Wall Slip, Melt Fracture

A more serious error in shear rate occurs when there is wall slip. This can be particularly important for concentrated dispersions and 

Apparent viscosity versus apparent wall shear rate by capillaries of various radii R but constant L/R = 60 for a clay paper coating formulation wiA 68 wt % solids. Solid circles denote values extrapolated to infinite radius using eq. 6.2.18. From Laun and Hirsch (1989). 

It is usually possible to correct this apparent wall slip and determine the true viscosity of the sample by extrapolating to infinite diameter. Apparent wall shear rates measured at constant extrusion pressure (i.e., constant Tw) for a constant L/R are plotted against l/R according to the relation first developed by Mooney (1931) 

Shear stress versus shear rate for a high density polyethylene melt showing flow instabilities and evidence of slip. Adapted from Uhland (1979). 

If melt distortion limits shear stress for highly viscous (and elastic) materials, turbulent flow potentially puts an upper limit on capillary rheometry of low viscosity fluids. The classical Reynolds number criteria for the onset of turbulence in tube flow gives 

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These observations lead to the conclusion that melt firacture is the result of a hydrodynamic instability that occurs in the elongational flow upstream of the contraction. This conclusion concurs with the forecasts made in many other studies [2-4]. In particular, it should be noted that inertia, which produces similar phenomena in classical turbulent regimes, is not involved here as the Rejmolds numbers for the flows considered in this study are very low (less than unity). Moreover, for the moderately entangled polymers considered here flow takes place with adhesion at the wall, and melt fracture could be observed independently of the occurrence of slip [7, 41]. 

The site of the sharkskin distortion is again the die exit, and so is the screw thread pattern. The site of, and the mechanism for the gross extrudate distortion are problems that have no clear answers. The work of White and Ballenger, Oyanagi, den Otter, and Bergem clearly demonstrates that some instability in the entrance flow patterns is involved in HDPE melt fracture. Clear evidence for this can be found in Fig. 12.18. Slip at the capillary wall, to quote den Otter, does not appear to be essential for the instability region, although it may occasionally accompany it. ... 

De Gennes (2007) has constructed a model for slippage planes in a sheared melt, based on a balance between reptation bridging and shear debonding (slip stick model). He proposed that slippage occurs on solid walls either at the container surface or on dust particles floating in the melt. There is critical stress for slippage, approximately equal to Ys of the plateau modulus, which means that melt fracture is expected at moderate stresses. 

Polymer chains anchored on solid surfaces play a key role on the flow behavior of polymer melts. An important practical example is that of constant speed extrusion processes where various flow instabilities (called sharkskin , periodic deformation or melt fracture) have been observed to develop above given shear stress thresholds. The origin of these anomalies has long remained poorly understood [123-138]. It is now well admitted that these anomalies are related to the appearance of flow with slip at the wall. It is reasonable to think that the onset of wall slip is related to the strength of the interactions between the solid surface and the melt, and thus should be sensitive to the presence of polymer chains attached to the surface. 

It is simplest to think of sharkskin as a result of a quasi-periodic perturbation on the overall extrudate swell. This small amplitude fluctuation of extrudate swell arises from the oscillation of the boundary condition at the exit wall that produces an oscillation of the local stress level as the interfacial chains suffer a conformational instability. The local boundary condition oscillates between noslip and slip, resulting in the fluctuation of the stress level at the die exit. To determine whether some sort of melt fracture occurs, we need to know not only the... 

J.-M. Piau, N. El Kissi and B. Tremblay, Influence of upstream instabilities and wall slip on melt fracture and sharkskin phenomena during silicones extension through orifice dies, J. Non-Newtonian Fluid Mech., 34 (1990) 145-180. 

During the extrusion of polymers different defects and flow instabilities occur at very low Reynolds numbers. The commonly known ones are sharkskin, melt fracture, slip at the wall and cork flow. These defects are of commercial importance, since they often limit the production rate in polymer processing. Many researchers have been interested in the subject, and thorough reviews on flow stability and melt fracture have been written in the last 30 years [1-4]. More recently, two review papers deahng with viscoelastic fluid mechanics and flow stability, were published by Denn [5] and Larson [6]. However, although much work has been done in the field of extrusion distortions, controversy still exists regarding the site of initiation and physical mechanisms of the instabilities. 

An important element in melt fracture is also wall slip phenomenon [5, 49]. It is related to the so-called sharkskin, or sharkskin melt fracture, which is also called surface melt fracture. It is a low amplitude surface distortion of extruded polymer. Sharkskin is generally observed in case of linear polymers with narrow MWD, below the oscillating stick-slip transition. Sometimes (but not always), there is a change... 

Sharkskin, when the surface of the extrudate becomes visibly opaque, occurs at a wall shear stress level that is typically of the order of 0.1 MPa. At higher wall shear stress, typically of the order of 0.3 MPa, the flow becomes unsteady and the extrudate alternates between sharkskin and smooth segments (stick-slip, spurt flow, or cyclic melt fracture) [52, 53]. 

This process is particularly advantageous with polymers that melt fracture at relatively low rates, such as PER In superextrusion, the polymer melt is believed to slip relatively uniformly along the die wall. The occurrence of slip in extruder dies has been studied by a number of investigators, e.g., [166, 168]. However, it is still not clear whether the slip is actual loss of contact of polymer melt and metal wall or whether it is failure of a thin polymeric layer very close to the metal surface. 

A number of other mechanisms [53-65] have been suggested for melt fracture. Based on a stick-slip mechanism, it is purported [53] that, above a critical shear stress, die polymer experiences intermittent slipping due to a lack of adhesion between itself and die wall, in order to relieve the excessive deformation energy adsorbed during the flow. The stick-slip mechanism has attracted a lot of attention [53-63], both theoretically and experimentally. The other school of drought [64,65] is based on thermodynamic argument, according to which, melt fracture can initiate anywhere in the flow field when reduction in the fluid entropy due to molecular orientation reaches a critical value beyond which the second law of thermodynamics is violated and flow instability is induced [64]. 

Wall slip with concentrated dispersions Melt fracture at r,. lO Pa... 

Except for nummcal constants, the equations for calculating shear rate are the same as fOT the csq>illary. The constant 0.79 in the representative shear rate equation can be obtained following the derivation given in Example 6.2.1 (see also Laun, 1983, Appendix A). Varying slit thickness, H, can be used like capillary radius to test for wall slip. In fact, the studies by Lim and Schowalter (1989) and by Geiger (1989) referred to in Section 6.2 were done with slit dies. Slip or melt fracture in polymer melts occurs at about the same wall shear stress as for capillaries, lO Pa. 

Slip/stick occurs when the shear rate at the die wall exceeds the adhesive force of the melt to the surface. When this occurs, the melt jerks forward as a plug, relieving the pressure behind it and allowing the oriented chain segments to recoil somewhat. Once the pressure is relieved the rate of movement of the polymer slows and it re-adheres to the die wall. Shear flow resumes until once again the shear rate exceeds the critical value [91]. The effect is also known as spurting due to the erratic polymer output associated with it. During slip/stick flow the pressure within the die fluctuates and the polymer output is unsteady, both of which may vary periodically or erratically. The effects of stick/slip are closely related to those of melt fracture. 

Several artieles in the technical literature suggest that melt fracture is caused by the violation of the no-slip boundary condition at the tube wall. In other words, at high enough flow rates, v (R) equals V, which is called... 

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