Extensional flow viscosity

An increase in extensional flow viscosity in film blowing, fiber spinning, and bottle blowing, etc., is usually advantageous, but the change in viscosity will depend very much on the polymer structure [17]. 

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) ... 

It is well known that LCB has a pronounced effect on the flow behavior of polymers under shear and extensional flow. Increasing LCB will increase elasticity and the shear rate sensitivity of the melt viscosity ( ). Environmental stress cracking and low-temperature brittleness can be strongly influenced by the LCB. Thus, the ability to measure long chain branching and its molecular weight distribution is critical in order to tailor product performance. 

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... 

Fig. 22. Radius of drops produced by capillary breakup (solid lines) and binary breakup (dotted lines) in a hyperbolic extensional flow for different viscosity ratios (p) and scaled shear rate (p,cylo) (Janssen and Meijer, 1993). The initial amplitude of the surface disturbances is ao = 10 9 m. Note that significantly smaller drops are produced by capillary breakup for high viscosity ratios.

Oscillatory shear experiments are the preferred method to study the rheological behavior due to particle interactions because they directly probe these interactions without the influence of the external flow field as encountered in steady shear experiments. However, phenomena that arise due to the external flow, such as shear thickening, can only be investigated in steady shear experiments. Additionally, the analysis is complicated by the different response of the material to shear and extensional flow. For example, very strong deviations from Trouton s ratio (extensional viscosity is three times the shear viscosity) were found for suspensions [113]. 

Demonstrations are given of the importance of extensional or elongational viscosity in the foam process. New polypropylenes are compared in extensional flow and it is shown how rheological differences allow the prodnction of low density foam on tandem extrnsion equipment. 6 refs. 

To reach steady state, the residence time of the fluid in a constant stretch rate needs to be sufficiently long. For some polymer melts, this has been attained however, for polymer solutions this has proved to be a real challenge. It was not until the results of a world wide round robin test using the same polymer solution, code named Ml, became available that the difficulties in attaining steady state in most extensional rheometers became clearer. The fluid Ml consisted of a 0.244% polyisobutylene in a mixed solvent consisting of 7% kerosene in polybutene. The viscosity varied over a couple of decades on a logarithmic scale depending on the instrument used. The data analysis showed the cause to be different residence times in the extensional flow field... 

If an extensional force is also applied in addition to the pure shear force (for types of flow, see Fig. 9.2), the critical value of the Weber number is considerably lower. It is possible to break up droplets in an extensional flow even when the viscosity ratios are very high. Thus, extensional flow is significantly more effective than pure shear flow when attempting to disperse droplets and break up high-viscosity gels or polymer particles. 

Figure 9.13 Critical Weber number for breaking up droplets as a function of the viscosity ratio, in pure shear flow and in extensional flow...

In extensional flow, droplets or high-viscosity particles are drawn out into filaments that ultimately break up into smaller droplets. For the droplets to break up, the load must be maintained for a certain period of time. It can also be beneficial to deform the droplet, allow it to relax briefly and then apply the load again. This enables elastic restoring forces in high-viscosity droplets to be overcome. 

Figure 9.14 Droplet deformation as a function of the duration of deformation for different flow fields (ratio of shear and extensional flow) for a viscosity ratio of X = 3 the larger a, the larger the ratio of extensional flow a=0 corresponds to pure shear flow...

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