Viscoelastic coupled

The first finite element schemes for differential viscoelastic models that yielded numerically stable results for non-zero Weissenberg numbers appeared less than two decades ago. These schemes were later improved and shown that for some benchmark viscoelastic problems, such as flow through a two-dimensional section with an abrupt contraction (usually a width reduction of four to one), they can generate simulations that were qualitatively comparable with the experimental evidence. A notable example was the coupled scheme developed by Marchal and Crochet (1987) for the solution of Maxwell and Oldroyd constitutive equations. To achieve stability they used element subdivision for the stress approximations and applied inconsistent streamline upwinding to the stress terms in the discretized equations. In another attempt, Luo and Tanner (1989) developed a typical decoupled scheme that started with the solution of the constitutive equation for a fixed-flow field (e.g. obtained by initially assuming non-elastic fluid behaviour). The extra stress found at this step was subsequently inserted into the equation of motion as a pseudo-body force and the flow field was updated. These authors also used inconsistent streamline upwinding to maintain the stability of the scheme. 

In this chapter we examine the elastic behavior of polymers. We shall see that this behavior is quite different from the elasticity displayed by metals and substances composed of small molecules. This is a direct consequence of the chain structure of the polymer molecules. In many polymers elasticity does not occur alone, but coupled with viscous phenomena. The combination of these effects is called viscoelasticity. We shall examine this behavior as well. 

Polyolefin melts have a high degree of viscoelastic memory or elasticity. First normal stress differences of polyolefins, a rheological measure of melt elasticity, are shown in Figure 9 (30). At a fixed molecular weight and shear rate, the first normal stress difference increases as MJM increases. The high shear rate obtained in fine capillaries, typically on the order of 10 , coupled with the viscoelastic memory, causes the filament to swell (die swell or... 

As mentioned earlier, the contact-mechanics-based experimental studies of interfacial adhesion primarily include (1) direct measurements of surface and interfacial energies of polymers and self-assembled monolayers (2) quantitative studies on the role of interfacial coupling agents in the adhesion of elastomers (3) adhesion of microparticles on surfaces and (4) adhesion of viscoelastic polymer particles. In these studies, a variety of experimental tools have been employed by different researchers. Each one of these tools offers certain advantages over the others. These experimental studies are reviewed in Section 4. 

Usually tj/ is very much larger than Fq. This is why practical fracture energies for adhesive joints are almost always orders of magnitude greater than works of adhesion or cohesion. However, a modest increase in Fq may result in a large increase in adhesion as and Fo are usually coupled. For some mechanically simple systems where is largely associated with viscoelastic loss, a multiplicative relation has been found ... 

Many of the new plastics, blends, and material systems require special, enhanced processing features or techniques to be successfully injection molded. The associated materials evolution has resulted in new plastics or grades, many of which are more viscoelastic. That is, they exhibit greater melt elasticity. The advanced molding technology has started to address the coupling of viscoelastic material responses with the process parameters. This requires an understanding of plastics as viscoelastic fluids, rather than as purely viscous liquids, as is commonly held... 

The results from EQCM studies on conducting polymer films can be ambiguous because the measured mass change results from a combination of independent ion transport, coupled ion transport (i.e., salt transport), and solvent transport. In addition, changes in the viscoelasticity of the films can cause apparent mass changes. The latter problem can be minimized by checking the frequency response of the EQCM,174 while the various mass transport components can be separated by careful data analysis.175,176... 

The most complete model to date for describing Case II diffusion is that of Thomas and Windle (13-16). They envision the process as a coupled swelling-diffusion problem in which the swelling rate is treated as a linear viscoelastic deformation driven by osmotic pressure. This model leads to the idea of a precursor phase propagating ahead of a moving boundary, as we have depicted in Figure 4. While Thomas and Windle have used numerical methods to examine in detail the predictions of their model, this model is difficult to test with the data obtained here. 

Effect of Viscoelastic Film on Coupling, and Inner Slip... 

We begin in Section II with a review of the fundamental concepts of hydrodynamics and boundary conditions. In Section III, we present some common descriptions of coupling, followed in Section IV by a discussion of viscoelastic adsorbate films and the so-called inner slip. In Section V, we consider with the concept of stochastic boundary conditions, which we believe will be an important topic in situations where random fluctuations are strong. Finally, in Section VI, we present our concluding ideas and discuss some areas for future study. 

We now turn our attention to the interstitial viscoelastic film between the solid and liquid, and we discuss its effect on coupling and boundary conditions. 

Shanahan and Carre [31-36, 55, 56] have done extensive theoretical work on the coating of viscoelastic surfaces and the effect of soft surfaces on hydrodynamic forces. Again, we have considered this area in a recent review [44]. This area is important in how energy is transferred or lost at the interface. Coupling changes at an inner interface can result in either an increase or decease in the energy dissipated. This has been discussed and observed for a number of acoustic systems [40, 41, 54, 57, 58]. 

Temperature variations during the formation of LDPE foam sheet were investigated. A thermal model was coupled with a viscoelastic growth model, and an iterative finite difference technique was used to solve unsteady heat transfer equations and viscoelastic growth equations. The heat transfer characteristic time became comparable to the expansion time when the sheet thickness decreased to the millimetre range, during which foam thickness and density became sensitive to temperature effects. 12 refs. USA... 

Each of the viscoelastic parameters G°, rj0, and Je° has associated with it a characteristic molecular weight which either measures an equivalent spacing of entanglement couples along the chain (Me, deduced from G with the kinetic theory of rubber elasticity), or marks the onset of behavior attributed to the presence of entanglements (Mc and AT, deduced from r/0 and Je° as functions of molecular weight). Table 5.2 lists Me, Mc, and M c for several polymers. Aside from certain difficulties in their evaluation, each is a rather direct and independent reflection of experimental fact. 

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