and then they were depletion-flocculated by addition of a nonadsorbing polyisobutylene polymer. Figure 7-9 shows curves of the relative viscosity versus shear stress for several concentrations of polymer at a particle volume fraction of 0 = 0.40. Note that a polymer concentration of 0.1 % by weight is too low to produce flocculation, and the viscosity is only modestly elevated from that of the solvent. For weight percentages of 0.4-1.0%, however, there is a 3-6 decade increase in the zero-shear viscosity ... 

Figure 11 shows the relative-viscosity-concentration behavior for a variety of hard-sphere suspensions of uniform-size glass beads. Even though the particle size was varied substantially (0.1 to 440 xm), the relative viscosity is independent of the particle size. However, when the particle diameter was small ( 1 fJLm), the relative viscosity was calculated at high shear rates, so that the effect of Brownian motion was negligible. Figure 8 shows that becomes independent of the particle size at high shear stress (or shear rate). 

Thixotropy is a rheological property that results in yield stress on standing. Thixotropic flow is defined as a reversible, time-dependent, isothermal gel-sol transition. Thixotropic systems exhibit easy flow at relatively high shear rates. However, when the shear stress is removed, the system is slowly reformed into a structured vehicle. The usual property of thixotropy results from the breakdown and buildup of floccules under stress. A small amount of particle settling takes place until the system develops a sufficiently high yield value. The primary advantage of thixotropic flow is that it confers pourability under shear stress and viscosity and sufficiently high yield stress when the shear stress is removed at rest. 

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