Ratio swelling

This example illustrates the simplified approach to film blowing. Unfortunately in practice the situation is more complex in that the film thickness is influenced by draw-down, relaxation of induced stresses/strains and melt flow phenomena such as die swell. In fact the situation is similar to that described for blow moulding (see below) and the type of analysis outlined in that section could be used to allow for the effects of die swell. However, since the most practical problems in film blowing require iterative type solutions involving melt flow characteristics, volume flow rates, swell ratios, etc the study of these is delayed until Chapter 5 where a more rigorous approach to polymer flow has been adopted. 

This expression therefore enables the thickness of the moulded article to be calculated from a knowledge of the die dimensions, the swelling ratio and the mould diameter. The following example illustrates the use of this analysis. A further example on blow moulding may be found towards the end of Chapter 5 where there is also an example to illustrate how the amount of sagging of the parison may be estimated. 

Example 4.4 A blow moulding die has an outside diameter of 30 mm and an inside diameter of 27 mm. The parison is inflated with a pressure of 0.4 MN/m to produce a plastic bottle of diameter 50 mm. If the extrusion rate used causes a thickness swelling ratio of 2, estimate the wall thickness of the bottle. Comment on the suitability of the production conditions if melt fracture occurs at a stress of 6 MN/m. ... 

A blow moulding die which has an outside diameter of 40 mm and a die gap of 2 mm is used to produce a plastic bottle with a diameter of 70 mm. If the swelling ratio of the melt in the thickness direction is 1.8 estimate... 

Swelling Ratios Due to Shear Stresses (a) Long Capillary... 

So from the deflnition of swelling ratio and using the subscripts S and R to denote Shear swelling in the Radial direction then... 

Equations (5.51), (5.52) and (5.53) can be cumbersome if they are to be used regularly so the relationships between swelling ratio and recoverable strain are often presented graphically as shown in Fig. 5.11. 

Fig. 5.11 Variation of Swelling Ratio for Capillary and Slit Dies...

Swelling Ratio Due to Tensile Stresses (a) Short Capillary (zero length)... 

By similar analysis it may be shown that for a short rectangular slit the swelling ratios in the width (T) and thickness (//) directions are given by... 

In addition, if the swelling of the extrudate is measured in each of these two tests then the swelling ratio using the long die will be Bsr and the swelling ratio using the short die will be Ber (see Section 5.6). Using equation (5.44) and (5.47) this enables the shear and tensile components of the recoverable strains to be calculated and from them the shear and tensile moduli. 

Assuming that swelling results from shear effects only then from Fig. 5.13 at yr = 4.33, the swelling ratios are... 

Figure 18 The variation of the swelling ratio of activated seed particles according to Morton equation Xmy 0.4, Xyp = 0). (a) VyIVp = 1.0, (b) VylVp = 3.0.

Figure 7 Effect of shearing history on swelling ratio for HP LDPE sample (A) Brabender worked at 190°C (A) solvent treated sample. Source Ref. 39.

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... 

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... 

Fig. 4. Swelling ratio of PAAm hydrogels containing varying amount of AAc units as a function of CuCl2 concentration in the outer solution. Curves are numbered with respect to increasing ionic group content 0 (0), 36.5 (J), 107 (2), 145 (3), and 212 mM (4). From Rieka and Tanaka [101]...

Fig. 2 a, b. Dependence of the maximum Newton viscosity (t/0) (a) and swelling ratio of the extrudate (D) (b) on the molecular mass of cis-1,4-polyisoprene, unfilled and filled to 33% by mass. Filler 1 — not 2 — CaC03 with specific surface areas 2-3 m2/g 3 — ash PM —15 with specific surface areas 12-18m2/g 4 — ash PM-100 with specific surface areas 90-100 m2/g... 

Polyelectrolyte complexes composed of various weight ratios of chitosan and hyaluronic acid were found to swell rapidly, reaching equilibrium within 30 min, and exhibited relatively high swelling ratios of 250-325% at room temperature. The swelling ratio increased when the pH of the buffer was below pH 6, as a result of the dissociation of the ionic bonds, and with increments of temperature. Therefore, the swelling ratios of the films were pH-and temperature-dependent. The amount of free water in the complex films increased with increasing chitosan content up to 64% free water, with an additional bound-water content of over 12% [29]. 

Correlations are needed to predict whether two-phase flow will occur after vapor venting is initiated by rupture disc failure or relief valve opening. Research is needed in this area, but for the present we recommend the following correlations to predict batch swell. For systems with low viscosity (less than 500 cp) an equation based on bubble column hold-up is used to obtain a swell ratio ... 

For fluids with viscosity greater than 500cp, no good general relationship is available. E jq)erimental work on one system allowed a swell ratio correlation of the following form ... 

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