Viscoelastic behavior shear effect

The dynamic viscoelasticity of particulate gels of silicone gel and lightly doped poly-p-phenylene (PPP) particles has been studied under ac excitation [55]. The influence of the dielectric constant of the PPP particles has been investigated in detail. It is well known that the dielectric constant varies with the frequency of the applied field, the content of doping, or the measured temperature. In Fig. 11 is displayed the relationship between an increase in shear modulus induced by ac excitation of 0.4kV/mm and the dielectric constant of PPP particles, which was varied by changing the frequency of the applied field. AG increases with s2 and then reaches a constant value. Although the composite gel of PPP particles has dc conductivity, the viscoelastic behavior of the gel in an electric field is qualitatively explained by the model in Sect. 4.2.1, in which the effect of dc conductivity is neglected. 

The rheological properties of a fluid interface may be characterized by four parameters surface shear viscosity and elasticity, and surface dilational viscosity and elasticity. When polymer monolayers are present at such interfaces, viscoelastic behavior has been observed (1,2), but theoretical progress has been slow. The adsorption of amphiphilic polymers at the interface in liquid emulsions stabilizes the particles mainly through osmotic pressure developed upon close approach. This has become known as steric stabilization (3,4.5). In this paper, the dynamic behavior of amphiphilic, hydrophobically modified hydroxyethyl celluloses (HM-HEC), was studied. In previous studies HM-HEC s were found to greatly reduce liquid/liquid interfacial tensions even at very low polymer concentrations, and were extremely effective emulsifiers for organic liquids in water (6). 

Filler-filler interaction (Payne effect) - The introduction of reinforcing fillers into rubbery matrices strongly modifies the viscoelastic behavior of the materials. In dynamic mechanical measurements, with increasing strain amplitude, reinforced samples display a decrease of the storage shear modulus G. This phenomenon is commonly known as the Payne effect and is due to progressive destruction of the filler-filler interaction [46, 47]. The AG values calculated from the difference in the G values measured at 0.56% strain and at 100% strain in the unvulcanized state are used to quantify the Payne effect. 

Pad Elastic and Shear Modulus Units of (MPa) or (psi). These moduli determine the mechanical stability and flexibility of pads during polishing under the load and rotational constraints. The pad s viscoelastic behavior is important in determining the planarization effectiveness and in the feature size effect observed during CMP. 

The Rivlin-Ericksen constitutive equation gives a good account of some characteristics of both the time dependence of the viscoelastic behavior and the normal stress effects. This relationship is based on the assumption that the stress depends not only on the velocity (x ) and the shear rate gradient (dxi/dx ) but also on derivatives of higher order (%, dXp/dXq. .. 8xf /8xi). As a consequence of the principle of material... 

In order to describe the viscoelastic behavior of a system subjected to multiaxial tensions, it is convenient to separate the shear (deviatoric) effects from the purely dilatational components. This is due to the fact that in... 

The shearing characteristics of non-Newtonian fluids are illustrated in Fig. 7. Curves A and B represent viscoelastic behavior. Curve C illustrates the behavior if the fluid thins with increasing shear, generally referred to as shear thinning or pseudoplasticity. The opposite effect of shear thickening or dilatancy is shown as curve D. 

This chapter is an in-depth review on rheology of suspensions. The area covered includes steady shear viscosity, apparent yield stress, viscoelastic behavior, and compression yield stress. The suspensions have been classified by groups hard sphere, soft sphere, monodis-perse, poly disperse, flocculated, and stable systems. The particle shape effects are also discussed. The steady shear rheological behaviors discussed include low- and high-shear limit viscosity, shear thinning, shear thickening, and discontinuity. The steady shear rheology of ternary systems (i.e., oil-water-solid) is also discussed. 

In fluids with time-dependent behavior, the effects of time can be either reversible or irreversible. If the time effects are reversible, the fluids are either thixotropic or rheopectic. Thixotropy is the continuous decrease of apparent viscosity with time under shear and the subsequent recovery of viscosity when the flow is discontinued. Rheopexy is the continuous increase of apparent viscosity with time under shear it is also described by the term anti-thixotropy. A good review on thixotropy was given by Mewis [45]. Polymer melts do exhibit some thixotropic effects however, thixotropy can also occur in inelastic fluids. The time scale of thixotropy is not necessarily associated with the time scale for viscoelastic relaxation. 

For a one-dimensional steady shear flow of a fluid between two planes, the velocities of an inflnitesimal element of fluid in the y- and z-directions are zero. The velocity in the x-direction is a function of y only. Note that in addition to the shear stress Tyx (refer to r subsequently) there are three normal stresses denoted by Txx, tyy, Tzz within the sheared fluid. Weissenberg in 1947 [6] was the first to observe that the shearing motion of a viscoelastic fluid gives rise to unequal normal stresses, known as Weissenberg effects. Since the pressure in a non-Newtonian fluid cannot be defined, and as the normal stress differences [2, 3], Txx — Tyy = Vi and Tyy — Tzz = V2, are more readily measured than the individual stresses, it is therefore customary to express N and N2 together with the shear stress t as functions of the shear rate /yx to describe the viscoelastic behavior of a material in a simple shear flow. 

This section considers the behavior of polymeric liquids in steady, simple shear flows - the shear-rate dependence of viscosity and the development of differences in normal stress. Also considered in this section is an elastic-recoil phenomenon, called die swell, that is important in melt processing. These properties belong to the realm of nonlinear viscoelastic behavior. In contrast to linear viscoelasticity, neither strain nor strain rate is always small, Boltzmann superposition no longer applies, and, as illustrated in Fig. 3.16, the chains are displaced significantly from their equilibrium conformations. The large-scale organization of the chains (i.e. the physical structure of the liquid, so to speak) is altered by the flow. The effects of finite strain appear, much as they do when a polymer network is deformed appreciably. 

Viscoelastic behavior in simple extension or in bulk longitudinal deformation will in general combine the features of shear and bulk viscoelasticity, since the moduli E t) and M t) depend on both (7(0 and K t), as shown by equations 51 and 58 of Chapter 1 ( and analogous relations for E and M ). However, as already pointed out, shear effects predominate in E(t) and E. and bulk effects predominate... 

Figure 7.1 Complex shear modulus (a) and complex shear compliance (b) for standard polyisobutylene reduced to 25° C. Points from averaged experimental measurements curves from a theoretical model for viscoelastic behaviour. (Reproduced from Marvin, R.S. and Oser, H. (1962) Model for the viscoelastic behavior of rubberlike polymers including entanglement effects. I. Res. Natl Bur. Stand. B, 66, 17 . Copyright (1962).)...

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