Instability, polymer flows

Many polymers exhibit neither a measurable stick-slip transition nor flow oscillation. For example, commercial polystyrene (PS), polypropylene (PP), and low density polyethylene (LDPE) usually do not undergo a flow discontinuity transition nor oscillating flow. This does not mean that their extrudate would remain smooth. The often observed spiral-like extrudate distortion of PS, LDPE and PP, among other polymer melts, normally arises from a secondary (vortex) flow in the barrel due to a sharp die entry and is unrelated to interfacial slip. Section 11 discusses this type of extrudate distortion in some detail. Here we focus on the question of why polymers such as PS often do not exhibit interfacial flow instabilities and flow discontinuity. The answer is contained in the celebrated formula Eqs. (3) or (5). For a polymer to show an observable wall slip on a length scale of 1 mm requires a viscosity ratio q/q equal to 105 or larger. In other words, there should be a sufficient level of bulk chain entanglement at the critical stress for an interfacial breakdown (i.e., disentanglement transition between adsorbed and unbound chains). The above-mentioned commercial polymers do not meet this criterion. 

The characteristic curve of extrudate flow including adherence to the walls, and hence representative of shghtly to moderately entangled polymer flow in sudden two-dimensional or axisymmetrical contractions [7, 32], is represented in Fig 2. It shows a slope discontinuity above a certain pressm-e level, which depends on the pol3uner-die pair considered. With low flow rates, the flow is stable. Indeed, for these regimes, allowing for entrance effects, the flow curve is in fact representative of the shear rheometry of the polymer imder consideration, at low shear rates [34]. The slope discontinuity of the head loss curve indicates a modification in the structure of flow. It will be seen that this corresponds to the triggering of a hydrodynamic instability upstream of the contraction. 

E. Boudreaux, Jr., and J. A. Cuculo, Polymer flow instability A review and analysis, J. 

Melt fracture has been a very perplexing but fascinating problem ever since it was discovered. Another problem that seems to have the same degree of perplexity and fascination is draw resonance. Both are instabilities in polymer flows. (Draw resonance may also occur in Newtonian fluids.) Draw resonance is a periodic variation in the diameter of a spinning thread line above a critical drawdown ratio. Polypropylene and high-density polyethylene are both particularly susceptible to draw resonance. Petrie and Denn have presented a comprehensive review of the numerous theoretical and experimental studies of draw resonance conducted prior to 1976 [99]. 

The polymer melt is forced from the metering section into a bypass flow channel by incorporating a multi-flighted screw section with reversed pitch and shallow channels between the metering section and the extraction section. The bypass channel has one or more adjustable restrictions to control the rate of flow into the extraction section. The polymer flows from the bypass channel into the beginning of the extraction section. Maddock and Matzuk concluded that bypass venting allows a wider range of operation, is less susceptible to instabilities, and is less operator-sensitive. 

The biaxial strain data, and in particular the results shown in Fig. 6 of the apparent true stress at Xg = 2.2 versus temperature, shows a region of instability observed around 157-165°C. We suggest that this has the same origin as the changes in the conformational state of the or-PS melt observed from the spectral data. At temperatures above 165 C, the dynamics of the chains are sudi that the majority of restraints are overcome within the time scale of the experiment. Hence the polymer flows more easily althou some associative ability may still remain. It is interesting to note that the transition temperature observed at 165 C in a variety of experiments corresponds to a temperature which Boyer has derined as a liquid-liquid transition temperature, T/j, for atactic polystyrene of comparable molecular weight as determined by analysis of zero shear melt viscosity data.i ... 

Forced-Convection Flow. Heat transfer in pol3rmer processing is often dominated by the uVT flow advectlon terms the "Peclet Number" Pe - pcUL/k can be on the order of 10 -10 due to the polymer s low thermal conductivity. However, the inclusion of the first-order advective term tends to cause instabilities in numerical simulations, and the reader is directed to Reference (7) for a valuable treatment of this subject. Our flow code uses a method known as "streamline upwindlng" to avoid these Instabilities, and this example is intended to illustrate the performance of this feature. 

Wang, S.-Q. Molecular Transitions and Dynamics at Polymer/Wall Interfaces Origins of Flow Instabilities and Wall Slip. VoL 138, pp. 227-276. 

E. C. Kumbur, K. V. Sharp, and M. M. Mench. Liquid droplet behavior and instability in a polymer electrolyte fuel cell flow channel. Journal of Power Sources 161 (2006) 333-345. 

Tzoganakis, C. and Perdikoulias, J., Interfacial Instabilities in Coextrusion Flows of Low-Density Polyethylenes Experimental Studies, Polym. Eng. ScL, 40, 1056 (2000)... 

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