Elasticity visco

A considerable number of experimental extensions have been developed in recent years. Luckliam et al [5] and Dan [ ] review examples of dynamic measurements in the SFA. Studying the visco-elastic response of surfactant films [ ] or adsorbed polymers [7, 9] promises to yield new insights into molecular mechanisms of frictional energy loss in boundary-lubricated systems [28, 70]. 

Polyethylene can be compounded on any of the standard types of mixing equipment used for visco-elastic materials. For laboratory purposes a two-roll mill is suitable operating temperatures varying from about 90°C to about 140°C according to the type of polymer. On the industrial scale, compounding is undertaken either in internal mixers, or more particularly, extrusion compounders. 

The help of many collegues is gratefully acknowledged The polyglycidyl compound was synthesized by Dr. Ch. Monnier. Ms. Ch. Irrgang and Dr. J. Vogt studied visco-elasticity and Dr. W. Sieber provided results on the density of the polymers. Mr. D. Martin and Mr. P. Rohrbasser assisted the experimental work. 

See literature on visco-elasticity, for example J.D. Ferry, The Visco-elastic Properties of Polymers, 3rd Ed, Wiley, New York, 1980. 

Visco-elastic fluids like pectin gels, behave like elastic solids and viscous liquids, and can only be clearly characterized by means of an oscillation test. In these tests the substance of interest is subjected to a harmonically oscillating shear deformation. This deformation y is given by a sine function, [ y = Yo sin ( t) ] by yo the deformation amplitude, and the angular velocity. The response of the system is an oscillating shear stress x with the same angular velocity . 

The mathematical dependence applies only in the linear visco-elastic region. In this region the sample can be deformed up to a maximum deformation (yo, ax) without destroying the structure of the sample. 

Visco-elastic substances can be described with the spring/shock-absorber model of Kevin and Voigt, and have phase displacements of 0° to 90°. In analogy to other time dependent processes in physics, the oscillation tests are evaluated with complex arithmetics. Obtained are the complex quantities ... 

The linear visco-elastic range ends when the elastic modulus G starts to fall off with the further increase of the strain amplitude. This value is called the critical amplitude yi This is the maximum amplitude that can be used for non-destructive dynamic oscillation measurements... 

Figure. 9 Visco-elastic range of pectin gels Strain frequency sweep...

Gels made from citrus pectin have a small linear visco-elastic range. To puncture the gels takes a big but only short time effort. The gel breaks into small lumps immediately. In the... 

These data show clearly that that the intrinsic behavior in pure metals is visco-elastic with the velocity proportional to the applied stress (Newtonian viscosity). Although there is a large literature that speaks of a quasi-static Peierls-Nabarro stress, this is a fiction, probably resulting from studying of insufficiently pure metals. 

Silicone oils have very desirable visco-elastic properties, and are very stable. They have been used for many years for breast implants, as a cosmetic to improve appearance. There are many lawsuits charging that silicone oil can leak out of the containing sacks and cause adverse physiological reactions. The current customers either abandon the breast implant or use salt water implants, which do not have the same desirable viscoelastic properties. 

Yamamoto M. The visco-elastic properties of network structure. 1. General formalism. J Phys Soc Jpn 1956 11 413-421. 

A more detailed discussion of the visco-elastic properties of rubber-like elastomers for composite propellants was recently given in a paper by Landel and T. L. Smith [8]. 

A final remark should be made as to the validity of eq. (2.13). This equation suggests the existence of a set of independent relaxation mechanisms. A general proof for the existence of such mechanisms could be given for visco-elastic solids in terms of the thermodynamics of irreversible processes (52) at small deviation from equilibrium. For liquid systems, however, difficulties arise from the fact that in these systems displacements occur which are not related to the thermodynamic functions. 

As mentioned in Section 2.2, in the theory of dilute solutions the single polymer chain is treated as a separate visco-elastic system. From this point of view a short review of the pertinent general theory seems desirable. 

The well-known theory of Zimm (80) for an infinitely dilute solution of chain molecules will be discussed in more detail. Other theories are considered as special cases [Rouse (16), Bueche (53)] or refinements [Ptitsyn and Eizner (84), Hearst (85) and Tschoegl (36)]. If a linear polymer chain is built up of IV subchains, there are IV — 1 junction-points and two end-points. At these points beads of equal diameter are assumed. In this way the hydrodynamic interaction with the solvent is accomplished. The positions of the said IV + 1 beads are described by 3 (IV + 1) Cartesian coordinates. This system is considered as a visco-elastic system in the sense of the previous section. 

In general these factors determine cost, mechanical and visco-elastic properties, resistance to degrading environments and influences, processing characteristics of the compound, and special requirements such as flame resistance, oil resistance, low temperature flexibility, chemical resistance wear and abrasion resistance and non-toxicity requirements for application in contact with foodstuff, etc. 

The first reports on the drag reduction phenomenon are found in publications by Blatch (1906), Forrest (1931), as well as by Brautlecht (1933), who measured the flow behaviour of paper pulps. In independent studies made by Mysels (1949) and Toms (1948) this phenomenon was observed in the turbulent flow of gasoline in pipes when aluminum soaps were added and, in Toms experiments, when polymethylmethacrylate in monochlorobenzene was used. The reduction of friction is therefore often termed the Toms effect . This flow behaviour is also known in the literature as the Non-Newtonian- , visco-elastic- , Texas- or Texas-Toms-effect , due to the contributions made by Texan researchers. It is also more generally known, and this term will be used in this paper exclusively, as the drag-reduction effect of flow additives. 

Assuming T>Tg for reversible flow processes (visco-elastic behaviour) Eq. (32) yields... 

---