Stick-slip flow

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. 

Ghoreishy, M. H. R. and Nassehi, V., 1997. Modelling the transient flow of rubber compounds in the dispersive section of an internal mixer with slip-stick boundary conditions. Adv. Poly. Tech. 16, 45-68. 

In summary, the origin of the oscillating flow (sometimes termed slip-stick regime) observed in the constant piston speed mode is the oscillation of the HBC between the no-slip and slip states due to a reversible coil-stretch transition of either adsorbed chains or the first layer of unbound chains entrapped with the adsorbed chains. The experimental demonstration of an abrupt large stick-slip... 

In a series of papers, Felderhof has devised various methods to solve anew one- and two-sphere Stokes flow problems. First, the classical method of reflections (Happel and Brenner, 1965) was modified and employed to examine two-sphere interactions with mixed slip-stick boundary conditions (Felderhof, 1977 Renland et al, 1978). A novel feature of the latter approach is the use of superposition of forces rather than of velocities as such, the mobility matrix (rather than its inverse, the grand resistance matrix) was derived. Calculations based thereon proved easier, and convergence was more rapid explicit results through terms of 0(/T7) were derived, where p is the nondimensional center-to-center distance between spheres. In a related work, Schmitz and Felderhof (1978) solved Stokes equations around a sphere by the so-called Cartesian ansatz method, avoiding the use of spherical coordinates. They also devised a second method (Schmitz and Felderhof, 1982a), in which... 

A term slip modifier is often used in extrusion of plastics and composite materials where slip-stick of the hot melt at the die is typically observed at too slow or too fast melt flow (see Chapter 17). To avoid confusion, we will use in this chapter the term slip enhancer or friction enhancer. Friction enhancer is a material that increases friction between two surfaces so as to attain a specihc friction level in a controlled manner. 

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]. 

Finally, we shall mention the slip-stick melt fracture phenomenon — a phenomenon often observed in polymer extrusion — which is much related to the relative positions of the /Ltg(t, E) and pcit) processes. The phenomenon is a well-known problem in the polymer processing industry because it limits the output of polymer through an extruder. In a capillary flow, the decline of the viscosity observed as the shear rate (or flow rate) increases from the Newtonian region is much related to the damping factor... 

Harrison et al. also indicated that a uniform lubricating layer at the die wall interface must occur to eliminate the slip-stick phenomenon responsible for forced flow. Development of a lubricating layer was dependent on the length of the die (a minimum length required), wall shear stress and upstream pressure loss. They represent the frictional forces at the die wall interface and the estimated pressure loss at zero die length in the barrel of the ram extruder. The method for deriving these values is described in Ref. 27. These parameters allow for a quantitative comparison between formulations and process however, no specific values can be targeted since they vary with materials. 

Linear polymers that exhibit sharkskin typically also exhibit a discontinuity in the shear flow curve known as slip-stick. The phenomenon is illustrated in Figure 12.12 for an LLDPE in a piston-driven capillary rheometer. At a critical wall stress there... 

MODELLING THE TRANSIENT FLOW OF RUBBER COMPOUNDS IN THE DISPERSIVE SECTION OF AN INTERNAL MIXER WITH SLIP-STICK BOUNDARY CONDITIONS... 

It is true that linear polymers do not show large vortices in planar entry flow, although they may occiu in axisymmetric flow (White et al., 1987). However, it is known that the origin of fracture for PS is the die entry. In fact, HDPE and LLDPE are the only polymers of the group presented here that readily show any indication of slip-stick in the flow curve. The rest show no indication of fracture in the flow curve, and apparently the origin of fracture is in the die entry. In spite of this, it is interesting to note that Za- for the branched polymer, LDPE, falls on a curve separate from that for the linear polymers. 

It is obvious that in rubber processing there will be slip, because the surface of processing equipment in contact with gum rubbers and compounds is usually shiny. This is in contrast to plastic processing equipment, in which the surfaces become coated with a thin layer of the degraded material. With plastics this fact indicates the velocity of the melt at the metal interface is zero, i.e., laminar shear flow. A study of slip is multi-faceted, because there are many types of slip, a steady slip, slip with a lubricated layer, slip-stick, slip involving a fracture at the interface or ruhhing like a dynamic friction measurement. 

The deformation of molten polyethylene may take place in either constrained or nnconstrained systems. The former is exemplified by flow in a channel, such as that encountered in an extmder or an injection molding die. The latter involves elongation of the melt without the benefit of walls to constrain its shape, typified by film blowing or the drawing of an extrudate to form a fiber. Flow in a eonstrained system involves shear deformation whenever the polymer adheres to the walls. When adhesion to the wall fails, slip/stick or plug flow oeeurs, neither of which is desirable in the ordinary eourse of polyethylene pro-... 

Fig. 2 shows the flow curve for the neat exact 5361 at loot). The instability problem of the metallocene based polymers with narrow molecular distribution is well known. Fig. 3 shows the photographs of the extrudate samples with varying Dechlorane concentration collected during the capillary rheometers measurement. It is interesting to see that while the severe instabilities such as slip-stick and gross-melt fracture were observed at the shear rate from 177.8 s to 3162.2 s for the neat Exact resin, the severe instability appeared at the shear rate between 177.8 s and 562.2 s but disappeared at the shear rate above 1000.1 s for Exact/10% Dechlorane suspension. The shark-skin like instabilities were observed above the Dechlorane concentration of 20% and the shear rate at which the instability started to appear was decreased as the Dechlorane concentration was increased. Since the viscosity of the Dechlorane-filled systems was higher than that of the neat resin at all rates of shear, the instabilities are expected to develop the melt fracture at even lower shear rates. The shear viscosity vs. shear rate relationships measured with plate-plate rheometers and capillary rheometers are shown in Fig. 4. In this figure it is seen that both sets of data are reasonably matched. It is observed that at low shear rate range the viscosity increment due to the increase in the filler concentration is more pronounced than that at high shear rate. Both plate-plate and capillary measurements were carried out with constant shear rate (CSR) mode. While the capillary rheometer could accurately follow the preset shear rate values the plate-plate rheometer couldn t keep up with the preset shear rate values. Above two observations are due to the yield stress developed at low shear rate. At low shear rate particle-particle interaction dominates the flow phenomena and the yield stress was observed. At high shear rate hydrodynamic effect dominates the flow phenomena.

Foam rheology has been a challenging area of research of interest for the yield behavior and stick-slip flow behavior (see the review by Kraynik [229]). Recent studies by Durian and co-workers combine simulations [230] and a dynamic light scattering technique suited to turbid systems [231], diffusing wave spectroscopy (DWS), to characterize coarsening and shear-induced rearrangements in foams. The dynamics follow stick-slip behavior similar to that found in earthquake faults and friction (see Section XU-2D). 

Imposition of no-slip velocity conditions at solid walls is based on the assumption that the shear stress at these surfaces always remains below a critical value to allow a complete welting of the wall by the fluid. This iraplie.s that the fluid is constantly sticking to the wall and is moving with a velocity exactly equal to the wall velocity. It is well known that in polymer flow processes the shear stress at the domain walls frequently surpasses the critical threshold and fluid slippage at the solid surfaces occurs. Wall-slip phenomenon is described by Navier s slip condition, which is a relationship between the tangential component of the momentum flux at the wall and the local slip velocity (Sillrman and Scriven, 1980). In a two-dimensional domain this relationship is expressed as... 

G is a multiplier which is zero at locations where slip condition does not apply and is a sufficiently large number at the nodes where slip may occur. It is important to note that, when the shear stress at a wall exceeds the threshold of slip and the fluid slides over the solid surface, this may reduce the shearing to below the critical value resulting in a renewed stick. Therefore imposition of wall slip introduces a form of non-linearity into the flow model which should be handled via an iterative loop. The slip coefficient (i.e. /I in the Navier s slip condition given as Equation (3.59) is defined as... 

This stick-slip cycle, observed for all types of film compounds ranging from long-chain (e.g., hexadecane) to spheroidal [e.g., octamethylcyclotetra-siloxane (OMCTS)] hydrocarbons [21], has been attributed by Gee et al. [30] to the formation of solid-like films that pin the walls together (region of sticking) and must be made to flow plastically in order for the walls to slip. This suggests that the structure of the walls induces the formation of a solid film when the walls are properly registered and that this film melts when... 

Stick Slip Flow. The continuous sudden stoppage and resumption of catalyst flow in a standpipe. This is usually caused by underaeration. 

Stick-Slip Flow is erratic circulation caused when the catalyst packs and bridges across the standpipe. 

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