Abstract
The stability of isothermal film casting of polymeric fluids to infinitesimal and finite-amplitude disturbances was investigated using a modified Giesekus rheological model. The linear stability analysis indicates that extensional-thickening elongational viscosity enhances stability, whereas extensional-thinning elongational viscosity or shear-thinning shear viscosity reduces stability. An upper critical draw ratio is present when a sharp rise exists in the elongational viscosity curve. The stability limits predicted by the linear stability analysis for infinitesimal disturbances were validated by the nonlinear stability analysis for finite-amplitude disturbances. Also, the growth rate and frequency of oscillation predicted by the linear stability analysis were found to agree with those predicted by the nonlinear stability analysis for the initial growth of the disturbances. The results from the nonlinear stability analysis showed that just beyond the critical draw ratio, the sustained disturbance was sinusoidal. However, further beyond the critical draw ratio, the sustained disturbance consisted of narrow, sharp peaks alternating with wide, thin troughs.
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