Rotational flows, polymer behavior

Polymer melts and solutions show pronounced non-Newtonian flow behavior. In rotational flows, polymer solutions typically show a shear-thinning behavior (2i, 22) where the apparent viscosity reduces as the shear rate is increased. In extensional, or stretching flows, however, polymer solutions often show a marked increase in viscosity as the shear rate is increased, termed dilatancy (23-26), Stretching flows are of considerable importance and generally occur in flows through orifices, filters, porous media, constrictions in pipes, and in any flow possessing turbulence or vorticity, in fact as a component of most real flow systems. 

The validity of Frenkel s model is limited to Newtonian flow and can only be used to predict the early stage of the coalescence process, when the diameter of the two spherical particles remains nearly unchanged. The inadequacy of a Newtonian model in describing the coalescence of polymers was also demonstrated in other studies, as reviewed by Mazur, and has led to the development of models as well as alternative methods for the characterization of the coalescence behavior of polymers for rotational molding applications.Based on theoretical and experimental analyses of the coalescence phenomenon, the material properties of primary interest in the evaluation of resin coalescence behavior in rotational molding have been identifled as the resin viscosity, surface tension, and elasticity. 

Most practitioners deflne the flow behavior of polymers based on the melt flow index however, this property is not entirely relevant to the rotational molding process because it is essentially a shear-free and pressure-free process. The use of zero-shear viscosity has been proposed as a better way to assess the coalescence behavior of resins. Resins with lower zero-shear viscosity coalesce at a faster rate and can thus be processed using a shorter molding cycle.The coalescence of individual powder particles is initiated as the particles stick and melt onto the mold surface or melt front. As the melt deposition process continues, pockets of air remain trapped between partially fused particles and lead to the formation of bubbles. In the rotational molding process, the coalescence of particles occurs at a temperature range close to the melting point of the material thus, from a processing standpoint, low values of zero-shear viscosity at low temperatures (i.e., close to the temperature at which the particles adhere to the mold surface) are preferable. 

The cone-and-plate and parallel-plate rheometers are rotational devices used to characterize the viscosity of molten polymers. The type of information obtained from these two types of rheometers is very similar. Both types of rheometers can be used to evaluate the shear rate-viscosity behavior at relatively low vales of shear rate therefore, allowing the experimental determination of the first region of the curve shown in Figure 22.6 and thus the determination of the zero-shear-rate viscosity. The rheological behavior observed in this region of the shear rate-viscosity curve cannot be described by the power-law model. On the other hand, besides describing the polymer viscosity at low shear rates, the cone-and-plate and parallel-plate rheometers are also useful as dynamic rheometers and they can yield more information about the stmcture/flow behavior of liquid polymeric materials, especially molten polymers. 

When a polymer chain is placed in a flow field, the coil stretches out of its equilibrium state and rotates in the flow field. These conformation changes dramatically impact the global flow response of a polymer solution, beyond simply enhancing the viscosity of the solution. Shear thinning and viscoelasticity are two key behaviors observed in polymer solution flows. Rotation of the polymer chain in a shear flow leads to shear thinning, in which the viscosity decreases with increasing shear rate. The power law model is a simple model used to describe this behavior, where the viscosity is given by... 

However, these simple empirical expressions are far from universal, and fail to account for effects specific to nonlinear behavior, such as the appearance of finite first and second normal stress differences (Tyy = Ni(y) and <7yy — steady shear flow. (For a linear viscoelastic material in shear, ctxx, Cyy and a-zz are equal to the applied pressure, usually atmospheric pressure.) TTiese may be linked to the development of molecular anisotropy in polymer melts subject to flow, and are responsible for the Weissenberg effect, which refers to the tendency for a nonlinear viscoelastic fluid to climb a rotating rod inserted into it, as well as practically important phenomena such as die swell [20]. 

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