Extensional mixing

Mixing, extensional Mixing, fundamentals Mixing, general... 

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... 

Figure E7.2 compares a stepwise increase in interfacial area in simple shear flow with optimal initial orientation, and simple shear flow where, at the beginning of each step, the interfacial area element is placed 45° to the direction of shear. The figure shows that, whereas in the former case the area ratio after four shear units is 4.1, in the latter case the ratio is 6.1, with a theoretical value of 7.3 when the 45° between the plane and direction of shear is maintained at all times. We note, however, that it is quite difficult to generate steady extensional flows for times sufficiently long to attain the required total elongational strain. This is why a mixing protocol of stepwise stretching and folding (bakers transformation) is so efficient. Not only does it impose elongational stretching, but it also distributes the surface area elements over the volume.

Also noteworthy is the appreciable coalescence caused by the shear flows in the single screws, of the rheology section of the TSMEE following the mixing element section. Flow of dispersed immiscible blends involves continuous breakdown and coalescence of the dispersed domains (122). Shear flows, where droplet-to-droplet collisions are frequent—in contrast to extensional flows—favor coalescence over dispersion. The presence of compatibilizers shifts the balance toward reduced coalescence rate. Macosko et al. (123) attribute this to the entropic repulsion of the compatibilizer molecules located at the interface as they balance the van der Waals forces and reduce coalescence, as shown on Fig. 11.36. 

For a complex fluid, the stress depends not only on whether the flow is a shearing, extensional, or mixed type, but also on the whole history of the velocity gradient. Thus, the... 

It is of interest to study flows of mixed or intermediate character that combine the characteristics of shearing and extensional flows. In two dimensions, the most general velocity gradient can be represented as... 

MIXED FLOW. Other flows with extensional components also have coil-stretch transitions. The smaller the extensional component is relative to the overall strain rate, the higher the overall strain rate at which the transition takes place (Giesekus 1962, 1966) A steady planar flow, for example, can be considered to be a mixture of a shearing and an extensional flow in such a mixed flow, the velocity gradient tensor, Vv, can be expressed as (Fuller and Leal 1980, 1981)... 

Experimental materials characterisation. Linear and non linear viscoelastic response, simple shear, extensional flow and mixed shear behaviour. 

Another way of identifying a specimen is to look it up in Identification-lists belonging to a flora or a revision, where a duplicate of the specimen may have been cited. Provided that no different species got mixed up under the same collecting number, you have found the name. This sort of identification is determination by means of verification of extensionally defined membership, the duplicate in your hands, e.g. collected by C.A. Backer under number 18132, belongs according by the list by Bosnian fi de Haas ( 1983. Blumea 28, 483) to species nr. 7, corresponding with Tephrosia luzonensis. The set of specimens these authors have studied and listed in this identification list forms thus the extensionally defined set of specimens. 

The convergent flow at the die entrance provides strong elongational flow. In 1989 Laun and Schuch, derived for Newtonian liquids that P = 1.640j2, The relation is satisfactory for homopolymers, but for the blend, the prediction is about one decade too low. On the other hand, this type of flow provides excellent means for mixing highly viscous dispersed phase. An extensional... 

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