Draw resonance

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Draw resonance is a flow instability seen in polymer drawing processes such as melt spinning of fibres, cast film casting, and film blowing. When the draw ratio (the ratio between the take-up speed and the speed of the melt as it leaves the die) exceeds a critical value, the cross-section of the moving filament or film stops being steady and instead oscillates periodically with time, producing a regular thick-thin pattern down the line. The amplitude of the oscillation grows with the draw ratio until the line either runs in a permanently pulsing state or breaks.

The first theoretical analysis was given by J. R. A. Pearson and M. A. Matovich in 1969, in the second of a pair of papers on the spinning of a molten threadline. Treating the melt as an isothermal Newtonian fluid and ignoring inertia, gravity, and surface tension, they found that the steady solution loses stability when the draw ratio reaches roughly 20.21. This number, often quoted as the Newtonian critical draw ratio, is the benchmark that all later theoretical work has been compared against.

Fisher and Denn later recovered the same value through a different route and extended the analysis to power-law and viscoelastic fluids. Kase showed independently, using a kinematic-wave argument, that the same critical draw ratio drops out very naturally if one tracks the residence time of mass disturbances along the spinline.

In cast film extrusion the same instability appears as periodic gauge bands across the web. In blown film, the picture is more complicated because of the inflation step and the coupling to crystallization at the frost line, but Cain and Denn showed that one of the unstable modes of the steady film blowing solution is mathematically of the draw-resonance type.

The behaviour of real polymer melts is rarely Newtonian, and the critical draw ratio depends sensitively on how the melt strain-hardens. Strain hardening in extension, which is typical of low-density polyethylene and other long-chain branched melts, raises the critical draw ratio and stabilizes the line. Strongly shear-thinning, weakly strain-hardening melts such as LLDPE can be more prone to draw resonance, which is one practical reason why blends of LDPE and LLDPE are often easier to spin or cast than either component alone.

References

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