Experimental Evidence for an Intrinsic Route to Polymer Melt Fracture Phenomena: A Nonlinear Instability of Viscoelastic Poiseuille Flow

The production rate of polymer fibers by extrusion is usually limited by the appearance of a series of instabilities (“melt fracture”) that lead to unwanted undulations of the surface. We present both qualitative and quantitative experimental evidence that—in addition to previously known polymer-specific scenarios—there is an intrinsic route towards melt fracture type phenomena: a nonlinear (“subcritical”) instability of viscoelastic Poiseuille flow.

Figure 1

Direct observation of the extrusion for different speeds for a 0.4% borax solution: (a) for the lowest speed ($\mathrm{W}\mathrm{i}=2.8$) the surface is smooth (b) intermediate speed ($\mathrm{W}\mathrm{i}=4.9$): development of a small roughness (c) at the highest speed ($\mathrm{W}\mathrm{i}=8.4$) the melt fracture is well developed.

Figure 2

The root mean square amplitude of the extrudate surface roughness (obtained by analyzing the pictures) as a function of the maximum shear rate inside the capillary. For low shear rates the roughness is almost constant (smaller than one pixel), while for shear rates greater than a critical value it becomes much larger, so the transition to melt fracture is well defined. Note the dynamical hysteresis obtained upon increasing (diamonds) and decreasing (circles) the extrusion speed.

Figure 3

Elastic (normal) stresses and viscosity (inset) as a function of the shear rate measured on a Reologica Stress-Tech rheometer with a $40\mathrm{m}\mathrm{m}/4°$ cone-plate geometry for a 0.2% borax solution. The line is a fit to a quadratic shear-rate dependence, corresponding to the Oldroyd-B model. For higher shear rates and depending on the crosslinker concentration, the solution becomes strongly shear thinning, which is the usual observation for polymer solutions and melts exhibiting melt fracture. However, it has already been established (Ref. 8) that the first instabilities, which interest us here, occur before this shear thinning region; these two phenomena appear to be disconnected.

Figure 4

Characteristic frequency of the instability for different borax concentrations, determined from the location of the peak in power spectra of diameter thickness fluctuations time series. The dashed lines delimit the frequency associated with the unstable band calculated in the nonlinear stability analysis.