Rheology Newtonian behavior

Rheology. Both PB and PMP melts exhibit strong non-Newtonian behavior thek apparent melt viscosity decreases with an increase in shear stress (27,28). Melt viscosities of both resins depend on temperature (24,27). The activation energy for PB viscous flow is 46 kj /mol (11 kcal/mol) (39), and for PMP, 77 kJ/mol (18.4 kcal/mol) (28). Equipment used for PP processing is usually suitable for PB and PMP processing as well however, adjustments in the processing conditions must be made to account for the differences in melt temperatures and rheology. 

The rheological properties change behavior, relative to more dilute solutions, above cp = 0.2, where non-Newtonian behavior is then exhibited. The power law dependence of rj on cp is in harmony with the Zimm rather than the Rouse model, which suggests that hydrodynamic interactions between these polymers, in a mean field sense, are important. Electrical properties also begin to deviate for Nafion solutions above cp = 0.2, and mechanical percolation is essentially the same for the sodium and acid forms. 

At temperatures above the Tg, bitumens generally show Newtonian behavior. Below the Tg bitumens have rheological properties similar to elastomers. 

The presentation in this chapter dwells rather heavily on the classification, measurement, and interpretation of non-Newtonian behavior. These rheological fundamentals have frequently been presented in literature which is unfamiliar to the engineer and have usually included much discussion of factors which at the present time are of minor engineering interest. Accordingly, it was felt that one of the primary needs in this field was a concise summary of these fundamentals and common definitions. It is hoped that thereby future developments may be undertaken in an orderly and rigorous manner, as contrasted to the relatively fruitless empiricism which has enveloped areas of this field in the past. 

CMCs in the absence of added electrolyte may be greatly influenced by electrovis-cous effects marked decreases in intrinsic viscosity on electrolyte addition have been observed in many cases36). Peculiar and highly interesting rheological properties of surfactant solutions include observations of strongly non-Newtonian behavior as well as of viscoelasticity these are yet incompletely understood. 

The rheological properties show particularly large changes and in many cases the solutions show a non-Newtonian behavior and for a number of cases pronounced viscoelasticity has been demonstrated. That the classification of a certain surfactant depends very much on temperature is probably best illustrated by the viscosity of... 

Solidified milk fat displays non-Newtonian behavior. It acts as a plastic material with a yield value (Sone, 1961 deMan and Beers, 1987). Throughout its wide melting range, milk fat, like butter, exhibits viscoelasticity, possessing both solid and liquid-like characteristics (Sone, 1961 Shama and Sherman, 1968 Jensen and Clark, 1988 Kleyn, 1992 Shukla and Rizvi, 1995). Several models to describe the complex rheological behavior of milk fat have been proposed. Figure 7.12 shows the corresponding stress-strain curves for the models discussed. 

Real materials are neither truly Hookean nor truly Newtonian, though some exhibit Hookean or Newtonian behavior under certain conditions (Barnes et al., 1989). Real materials may exhibit nonlinearity, which is a lack of direct proportionality between stress and strain, or between stress and strain rate. Real materials may exhibit either predominantly elastic behavior or predominantly viscous behavior, or a measurable combination of the two, depending on the stress or strain and the duration of its application (Barnes et al., 1989). Such materials are termed viscoelastic. Barnes et al. (1989) pointed out that it is better to classify rheological behavior than to classify materials, a given material can then be included in more than one rheological class depending on experimental conditions. 

The major characteristic of a polymeric reactor that is different from most other types of reactors discussed earlier is the viscous and often non-Newtonian behavior of the fluid. Shear-dependent rheological properties cause difficulties in the estimation of the design parameters, particularly when the viscosity is also time-dependent. While significant literature on the design parameters for a mechanically agitated vessel containing power-law fluid is available, similar information for viscoelastic fluid is lacking. 

Let us first consider an inverted W/O emulsion made of 10% of 0.1 M NaCl large droplets dispersed in sorbitan monooleate (Span 80), a liquid surfactant which also acts as the dispersing continuous phase. At this low droplet volume fraction, the rheological properties of the premixed emulsion is essentially determined by the continuous medium. The rheological behavior of the oil phase can be described as follows it exhibits a Newtonian behavior with a viscosity of 1 Pa s up to 1000 s 1 and a pronounced shear thinning behavior above this threshold value. Between 1000 s 1 and 3000 s1, although the stress is approximately unchanged, the viscosity ratio is increased by a factor of 4. 

Previous investigations (4, 5,6,7,8) have shown that block copolymers exhibit unusual melt rheological properties such as a very high viscosity, elasticity, and non-Newtonian behavior even at very low shear rates which are all attributed to the multiphase structure resulting from the incompatibility between the two copolymer units in the melt state. 

In Eqs. (6) and (7) e represents the internal energy per unit mas, q the heat flux vector due to molecular transport, Sh the volumetric heat production rate, ta, the mass fraction of species i, Ji the mass flux vector of species i due to molecular transport, and 5, the net production rate of species i per unit volume. In many chemical engineering applications the viscous dissipation term (—t Vm) appearing in Eq. (6) can safely be neglected. For closure of the above set of equations, an equation of state for the density p and constitutive equations for the viscous stress tensor r, the heat flux vector q, and the mass flux vector 7, are required. In the absence of detailed knowledge on the true rheology of the fluid, Newtonian behavior is often assumed. Thus, for t the following expression is used ... 

Rheological Behavior. Figure 4 shows the room-temperature steady-shear viscosity as a function of shear rate for PDM-PMAS polymers and their precursors. Polymers with Ciq, C12, and C14 side chains exhibit Newtonian behavior over the range of shear rates monitored. 

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