Wall Slip and Extrusion Instabilities

The no-slip boundary condition is introduced in every text on fluid mechanics as a fundamental principle of the disciphne, and students are expected to accept the condition as obvious. No-slip is not obvious, however, nor was it obvious to the founders of the disciphne of fluid mechanics in the nineteenth century. Navier, in 1823, believed that there should be a relative ( slip ) velocity between the fluid and the solid surface that would be proportional to the shear stress at the wall in modern terminology we would write Navier s hypothesis as (cf. Equation 2.30) 

Wise and co-workers used an infrared (IR) evanescent wave spectroscopy technique to follow the disappearance of a tracer of deuterated 1,4-polybutadiene (PBDE) displaced in a channel by unlabeled PBDE of the same molecular weight. Linear PBDE is a convenient polymer for experimental research because it flows at room temperature and has a viscosity that is relatively insensitive to shear rate. One face of the channel was fabricated from a ZnSe IR crystal, and the deuterated polymer was placed on the surface. The deuterated polymer was then allowed to equilibrate with hydrogenated polymer of the same molecular weight, and flow was initiated. The concentration of deuterated polymer in the wall region after the 

The general conclusion that can be reached from these experiments and others not mentioned here is that apparent slip is observed for some highly entangled linear polymers, while it has not been observed for branched polymers or for linear polymers with an insufficient number of entanglements per chain. None of the 

The notion that slip in a polymer melt is a consequence of disentanglement of chains adsorbed to the wall from those in the bulk seems to have been proposed first 

The theory has only a single adjustable parameter, which corresponds to the Rouse time (the characteristic relaxation time for an unconfined chain) of the polymer, and it does a quite reasonable job of predicting the hnear viscoelastic response and the transient and steady-state shear and normal stresses in simple shear, ft is not as good as more complex tube-based models hke the pom-pom model, and it cannot be used for nonviscometric flows because of the absence of a continuum representation, but it contains structural details and is very useful for providing insight into the mechanics of slip. 

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There is an overview of wall slip and extrusion instabilities in polymer melts, with extensive... 

M. M. Denn, Extrusion Instabilities and Wall Slip, Annu. Rev Fluid Mech., 33, 265-287 (2001). 

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. 

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

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. 

Denn, M. (2001). Extrusion instabilities and wall slip. Annu. Rev. Fluid Mech. 33, 265. 

Delaunay D, Le Bot PH, Fulchiron R, Luye JF, Regnier G (2000b) Nature of contact between polymer and mold in injection molding. Part II Influence of mold deflection on pressure history and shrinkage. Polym Eng Sci 40 1692-1700 Denn MM (2001) Extrusion instabilities and wall slip. Annu Rev Fluid Mech 33 265-287 Denn MM (2004) Fifty years of non-Newtonian fluid dynamics. AIChE J 50 2335-2345 Dinh SH, Armstrong RC (1984) A rheological equation of state for semi-concentrated fiber suspensions. J Rheol 28 207-227... 

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