Isothermal melt viscosity

To use the Roller model requires the measurement of cure curves at several different temperatures so that Arrhenius plots may be made for the rate constant, k, and the Isothermal melt viscosity, n. The four model constants are then obtained from the Arrhenius plots. This entails considerable experimental work, especially for a method one would like to use in a more or less routine fashion. In addition, it is invalid in principle to... 

The pressure dependence of the melt viscosity (r ) can be estimated by using Equation 13.19 (derived from classical thermodynamics to relate the pressure and temperature coefficients of r [V]), where p is the hydrostatic pressure, K is the isothermal compressibility, a is the coefficient of volumetric thermal expansion, and d is a partial derivative. The sign of the pressure coefficient of the viscosity is opposite to the sign of the temperature coefficient. Consequently, since r decreases with increasing T, it increases with increasing p. Equation 13.20 is obtained by integrating Equation 13.19. 

More extensive investigations have been performed on HDPE/PP blends by Martuscelli et al. [1980] and Bartczak and Galeski [1986]. From the isothermal crystallization experiments, it was found that the rate of crystallization of the HDPE matrix was markedly reduced upon addition of small amounts of PP (10 wt%). The authors attributed this phenomenon to the increased melt-viscosity of the sample caused by the presence of solidified PP domains. Moreover, Plesek and Malac [1986] have calculated from the surface tensions of the homopolymers at T, that PP crystallization will not cause the nucleation of the HDPE phase, while in the reverse case HDPE crystals will induce the nucleation of PP. 

The same authors studied polypropylene samples PP-H-N, PP-H-R-B, PP-M-N, and PP-M-B in low-speed isothermal melt-spinning experiments at 180°C [93]. The apparent viscosities measured in that experiment are given in Figure 3.9. As seen, the viscosities are larger than those measured in simple elongational flow. Also, all the viscosities decrease with elongation rate, although those of the narrow samples do not decrease as rapidly as those of the broad-distribution samples. 

Drag flow is primarily determined by helix angle, barrel, and channel design pressure flow is determined by hehcal length, channel design, pressure rise, and melt viscosity. Extruder output, therefore, is a function of all these factors. Assuming newtonian, isothermal melt flow [2],... 

F/gwre 5. Isothermal (220 C) melt viscosity of poly [1,6-bis(p-carboxyphenoxy)... 

As discussed in the previous section, it is convenient to consider the output from the extruder as consisting of three components - drag flow, pressure flow and leakage. The derivation of the equation for output assumes that in the metering zone the melt has a constant viscosity and its flow is isothermal in a wide shallow channel. These conditions are most likely to be approached in the metering zone. 

In practice there are a number of other factors to be taken into account. For example, the above analysis assumes that this plastic is Newtonian, ie that it has a constant viscosity, r). In reality the plastic melt is non-Newtonian so that the viscosity will change with the different shear rates in each of the three runner sections analysed. In addition, the melt flow into the mould will not be isothermal - the plastic melt immediately in contact with the mould will solidify. This will continuously reduce the effective runner cross-section for the melt coming along behind. The effects of non-Newtonian and non-isothermal behaviour are dealt with in Chapter 5. 

Molten salt investigation methods can be divided into two classes thermodynamic and kinetic. In some cases, the analysis of melting diagrams and isotherms of physical-chemical properties such as density, surface tension, viscosity and electroconductivity enables the determination of the ionic composition of the melt. Direct investigation of the complex structure is performed using spectral methods [294]. 

Figure 28. Isotherms of the shear viscosities of (Li, Na)2C03. (Reprinted from Y. Sato, T. Yamamura, H. Zhu, M. Endo, T. Yamazaki, H. Kato, and T. Ejima, Viscosities of Alkali Carbonate Melts for MCFC, in Carbonate Fuel Cell Technology, D. Shores, H. Mam, I. Uchida, and J. R. Selman, eds., p. 427, Fig. 9, 1993. Reproduced by permission of the Electrochemical Society, Inc.)...

Generally, the rheology of polymer melts depends strongly on the temperature at which the measurement is carried out. It is well known that for thermorheological simplicity, isotherms of storage modulus (G (co)), loss modulus (G"(complex viscosity (r (co)) can be superimposed by horizontal shifts along the frequency axis ... 

The die land thickness differences can be compensated by using different land lengths such that the speed of the emerging melt is constant, resulting in a uniform product. If we assume a power-law viscosity model, a uniform pressure in the manifold and an isothermal die and melt, the average speed of the melt emerging from the die is... 

Although we analyze most polymer processes as isothermal problems, many are non-isothermal even at steady state conditions. The non-isothermal effects during flow are often difficult to analyze, and make analytical solutions cumbersome or, in many cases impossible. The non-isothermal behavior is complicated further when the energy equation and the momentum balance are fully coupled. This occurs when viscous dissipation is sufficiently high to raise the temperature enough to affect the viscosity of the melt. 

Parallel-Plate Flow of Newtonian Fluids A Newtonian polymeric melt with viscosity 0.21b(S/in2 and density 481b/ft3, is pumped in a parallel-plate pump at steady state and isothermal conditions. The plates are 2 in wide, 20 in long, and 0.2 in apart. It is required to maintain a flow rate of 50 lb/h. (a) Calculate the velocity of the moving plate for a total pressure rise of 100 psi. (b) Calculate the optimum gap size for the maximum pressure rise, (c) Evaluate the power input for the parts (a) and (b). (d) What can you say about the isothermal assumption ... 

White et al. (38,39) presented experimental and theoretical (isothermal linear stability analysis) results that indicate the following first, that polymer melts respond similarly to uniform elongational flow and to melt spinning second, that polymers whose elongational viscosity e) increases with time or strain result in a stable spinline, do not exhibit draw resonance, and undergo cohesive failure at high draw ratios. A prime example of such behavior is LDPE. On the other hand, polymer melts with a decreasing r + (t, e)... 

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