Some Viscoelastic Results

Some viscoelasticity results have been reported for bimodal PDMS [120], using a Rheovibron (an instrument for measuring the dynamic tensile moduli of polymers). Also, measurements have been made on permanent set for PDMS networks in compressive cyclic deformations [121]. There appeared to be less permanent set or "creep" in the case of the bimodal elastomers. This is consistent in a general way with some early results for polyurethane elastomers [122], Specifically, cyclic elongation measurements on unimodal and bimodal networks indicated that the bimodal ones survived many more cycles before the occurrence of fatigue failure. The number of cycles to failure was found to be approximately an order of magnitude higher for the bimodal networks, at the same modulus at 10% deformation [5] ... 

In this paper, we report some rheological results on the effect of addition of sodium bentonite, a commonly-used antisettling system, to a pesticide suspension concentrate. Steady state shear stress-shear rate measurements were carried out to obtain the yield value and viscosity as a function of shear rate. These e]q>eriments were supplemented by low deformation measurements to investigate the viscoelastic... 

Due to the clear correlation between molecular properties which can be calculated by computational methods and the physical properties of the nematic phase, the dielectric anisotropy (Ae) and the birefringence (An) can be predicted with reasonable accuracy by molecular modeling [28]. On the other hand, the viscoelastic terms and Kj, K2, are currently not really predictable, even if some recent results based on neural networks [3b], Monte Carlo simulations [29] and molecular mechanics approaches [30] give rise to some careful optimism (Figures 4.8 and 4.9). 

The zero mode is the self-diffusion of the center of mass whose diffusion coefficient is given by the Stokes-Einstein relation D = k TIN. The time Tj will be proportional to the time required for a chain to diffuse an end-to-end distance, that is, R )/D = t N b lk T. This means that for time scales longer than Tj the motion of the chain will be purely diffusive. On timescales shorter than Tj, it will exhibit viscoelastic modes. However, the dynamics of a single chain in a dilute solution is more complex due to long-range forces hydrodynamic interactions between distant monomers through the solvent are present and, in good solvents, excluded volume interactions also have to be taken into account. The correction of the Rouse model for hydrodynamic interaction was done by Zimm [79]. Erom a mathematical point of view, the problem becomes harder and requires approximations to arrive at some useful results. In this case, the translational diffusion coefficient obtained is... 

In summary, if G t), which is contained in Eqs. (4.30), (4.34)-(4.37), (4.49)-(4.51), (4.63) and (4.73), is known, all the linear viscoelastic quantities can be calculated. In other words, all the various viscoelastic properties of the polymer are related to each other through the relaxation modulus G t). This result is of course the consequence of the generalized Maxwell equation or equivalently Boltzmann s superposition principle. The experimental results of linear viscoelastic properties of various polymers support the phenomenological principle. Some viscoelastic properties play more important roles than the others in certain rheological processes related to... 

In this chapter, a brief theoretical background on the rheological behavior of viscoelashc worm-like micelles is given. It is followed by a discussion on the temperature-induced viscosity growth in a water-surfactant binary system of a nonionic fluorinated surfactant at various concentrations. Finally, some recent results on the formation of viscoelastic worm-like micelles in mixed nonionic fluorinated surfactants in an aqueous system are presented. 

Some Rheovibron viscoelasticity results have been reported for bimodal PDMS networks. Measurements are first carried out on uni-modal networks consisting of the chains used in combination in the bimodal networks. One of the important observations was the dependence of crystallinity on the network chain-length distribution. 

Disperse systems generally show complex viscoelastic behavior in the nonlinear region. The Lissajous figures observed in the linear region are elliptical, whereas in the nonlinear region they are skewed. To avoid this complex behavior, most of the dynamic measurements were only carried out in the linear region. In this section, some experimental results are shown for filler filled systems. 

For polyacrylamide there are two rheological effects which can be explained in terms of its random coil structure. Firstly, it was discussed above that polyacrylamide is much more sensitive than xanthan to solution salinity and hardness. This is explained by the fact that the salinity causes the molecular chain to collapse, which results in a much smaller molecule and hence in a lower viscosity solution. The second effect which can be explained in terms of the polyacrylamide random coil structure is the viscoelastic behaviour of this polymer. This is shown both in the dynamic oscillatory measurements and in the flow through the stepped capillaries (Chauveteau, 1981). When simple models of random chains are constructed, such as the Rouse model (Rouse, 1953 Bird et al, 1987), the internal structure of these bead and spring models gives rise to a spectrum of relaxation times, Analysis of this situation shows that these relaxation times define response times for the molecule, as indicated in the simple Maxwell model for a viscoelastic fluid discussed above. Thus, because of the internal structure of a flexible coil molecule, one would expect to observe some viscoelastic behaviour. This phenomenon is discussed in much more detail by Bird et al (1987b), in which a range of possible molecular models are discussed and the significance of these to the constitutive relationship between stress and deformation rate and deformation history is elaborated. 

The results of a number of studies on polymer rheology in porous media are then reviewed. Firstly, results for pseudoplastic fluids (mainly xanthan) are discussed and then results are reviewed for fluids showing some viscoelastic/extensional viscosity behaviour (e.g. HPAM, PEO). In all of these studies, flow is purely single-phase, and most experiments have been performed at 100% water saturation in the porous pack or core, although a few have been done at residual oil. 

The results presented in the previous sections assume that the contacting materials have well-defined elastic constants. In fact, most materials have at least some viscoelastic character, and it is important to understand how these effects should be taken into account. Viscoelastic effects enter into our analysis in two ways. First, it is possible that the overall elastic response of the system, described by the effective elastic constant, , is time-dependent. In the case where adhesion is present, the stress near the crack tip will be defined by stress intensity factors, K and K that are themselves time-dependent. A unique energy release rate cannot be defined in this case. We refer to this macroscopic manifestation of viscoelastic behavior as large-scale viscoelasticity . In this case one needs a procedure for determining the stress intensity factor that describes the current state of stress in the vicinity of the contact perimeter. Appropriate expressions for K are an essential result of treatments of large scale viscoelasticity, and these expressions are provided in Section 5.1. 

Since some of the constants involved in the equations are not known, it is not possible to obtain the absolute magnitude of the force of friction. Lumping the unknown constants, it is possible to obtain the nature of the variation of friction with speed if the viscoelastic properties are known. Some typical results are shown. Figure 11 shows the viscoelastic spectra H and L and the friction-speed relation derived by making use of that data. Figure 12 shows the calculated friction-speed curve for a SBR compound, which was obtained from the viscoelastic properties. 

McCartney, L.N. (1978) Crack propagation in linear viscoelastic solids some new results. Int. J. Fract. 14, 547-554... 

In the preceding sections, we have presented the material functions derived from various constitutive equations for steady-state simple shear flow. During the past three decades, numerous research groups have reported on measurements of the steady-state shear flow properties of flexible polymer solutions and melts. There are too many papers to cite them all here. The monographs by Bird et al. (1987) and Larson (1988) have presented many experimental results for steady-state shear flow of polymer solutions and melt. In this section we present some experimental results merely to show the shape of the material functions for steady-state shear flow of linear, flexible viscoelastic molten polymers and, also, the materials functions for steady-state shear flow predicted from some of the constitutive equations presented in the preceding sections. 

Ideally, the initial modulus and the incremental modulus should be the result of secondary bond stretching alone, and therefore, should give identical values for their respective flexural compliances. However, the initial compliance (or modulus) includes some viscoelastic deformation for deformation increments with very short relaxation times. After creeping for 3700 hours, all such short-time relaxations should have occurred such that flie incremental flexural compliance will be due to bond stretching alone. The corresponding incremental modulus (calculated as the inverse of the compliance) will be greater than the initial modulus determined on load up at the beginning of the creep test. 

The radiation and temperature dependent mechanical properties of viscoelastic materials (modulus and loss) are of great interest throughout the plastics, polymer, and rubber from initial design to routine production. There are a number of laboratory research instruments are available to determine these properties. All these hardness tests conducted on polymeric materials involve the penetration of the sample under consideration by loaded spheres or other geometric shapes [1]. Most of these tests are to some extent arbitrary because the penetration of an indenter into viscoelastic material increases with time. For example, standard durometer test (the "Shore A") is widely used to measure the static "hardness" or resistance to indentation. However, it does not measure basic material properties, and its results depend on the specimen geometry (it is difficult to make available the identity of the initial position of the devices on cylinder or spherical surfaces while measuring) and test conditions, and some arbitrary time must be selected to compare different materials. 

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. 

Most instmments make use of a probe geometry which gives an increasing area of contact as penetration proceeds. In this way, at some depth of penetration, the resisting force can become sufficient to balance the appHed force on the indentor. Unfortunately, many geometries, eg, diamonds, pyramids, and cones, do not permit the calculation of basic viscoelastic quantities from the results. Penetrometers of this type include the Pfund, Rockwell, Tukon, and Buchholz testers, used to measure indentation hardness which is dependent on modulus. 

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 ... 

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