Viscosities, apparent

Apparent viscosities were determined using a falling sphere method on samples that had been matured for more than a year. 

As in the NMR experiments the samples were magnetically oriented with the field direction perpendicular to the NMR tube axis. Crossed polarizers were mounted on the magnet for correlation of optical and viscometric data. After a rotation experiment was performed the sample was removed from the magnetic field and placed in a 25.0 0.02°C constant temperature bath. The velocity of the sphere falling along the axis of the NMR tube measured using a cathetometer and timer was used to calculate the Stokes law apparent viscosity. A Faxen correction (ll) of about 5 was applied to all data. 

The equations of motion for a memory-dependent nematic liquid undergoing reorientation in a magnetic field have recently been presented (lO). The equations were derived using the theory of micropolar continuum mechanics as introduced by Eringen (l2, 

In the special case when the memory can be neglected, the result is 

The validity of Equation 2 relies upon the assumption that the influence of the anisotropic environment of the polymer molecules on the solvent remains constant during a reorientation. It is therefore implied that the PBG helicies retain their original degree of parallelism on a scale which is large compared to the distance a solvent molecule diffuses during its spin lifetime. 

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Apparent viscosity (greases) NFT 60-139 ASTM D 1092 Forced passage of the grease in a capillary tube... 

The reported apparent viscosity is 200 poise. Estimate the coefficient of friction that corresponds to these data. Discuss any assumptions and approximations. 

Templeton obtained data of the following type for the rate of displacement of water in a 30-/im capillary by oil (n-cetane) (the capillary having previously been wet by water). The capillary was 10 cm long, and the driving pressure was 45 cm of water. When the meniscus was 2 cm from the oil end of the capillary, the velocity of motion of the meniscus was 3.6 x 10 cm/sec, and when the meniscus was 8 cm from the oil end, its velocity was 1 x 10 cm/sec. Water wet the capillary, and the water-oil interfacial tension was 30 dyn/cm. Calculate the apparent viscosities of the oil and the water. Assuming that both come out to be 0.9 of the actual bulk viscosities, calculate the thickness of the stagnant annular film of liquid in the capillary. 

Colloidal dispersions often display non-Newtonian behaviour, where the proportionality in equation (02.6.2) does not hold. This is particularly important for concentrated dispersions, which tend to be used in practice. Equation (02.6.2) can be used to define an apparent viscosity, happ, at a given shear rate. If q pp decreases witli increasing shear rate, tire dispersion is called shear tliinning (pseudoplastic) if it increases, tliis is known as shear tliickening (dilatant). The latter behaviour is typical of concentrated suspensions. If a finite shear stress has to be applied before tire suspension begins to flow, tliis is known as tire yield stress. The apparent viscosity may also change as a function of time, upon application of a fixed shear rate, related to tire fonnation or breakup of particle networks. Thixotropic dispersions show a decrease in q, pp with time, whereas an increase witli time is called rheopexy. 

Theoretically the apparent viscosity of generalized Newtonian fluids can be found using a simple shear flow (i.e. steady state, one-dimensional, constant shear stress). The rate of deformation tensor in a simple shear flow is given as... 

In addition to the apparent viscosity two other material parameters can be obtained using simple shear flow viscometry. These are primary and secondary nomial stress coefficients expressed, respectively, as... 

Polymers display pseudoplasticity, with apparent viscosity decreasing as 7 increases [Eq. (2.30) and Fig. 2.2]. 

Apply Eq. (2.27) to some of the data points to evaluate the apparent viscosity at different 7 s. The first section of Table 2.2 shows the results of such calculations. Note that the calculated 17 s are constant at low 7 values, indicating Newtonian behavior. Table 2.2 also expresses all 17 values relative to the Newtonian limiting value 17 - Comparison of Eqs. (2.28) and (2.29) shows that t7/t7im values decrease from the Newtonian limit by the fraction sinh" (j37)/j37. 

The apparent viscosity, defined as du/dj) drops with increased rate of strain. Dilatant fluids foUow a constitutive relation similar to that for pseudoplastics except that the viscosities increase with increased rate of strain, ie, n > 1 in equation 22. Dilatancy is observed in highly concentrated suspensions of very small particles such as titanium oxide in a sucrose solution. Bingham fluids display a linear stress—strain curve similar to Newtonian fluids, but have a nonzero intercept termed the yield stress (eq. 23) ... 

The fluid is formulated from a premium mineral od-base stock that is blended with the required additive to provide antiwear, mst and corrosion resistance, oxidation stabdity, and resistance to bacteria or fungus. The formulated base stock is then emulsified with ca 40% water by volume to the desired viscosity. Unlike od-in-water emulsions the viscosity of this type of fluid is dependent on both the water content, the viscosity of the od, and the type of emulsifier utilized. If the water content of the invert emulsion decreases as a result of evaporation, the viscosity decreases likewise, an increase in water content causes an increase in the apparent viscosity of the invert emulsion at water contents near 50% by volume the fluid may become a viscous gel. A hydrauHc system using a water-in-od emulsion should be kept above the freezing point of water if the water phase does not contain an antifreeze. Even if freezing does not occur at low temperatures, the emulsion may thicken, or break apart with subsequent dysfunction of the hydrauHc system. 

Apparent viscosity of a grease at low shear rates, eg, below about 10, is approximately equal to the yield stress divided by the shear rate. This... 

Fig. 15. Apparent viscosity vs rate of shear of three greases (53). To convert Pa s to P, multiply by 10.

For non-Newtonian fluids the correlations in Figure 35 can be used with generally acceptable accuracy when the process fluid viscosity is replaced by the apparent viscosity. For non-Newtonian fluids having power law behavior, the apparent viscosity can be obtained from shear rate estimated by... 

Refining and Fractionation. These processes are used to alter and select cellulose properties so the final sheet has the desired properties (51). Properties of recycled fibers differ from those of fibers prepared directly from wood. For example, recovered chemical fibers have lower freeness, an apparent viscosity leading to different water drainage characteristics on paper machines. Recovered fibers also have iacreased apparent density, lower sheet strength, iacreased sheet opacity, inferior fiber—fiber bonding properties, lower fiber sweUiag, lower fiber flexibiUty, lower water reteatioa, reduced fiber fibrillatioa, and much lower internal fiber delamination. 

Viscosity is equal to the slope of the flow curve, Tf = dr/dj. The quantity r/y is the viscosity Tj for a Newtonian Hquid and the apparent viscosity Tj for a non-Newtonian Hquid. The kinematic viscosity is the viscosity coefficient divided by the density, ly = tj/p. The fluidity is the reciprocal of the viscosity, (j) = 1/rj. The common units for viscosity, dyne seconds per square centimeter ((dyn-s)/cm ) or grams per centimeter second ((g/(cm-s)), called poise, which is usually expressed as centipoise (cP), have been replaced by the SI units of pascal seconds, ie, Pa-s and mPa-s, where 1 mPa-s = 1 cP. In the same manner the shear stress units of dynes per square centimeter, dyn/cmhave been replaced by Pascals, where 10 dyn/cm = 1 Pa, and newtons per square meter, where 1 N/m = 1 Pa. Shear rate is AH/AX, or length /time/length, so that values are given as per second (s ) in both systems. The SI units for kinematic viscosity are square centimeters per second, cm /s, ie, Stokes (St), and square millimeters per second, mm /s, ie, centistokes (cSt). Information is available for the official Society of Rheology nomenclature and units for a wide range of rheological parameters (11). 

Polymer melts are frequendy non-Newtonian. In this case the earlier expression given for the shear rate at the capillary wall does not hold. A correction factor (3n + 1)/4n, called the Rabinowitsch correction, must be appHed in such a way that equation 21 appHes, where 7 is the tme shear rate at the wall and nis 2l power law factor (eq. 22) determined from the slope of a log—log plot of the tme shear stress at the wad, T, vs 7. For a Newtonian hquid, n = 1. A tme apparent viscosity, Tj, can be calculated from equation 23. 

Processing PC resins by extmsion or injection-molding methods requires melt temperatures of 290—320°C. High melt viscosity at low shear rates prevents mold flash and drool. At injection shear rates, apparent viscosities decrease, and easy melt flow allows manufacture of large, complex parts. 

All fluids for which the viscosity varies with shear rate are non-Newtonian fluids. For uou-Newtouiau fluids the viscosity, defined as the ratio of shear stress to shear rate, is often called the apparent viscosity to emphasize the distiuc tiou from Newtonian behavior. Purely viscous, time-independent fluids, for which the apparent viscosity may be expressed as a function of shear rate, are called generalized Newtonian fluids. 

The term apparent viscosity (p. or t ) is often encountered but has been defined by both of the following equations. 

Figure 8.5. Apparent viscosity-shear rate curves for dilatant fluid, a Newtonian fluid and pseudoplastic fluid which have the same apparent viscosity at zero shear rate...

Typical of thermoplastics (see Chapter 8) the melts are pseudoplastic and also in common with most thermoplastics the zero shear rate apparent viscosity of linear polyethylene is related to the weight average molecular weight by the relationship... 

The melt viscosity is highly non-Newtonian in that the apparent viscosity drops considerably with increasing shear rate. Melt viscosities are about the average encountered with plastics materials but there is a considerable variation between grades. 

Studies of melt flow properties of polypropylene indicate that it is more non-Newtonian than polyethylene in that the apparent viscosity declines more rapidly with increase in shear rate. The melt viscosity is also more sensitive to temperature. Van der Wegt has shown that if the log (apparent viscosity) is plotted against log (shear stress) for a number of polypropylene grades differing in molecular weight, molecular weight distribution and measured at different temperatures the curves obtained have practically the same shape and differ only in position. 

Figure 12.16. Classification of liquids according to dependence of apparent viscosity in shear rate...

The strong dependence of apparent viscosity on shear rate. This necessitates particular care in the design of complex extrusion dies. 

With most homopolymers and copolymers the apparent viscosity is less dependent on temperature and shear stress (up to 10 dyn/cm ) than that of the polyolefins, thus simplifying die design. On the other hand the melt has a low elasticity and strength and this requires that extruded sections be... 

Property of a fluid whose apparent viscosity increases with shear rate. 

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