Stretching flow

During stretching flow, material is drawn from one cross-sectional area to another. This type of flow dominates fibre, film, blow molding, and vacuum forming processes (57). Let us assume that a filament of a molten polymer is hauled off under a force F (see Fig. 13.40). Taking the die of the extruder as the origin of the reference frame, the cross-sectional area A of the filament 

Accordingly, the measurements of both F and Q and the experimental determination of the values of v versus z permit us to determine the apparent extensional viscosity. This parameter can alternatively be obtained from the total strain, which, according to Eq. (13.117), is given by 

The zero shear rate viscosity of a narrow molecular weight distribution fraction of polystyrene is 6.5 x 10 poise at 160°C. If the molecular weight between entanglements in this polymer is about 18,000 g/mol, make a rough estimate of the shear rate k, above which this fraction will display non-Newtonian behavior. 

The steady-state compliance can be obtained by means of the approximation [see Eq. (8.64)] 

According to Eq. (9.33), the mean relaxation time of the entangled network is 

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Elongation flow fields are likely to be present whenever streamlines cease to be parallel and in particular converging flow typical of that at the entrance of, for example, a capillary flow device is known to develop strong stretching flow The strength of elongational flow at the entrance of a capillary can be determined by one of several equations [106]. In the case of capillary flow, an estimate of the normal (tensile) stress at the entrance can be obtained from ... 

Compression of a weakly structured food between parallel plates may achieve squeezing flow (Steffe, 1996). When lubricated parallel plates are used, the result is a form of biaxial extension. Biaxial extension may be used to measure biaxial viscosity, which is a reflection of resistance to radial stretching flow in a plane. Lubricated squeezing flow of a semi-solid... 

Fig. 3.2 Cases 1, 2, and 3 show steady, uniform extensional flows. Case 4 shows examples of more complex nonuniform stretching flows encountered in polymer processing operations. 

F. N. Cogswell, Stretching Flow Instahlities at the Exits of Extrusion Dies, J. Non-Newt. Fundam. Mech., 2, 37-47 (1977). 

It has already been shown before that in uniaxial extensional flow or stretching flow the length in the direction of the flow changes according to... 

Polymer orientation varies through the thickness of the injection-molded part owing to the fountain flow of the melt in the mold cavity. The flow at the center of the cross-section is deformed through extension and the highly stretched flow front rolls up to the cold mold surface, where orientation is frozen in a thin surface layer. The rest of the melt required to fill the cavity flows under this stationary frozen layer in more or less a plug fashion, with minimum orientation. Surface orientation in an injection-molded part can be significantly different from that in the core of the part. 

Cogswell F.N., "Stretching flow instabilities at the exits of extrusion dies," J. Non-Newtonian Fluid Mech., 2 (1977) 37-47. 

Cogswell, F. N. 1978. Converging flow and stretching flow a compilation, y. Non-Newtonian FluidMech. 4 23-38. 

Figure 13.41 (a) Shear flow and stretching flow behavior of (------) linear and... 

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. 

Draw resonance occurs in processes where the extrudate is exposed to a free surface stretching flow, such as blown film extrusion, fiber spinning, and blow molding. It manifests itself in a regular cyclic variation of the dimensions of the extrudate. An extensive review [169] and an analysis [170] of draw resonance were done by Petrie and Denn. Draw resonance occurs above a certain critical draw ratio while the polymer is still in the molten state when it is taken up and rapidly quenched after take-up. 

Janssen [294] studied the breakup of a viscous thread in stretching flow, both theoretically and experimentally. In a quiescent matrix one disturbance wavelength is dominant in an extending matrix the waves are continuously stretched. Different disturbance wavelengths are dominant at different times. As a result, the breakup is postponed in elongational flow compared to quiescent conditions. 

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