Stick-slip instability

Commercially available thermoplastic elastomers based on block copolymers of diisocyanates and polyols were used to delay sharkskin and stick-slip instabilities in the extrusion of linear low density polyethylene. When elastomer is added in a small mass fraction to LLDPE, it deposits at the die surface during extrusion and may postpone the onset of sharkskin instability to a 12-20 times higher rate of extrusion. ... 

Combined Tensile and Shear Faulting Although tensile faults could cause earthquakes that involve volume increases, they caimot explain non-DC earthquakes whose isotropic components indicate volume decreases. Tensile faults can open suddenly for a variety of reasons, but they would be expected to close gradually, and not to radiate elastic waves. If a tensile fault and a shear fault intersect, however, then stick-slip instability could cause sudden episodes of either opening or closing, with volume increases or decreases. The stresses around the... 

The example demonstrates that the instability and consequent energy dissipation, similar to those in the Tomlinson model, do exist in a real molecule system. Keep in mind, however, that it is observed only in a commensurate system in which the lattice constants of two monolayers are in a ratio of rational value. For incommensurate sliding, the situation is totally different. Results shown in Fig. 21(b) were obtained under the same conditions as those in Fig. 21 (a), but from an incommensurate system. The lateral force and tilt angle in Fig. 21(b) fluctuate randomly and no stick-slip motion is observed. In addition, the average lateral force is found much smaller, about one-fifth of the commensurate one. 

At the beginning of sliding, the system is accelerated because the driven force must excess the resistance from lubricating film. For this reason, the system actually jumps from A to the point B, instead of B, to gain a shear stress lower than the critical value This phenomenon, so called velocity-weakening has been regarded widely in the literatures as the cause for instability and stick-slip motion in lubricated systems. 

Important examples of stick-slip are earthquakes that have long been recognized as resulting from a stick-slip frictional instability. The use of a full constitutive law of rock friction that takes into account the time dependence of /is and the dependence of /j>k on speed and sliding distance can account for the rich variety of earthquake phenomena as seismogenesis and seismic coupling, pre- and post-seismic phenomena, and the insensitivity of earthquakes to stress transients [461],... 

During extrusion of polymer melts with high throughputs, the elastic melt properties can also lead to elastic instabilities which can result in surface distortions of the extrudate. One example are wavy distortions also described as sharkskin. Depending on the polymer, this can also lead to helical extrudate structures (stick-slip effect) or to very irregular extrudate structures (melt fracture) at even higher throughput rates [10]. 

Fig. 1. Typical flow curve of commercial LPE. There are five characteristic flow regimes (i) Newtonian (ii) shear thinning (iii) sharkskin (iv) flow discontinuity or stick-slip transition in controlled stress, and oscillating flow in controlled rate (v) slip flow. There are three leading types of extrudate distortion (a) sharkskin like, (b) alternating bamboo like in the shaded region, and (c) spiral like on the slip branch. Industrial extrusion of polyethylenes is most concerned with flow instabilities occurring in regimes (iii) to (v) where the three kinds of extrudate distortion must be dealt with. The unit shows the approximate levels of stress where the sharkskin and flow discontinuity occur respectively. There is appreciable molecular weight and temperature dependence of the critical stress for the discontinuity. Other highly entangled melts such as 1,4 polybutadienes also exhibit most of the features illustrated herein...

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. 

Linear polyethylenes (PE) are one polymer that possess an important ingredient necessary for a display of interfacial stick-slip transition. In the past, the coincidence that PE is both the most widely used polymer and most prone to suffer from melt flow instabilities has challenged the PE industry. Today we still face the task of how to effectively remove instabilities that result in various types of extrudate distortions. 

We have surveyed the most recent progress and presented a new molecular level understanding of melt flow instabilities and wall slip. This article can at best be regarded as a partial review because it advocates the molecular pictures emerging from our own work over the past few years [27-29,57,62,69]. Several results from many previous and current workers have been discussed to help illustrate, formulate and verify our own viewpoints. In our opinion, the emerging explicit molecular mechanisms have for the first time provided a unified and satisfactory understanding of the two major classes of interfacial melt flow instability phenomena (a) sharkskin-like extrudate distortion and (b) stick-slip (flow discontinuity) transition and oscillating flow. 

Directing Convection Marangoni Convection/ Evaporation/Self- assembly Coffee rings, polygonal network structures, fingering instabilities, cracks, chevron patterns, etc. Nanometer to micrometer Marangoni convection and stick-slip motion can determine the final patterns observed [132-134]... 

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]. 

If the friction coefficient is very high (i.e. near to the peak value) stick-slip occurs. The rubber does not slide smoothly but jumps forward in a jerky manner. It has been suggested that this phenomenon occurs only when the friction coefficient is decreasing with increasing velocity thereby producing an instability. 

The friction force increases linearly with the maximum interaction potential Vb. However, in a stick-slip situation, the friction force will not follow the sinusoidal pattern but a sawtooth pattern due to instabilities. The force Fp at which the jump occurs can be calculated using Eqs. (9.36) and (9.40) in combination with the... 

The negative slope in the friction-sliding velocity curve or the difference between static and kinematic coefficients of friction can lead to the so-called stick-slip vibratiOTis (see, e.g., [14, 59]). In most instances, researchers adopted the well-known mass-on-a-conveyor model to study the stick-slip vibrations (see, e.g., [17, 60, 61]). In this section, we will also consider this simple model - as shown in Fig. 4.1 - to investigate the effects of the negative damping instability mechanism. 

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