Extensional strain viscosity

At low shear rates, polymeric liquid properties are characterized by two constitutive parameters zero shear rate viscosity t]o and recoverable shear compliance Jq, which indicates fluid elasticity. At higher shear strain rates, rheological behavior is measured with a viscometer. Extensional strain viscosity, associated with extensional flow, occurs with film extrusion. 

Extensional flows occur when fluid deformation is the result of a stretching motion. Extensional viscosity is related to the stress required for the stretching. This stress is necessary to increase the normalized distance between two material entities in the same plane when the separation is s and the relative velocity is ds/dt. The deformation rate is the extensional strain rate, which is given by equation 13 (108) ... 

A method for measuring the uniaxial extensional viscosity of polymer soHds and melts uses a tensile tester in a Hquid oil bath to remove effects of gravity and provide temperature control cylindrical rods are used as specimens (218,219). The rod extmder may be part of the apparatus and may be combined with a device for clamping the extmded material (220). However, most of the mote recent versions use prepared rods, which are placed in the apparatus and heated to soften or melt the polymer (103,111,221—223). A constant stress or a constant strain rate is appHed, and the resultant extensional strain rate or stress, respectively, is measured. Similar techniques are used to study biaxial extension (101). 

Extensional flow describes the situation where the large molecules in the fluid are being stretched without rotation or shearing [5]. Figure 4.3.3(b) illustrates a hypothetical situation where a polymer material is being stretched uniaxially with a velocity of v at both ends. Given the extensional strain rate e (= 2v/L0) for this configuration, the instantaneous extensional viscosity r e is related to the extensional stress difference (oxx-OyY), as... 

This work shows that high shear rates are required before viscous effects make a significant contribution to the shear stress at low rates of shear the effects are minimal. However, Princen claims that, experimentally, this does not apply. Shear stress was observed to increase at moderate rates of shear [64]. This difference was attributed to the use of the dubious model of all continuous phase liquid being present in the thin films between the cells, with Plateau borders of no, or negligible, liquid content [65]. The opposite is more realistic i.e. most of the liquid continuous phase is confined to the Plateau borders. Princen used this model to determine the viscous contribution to the overall foam or emulsion viscosity, for extensional strain up to the elastic limit. The results indicate that significant contributions to the effective viscosity were observed at moderate strain, and that the foam viscosity could be several orders of magnitude higher than the continuous phase viscosity. 

Analyze lubricated squeezing flow to determine biaxial extensional viscosity (T)R), which is calculated from biaxial stress (cB) and biaxial extensional strain rate (eB). 

Often, it is not possible to reach a steady state in extension and it is convenient to define a transient extensional viscosity, tje, that is a function of time, t, and the extensional strain rate, e, (Barnes et al., 1989). 

Poly(bulylene succinate) (PBS) is another biodegradable polymer which is not commonly blended with polyolefins. However, Yang et al. [94] investigated the eflect of PBS content, extrusion rate, and extensional strain rate on the melt strength and extensional viscosity of LDPE/PBS blends using a melt-spinning technique, and developed extensional master curves. Based on both the extensional master curve and a neural network method, they compared the predicted extensional viscosities with the experimental data of the LDPE/PBS blends. 

Here dv/dr is the extensional strain rate, and 77 is the extensional viscosity. The correlation between the ideal extensional viscosity and the shear viscosity for a Newtonian fluid can be described by the Trouton s ratio (Trouton 1906), as given by... 

Several factors are found responsible for why numerous blend systems are not successful. First, the component polymers are usually not miscible with each other due to thermodynamic constraints, for example, lack of solubility and finite inter-fadal tension. Second, immiscible polymer blend preparation is often affected by kinetic constraints, for example, slower rate of deformation of the dispersed polymer and faster rate of coalescence of the droplets. In turn, these rates are directly influenced by the type of flow field, for example, shear versus extensional, strain history, chemical reactions, for example, grafting reactions at polymer-polymer interfaces or polymerization-induced phase separation, and polymer properties, such as viscosity and interfacial tension. Accordingly, the multidisciplinary efforts to analyze, understand, and design polymer blends with improved properties extend from synthesis and characterization to processing and manufacturing. Such efforts... 

Instead of imposing a constant stretch rate on a sample and measuring the steady-state stress, one may impose a constant stress and determine the resulting extensional strain. This is a creep experiment, and if the strain, initially zero, begins to increase linearly with time, a constant stretch rate is achieved. The extensional viscosity is again obtained as the ratio of the imposed stress to the resulting constant stretch rate. 

A. = ale, where A = extensional (elongational) viscosity, a viscosity coefficient when appHed stress is extensional stress (strain rate. This parameter is often used for characterising polymer solutions. 

The effect of the melt temperature on the vortex size development has been studied experimentally as well as theoretically. The most important results are depicted in Figme 7. It is obvious, that the vortex area primarily increases, reaches a maximum and then it decreases again with increasing temperature. This behavior can be explained by the temperature dependency of the nonmonotonic shape of the planar extensional viscosity predicted by e improved mWM model, which is depicted in Figure 8. In more detail, the planar extensional viscosity maximum moves fi om low extensional strain rates to higher ones for increasing melt temperatures. This seems to be the driving mechanism for the maximum appearance in the vortex size vs. temperature flmction. 

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