Extrudate swell

Extrudate Swell The extrudate swell of wood-filled plastics typically increases with the flow rate (shear rate), decreases with filler loading, and practically does not depend on the melt temperature. A nonfibrous filler, such as calcium carbonate, also suppresses swell of polyethylene, and in the case of medium-density polyethylene, a swell suppression was maximal at 30% of calcium carbonate (0.4 (xm particles) [32]. A similar effect was shown using HDPE filled with rice hulls (Table 17.13). 

The swell increase with the flow rate for neat HDPE was attributed to the higher shear that resulted in larger elastic forces to be released at the die exit. 

On the contrary, the swell decrease with the increase in filler content was attributed to the lesser amount of elastic polymer chains in the system to recover and swell at the exit. As the filler content was increased, the swell was approaching the Newtonian value of 13% [21]. 

TABLE 17.13 Increase of swell with the increase of flow rate at extrusion of neat HDPE and that filled with rice hulls 

Amount of rice hulls in HDPE Increase of swell with increase of flow rate 

It should be noted that extrudate swelling is not unique to viscoelastic fluids. It can also occur in an inelastic or purely viscous fluid this has been demonstrated experimentally and theoretically. Obviously, in an inelastic fluid, the mechanism of extrudate swell is not an elastic recovery of prior deformation. The swelling is caused by a significant rearrangement of the velocity profile as the polymer leaves the die this is shown in Fig. 7.114. 

It can be seen that the shear rates at the wall vary significantly. The wall shear rate in the corner is relatively low, while the highest shear rate occurs at the middle of the wall. Therefore, the elastic recovery in the middle will be larger than the elastic recovery at the corners. This results in bulged extrudate. It is not possible to obtain a perfectly square extrudate with a perfectly square flow channel. To eliminate this problem one has to modify the shape of the flow channel to compensate for the uneven swelling of the extrudate. A good die designer must anticipate the 

Accurate mathematical prediction of the die swell profile is quite difficult and, therefore, determination of the proper flow channel geometry to minimize uneven swelling by engineering calculations is generally not practical. The non-uniform extrudate swell and the correction of the flow channel geometry are illustrated in Fig. 7.116. 

The amount of swelling is very much dependent on the nature of the material. Some polymers exhibit considerable swell (100 to 300%), e.g., polyethylenes other polymers exhibit lower swell, e.g., polyvinylchloride. When PVC is extruded at relatively low temperatures (165 to 175°C), the swell ranges from 10 to 20% only. This is one of the reasons that PVC is such a popular material in profile extrusion it conforms quite well to the geometry of the die flow channel and has good melt strength. 

Dealy (1982) reviews the experimental methods used to measure extrudate or die swell. Typically the ratio of equilibrium extrudate diameter D, to die diameter 2R is measured 

Reservoir diameter and capillary L/R influence the equilibrium swell ratio. If / ,// 10 and L/R 40, then swell measurements are independent of rheometer geometry (Han, 1976). Of course, the onset of melt distortion sets an upper limit on shear stress for swell measurements. 

Theory and experiment show that Newtonian liquids swell at low Reynolds numbers but shrink as inertia becomes important = 1.13 for Re 2 and B = 0.87 for Re 100 (Middleman, 1977). Typically elastic liquids are extruded in the low Reynolds range, so the Newtonian result is subtracted from the experimental values to give an elastic swell  

Vlachopoulos (1981) and Tanner (1988a) have reviewed the various efforts to relate B to rheological material functions. The simplest and most widely used is Tanner s (1970a), which foilows from Lodge s work (1964) on recoverable strain. It assumes unconstrained recovery after steady shear and applies an integral model of the BKZ type (4.4.2) with one relaxation time. The result is 

Viscosity and N /2x i versus shear rate open points, cone and piate solid points, capillary extrudate swell L/R 81 V /2ti2 from eq. 6.2.27 with B = — 0.11. From 

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Mitsoulis, E., Valchopoulos, J. and Mirza, F. A., 1985. A numerical study of the effect of normal stresses and elongational viscosity on entry vortex growth and extrudate swell. Poly. Eng. Sci. 25, 677 -669. 

Representative plots of extrudate swelling ratio as a function of NBR content are shown in Fig. 3. Shear rate increases the die-swell in all blends. The change of die-swell with NBR content exhibits a decreasing trend up to 60% of NBR, and beyond this level it shows a saturation in die-swell. Preheating of blends exhibits the minimum at 50 50 ratio irrespective of shear rates. We... 

Representative plots of the extrudate swelling ratios with NBR content are shown in Fig. 9 as a function of... 

A representative example of the extrudate swelling behavior is shown in Fig. 15 as a function of blend ratio... 

Rheological parameters, such as relaxation time, shear modulus, and stored elastic energy, are determined from the extrudate swell and stress-strain data as previously described. Representative examples of the variation of these parameters with blend ratios for both blends are shown in Figs. 16-18. Figure 16 shows that relaxation time for both preblends without heating and... 

The plot of the extrudate swelling ratios with AU content are shown in Fig. 27 as a function of shear rate for both types of blends. The die-swell gradually decreases with the addition of AU in the blend up to the... 

Reinforcing fillers in general and high-structure carbon blacks in particular improve the extrusion characteristics of elastomers by decreasing extrudate swell. The extrudate swell decreases with increasing carbon black content [33]. 

The die-swell (extrudate swell) effect describes the significant expansion of the diameter of the fluid column after exiting from a small pipe (Figure 4.3.8(b)). Some polymer fluids can have a swelling of up to two or three times the exit diameter. A simple proposition for the mechanism of the die-swell phenomenon is that while the fluid is inside the exit pipe, it is subject to a velocity shear, similar to the pipe flow with a maximum shear stress at the wall [18]. This velocity shear stretches... 

Figure 7.56 Extrudate swelling in polystyrene melts for ( ) broad molecular weight distribution and (O, a) narrow molecular weight distribution samples. From Z. Tadmor and C. G. Gogos, Principles of Polymer Processing, Copyright 1979 by John Wiley Sons, Inc. This material is used by permission of John Wiley Sons, Inc.

Combine your results to obtain a value for the shear stress at the capillary wall, and use that value to estimate the extrudate swell, D/Dq for polystyrene using Figure 7.56. What effect does molecular weight have on die swell at these shear levels ... 

Other flow effects include extrudate swelling and melt fracture. The phenomenon of extrudate swell was elaborated upon in the context of polymer extrnsion (cf. Fignre 7.56). 

Figure 13 gives profiles of extrudate swelling after it left the molding tool and drawn at a constant force indicated by points (obtained photographically) the lines indicate extrudate profiles obtained by calculations on the basis of Eq. (13). 

J.A. Menjivar, E.N. Chang and L. Maciel, Extrudate Swell Behaviour of Wheat Flour Doughs, in "Theoretical and Applied Rheology", P.Moldenaers and R. Kennings (eds.), Elsevier Science B.V., 1992, pp. 714-716. 

Figure 2.32 Schematic diagram of extrudate swell during extrusion.

The coefficients Ti and b2, like non-Newtonian viscosity, are also found to be shear rate dependent. The non-Newtonian property of exhibiting normal stresses in shear flows plays an important role in processing under situations in which shear stresses vanish, as in extrudate swell, discussed later in this section. 

Extrudate swelling refers to the phenomenon observed with polymer melts and solutions that, when extruded, emerge with cross-sectional dimensions appreciably larger than those of the flow conduit. The ratio of the final jet diameter to that of the capillary D/Dq, for Newtonian fluids varies only from 1.12 at low shear rates to 0.87 at high rates. Polymer... 

Experimentally, as indicated in Fig. 12.13, we find that D/Dq depends on the shear stress at the wall xw (a flow variable) and the molecular weight distribution (MWD) (a structural variable) (22). The length-to-diameter ratio of the capillary (a geometric variable) also influences D/Dq. The swelling ratio at constant xw decreases exponentially with increasing L/Dq and becomes constant for L/Dq > 30. The reason for this decrease can be explained qualitatively as follows. Extrudate swelling is related to the ability of polymer melts and solutions to undergo delayed elastic strain recovery, as discussed in... 

Fig. 12.13 Extrudate swelling data for polystyrene melts , broad molecular weight sample O, , A, narrow distribution sample data at various temperatures. [Reprinted by permission from W. W. Graessley, S. D. Glasscock, and R. L. Crawley, Die Swell in Molten Polymers, Trans. Soc. Rheol., 14, 519 (1970).]...

Solutions of rigid polymer molecules (e.g., poly-/)-phenylene terephthalate) may also exhibit extrudate swelling because they too are entropy elastic, molecules exit the capillary in a fairly oriented state and become randomly oriented downstream. 

Equation 12.2-1 has been semiquantitatively successful in predicting extrudate swelling (25). However, White and Roman (27) have shown experimentally with a number of polymers that D/Dq is not a function of Sr only. Furthermore, they demonstrated that the success of the Tanner equation depends on the method of measurement of D/Do. 

Fig. 12.14 Effect of the method of measurement on the value of D/Do for HDPE. Curve 1, frozen extrudates Curve 2, extrudates annealed at 160°C in hot silicon oil Curve 3, photographs of extrudates emerging from capillary Curve 4, photographs of extrudates in hot silicon oil. [Reprinted by permission from J. L. White and J. F. Roman, Extrudate Swell During the Melt Spinning of Fibers-Influence of Rheological Properties and Take-up Force, J. Appl. Polym. Sci., 20, 1005 (1976).]...

Profiles are all extruded articles having a cross-sectional shape that differs from that of a circle, an annulus, or a very wide and thin rectangle (flat film or sheet). The cross-sectional shapes are usually complex, which, in terms of solving the flow problem in profile dies, means complex boundary conditions. Furthermore, profile dies are of nonuniform thickness, raising the possibility of transverse pressure drops and velocity components, and making the prediction of extrudate swelling for viscoelastic fluids very difficult. For these reasons, profile dies are built today on a trial-and-error basis, and final product shape is achieved with sizing devices that act on the extrudate after it leaves the profile die. 

What is important from a die-designing point of view is that the cross-sectional shapes of the die and the extrudates are different. Simply put, to produce a square cross-section extrudate, one needs a die that looks like a four-cornered star [Fig. 12.48(a)], whose sides are concave. The curvature of the walls of the die used depends on the variation of extrudate swelling with shear stress for the polymer used. The differences in the shapes and magnitudes of the cross-sectional areas are primarily due to the 0-dependence of the degree of extrudate swelling. 

J. L. White and J. F. Roman, Extrudate Swell During the Melt Spinning of Fibers—Influence of Rheological Properties and Take-up Force, J. Appl. Polym. Sci., 20, 1005 (1976). 

R. B. Bird, R. K. Prud homme, and M. Gottlieb, Extrudate Swell as Analyzed by Macroscopic Balances, The University of Wisconsin, Rheology Research Center Report RRC-35, 1975. 

Estimation Extrudate Swell of a Polymer Tenite 800 LDPE is extruded from a long horizontal pipe of diameter D ]. Using Eqs. 12.2-1 and 12.2-2 and the... 

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