Question 9.6: Extrusion of Polymers A polymer melt at 160°C with a relaxa......

The phenomenon of swelling is known as die swell. This is due to the viscoelastic properties of the polymer. This occurs in a fluid that is partly elastic and partly viscous. The fluid has the ability to remember the deformation to which it has been exposed. In this case, the residence times in the two dies are

t_{s h o r t}=\frac{V_{s h o r t}}{\dot{Q}}=\frac{\frac{\pi d^{2}}{4}L_{s h o r t}}{\dot{Q}}=\frac{\frac{\pi\times0.005^{2}}{4} \times 0.01}{634.5}= 0.3 \ s

t_{long}=\frac{V_{long}}{\dot{Q}}=\frac{\frac{\pi d^{2}}{4}L_{long}}{\dot{Q}}=\frac{\frac{\pi\times0.005^{2}}{4} \times 0.1}{634.5}= 3.0 \ s                   (9.13)

The Deborah number is a dimensionless group used in rheology to classify the behaviour of a fluid which is able to store elastic energy and is defined as the ratio of the fluid characteristic time to the process or observed time where the characteristic time is the stress relaxation time, τ:

D e={\frac{\tau}{t}}            (9.14)

and that is

D e_{sho r t}=\frac{\tau}{t}=\frac{0.9}{0.3}=3

D e_{long}=\frac{\tau}{t}=\frac{0.9}{3.0}=0.3                    (9.15)

The short die has the highest Deborah number. The elastic energy is therefore greatest in the shortest die in the fluid; hence, there is more swell.