Newtonian fluids melt viscosity measurements

Of the viscometric functions, the viscosity is by far the easiest to measure and is thus the most often reported. As in the case of Newtonian fluids, the viscosity of a polymer depends on temperature and pressure, but for polymeric fluids it also depends on shear rate, and this dependency is quite sensitive to molecular structure. In particular, the curve of viscosity versus shear rate can be used to infer the molecular weight distribution of a linear polymer as is explained in Chapter 8. And in certain cases it can also tell us something about the level of long-chain branching. This curve is also of central importance in plastics processing, where it is directly related to the energy required to extrude a melt. 

Unlike shear viscosity, extensional viscosity has no meaning unless the type of deformation is specified. The three types of extensional viscosity identified and measured are uniaxial or simple, biaxial, and pure shear. Uniaxial viscosity is the only one used to characterize fluids. It has been employed mainly in the study of polymer melts, but also for other fluids. For a Newtonian fluid, the uniaxial extensional viscosity is three times the shear viscosity ... 

Capillary viscometers are useful for measuring precise viscosities of a large number of fluids, ranging from dilute polymer solutions to polymer melts. Shear rates vary widely and depend on the instmments and the Hquid being studied. The shear rate at the capillary wall for a Newtonian fluid may be calculated from equation 18, where Q is the volumetric flow rate and r the radius of the capillary the shear stress at the wall is = r Ap/2L. 

Information about the behavior of shear thinning melts in twin screws can be derived from Eq. 7.13, in addition to the approximation of the measured values. The concept of representative viscosity based on Frederickson [3] is used for this purpose. The representative viscosity is the viscosity that provides the same pressure generation as a Newtonian fluid under the specified conditions. If we combine Eqs. 7.13 and 7.2, we obtain for the representative viscosity ... 

Melt Viscosity Equation of Sulfui>-DCP Solutions. An assumption is made that the sulfur-DCP solution is a Newtonian fluid, i.e., the viscosity measured by the Brookfield viscometer is independent of the spindle speed, which is related to shear rate. The linear plots of log (viscosity) vs. time as in Figures 8, 9, and 10 give the following equation for a given sulfur-DCP composition at a given temperature ... 

This standard covers measurement of the rheological properties of polymers with both stable and unstable melt viscosity parameters at various temperatures and shear rates. The test procedure lists typical test temperature conditions for polyethylene 190°C, for polypropylene 230°C, for poly(vinyl chloride) 170-205°C, however, this indicates that the most useful data are generally obtained at temperatures consistent with processing experience. The test method also prescribes using the Rabinowitsch shear rate correction (see above) and indicates that the basic rheology equations (17.10), (17.15) and (17.16) yield true shear rate and true viscosity for Newtonian fluids only for non-Newtonian fluids only the apparent shear rate and viscosity are obtained. 

For low viscosity Newtonian fluids, several methods for the measurements of have been developed [Wu, 1974]. However, the high viscosity of industrial polymer melts makes most of them irrelevant. The few remaining ones that can be used for determination of in polymer blends, can be divided into equilibrium and dynamic methods [Luciani et al., 1997]. 

ASTM D3835/2000 test method measures rheological properties of thermoplastic (and thermosetting) melts by using a capillary rheometer [4], The test method includes measurements of viscosity, shear rate, shear stress, swell ratio, and percent of extrudate swell. Assuming a newtonian fluid, to calculate melt viscosity j, use... 

In general, incompressible Newtonian fluids at constant temperature can be characterized by just two material constants the shear viscosity iio and the density p. Once these quantities are measured, the velocity distribution and the stresses in the fluid can, in principle, be found for any flow situation. In other words, different isothermal experiments on a Newtonian fluid would yield a single constant material property, namely, its viscosity. On the other hand, a variety of flow experiments performed on a thermoplastic melt, which is a non-Newtonian fluid, would yield a host of material functions that depend on shear rate, frequency, and time. 

Rubber and plastic melts can be considered, to a first approximation, as extremely high-viscosity fluids. This is only an approximation and it must be remembered that polymers generally show viscoelastic properties—a combination of viscous flow and elastic recovery. Viscosity, in turn, is the quantitative measure of resistance to flow under a given set of circumstances. The Greek letter that usually designates viscosity is Tj. For an ideal, Newtonian fluid, viscosity is simply the ratio between Shear Stress (t), the pressure placed on the fluid to create flow, and the Shear Rate (y), the rate of flow over time as seen in Equation 16C.1 ... 

Unlike shear viscosity, extensional viscosity has no meaning unless the type of deformation is specified. The three types of extensional viscosity identified aind measured are uniaxial or simple, biaxial, and pure shear. Uniaxial viscosity is the only one used to characterize fluids. It has been employed mainly in the study of polymer melts, but also for other fluids. For a Newtonian fluid, the uniaxial extensional viscosity is three times the shear viscosity ( fe)uni = 3/ . This is confirmed at very low shear rates in Figure 13, which provides a typical example of the extensional viscosity behavior of a polymer (129). The two other extensional viscosities are used to study elastomers in the form of films or sheets. Uniaxial and biaxial extensions are important in industry (118,125-128,130,132), the former for the spinning of textile fibers and roller spattering of paints, and the latter for blow molding, vacuum forming, film blowing, and foam processes. 

This apparent viscosity increases with shear rate for shear-thickening fluids, is independent of shear rate for Newtonian fluids, and decreases with shear rate for shear-thinning fluids (Figure 8.5). Therefore, while reporting the apparent viscosities of polymer melts or solutions, it is important to mention the shear rates or shear stresses used during the measurements. In this book, for the purpose of simplicity, apparent viscosity will be called as viscosity and be given the symbol tj. 

One of the most widely used rheometer configurations is a simple variant of the capillary flow viscometer. In this device, a concentrated polymer solution or melt undergoes Poiseuille flow in a narrow capillary, length L and internal radius R, under the action of an external pressure P. The capillary exit is typically open to the atmosphere, such that a pressure difference Ap = P - produces the driving force that leads to fluid flow (Figure 8.3). If the volumetric flow rate of fluid through the capillary Q is known (measured), Poiseuille s equation can be used to determine the fluid s viscosity if the fluid is Newtonian. 

Bueche-Ferry theory describes a very special second order fluid, the above statement means that a validity of this theory can only be expected at shear rates much lower than those, at which the measurements shown in Fig. 4.6 were possible. In fact, the course of the given experimental curves at low shear rates and frequencies is not known precisely enough. It is imaginable that the initial slope of these curves is, at extremely low shear rates or frequencies, still a factor two higher than the one estimated from the present measurements. This would be sufficient to explain the shift factor of Fig. 4.5, where has been calculated with the aid of the measured non-Newtonian viscosity of the melt. A similar argumentation may perhaps be valid with respect to the "too low /efi-values of the high molecular weight polystyrenes (Fig. 4.4). 

Newtonian flow n. An isothermal, laminar flow characterized by a viscosity that is independent of the level of shear, so that the shear rate at all points in the flowing liquid is directly proportional to the shear stress and vice versa. Simple liquids such as water and mineral oil usually exhibit Newtonian flow, whereas polymer melts and solutions usually do not, but are pseudoplastic. Newtonian flow can occur, at least ideally, under the influence of an infinitesimally small force. It is said to be distinguished from plastic flow, which occurs only when a finite minimum force is exceeded. Oils, at sufficiently low rates of shear, exhibit Newtonian flow. Munson BR, Young DF, Okiishi TH (2005) Fundamentals of fluid mechanics. John Wiley and Sons, New York. Kamide K, Dobashi T (2000) Physical chemistry of polymer solutions. Elsevier, New York. Van Wazer JR, Lyons JW, Kim KY, Colwell RE (1963) Viscosity and flow measurement. Interscience Publishers Inc., New York. 

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