Viscoelastic solution

Failure can be considered as an actual rupture (stress-rupture) or an excessive creep deformation. Correlation of stress relaxation and creep data has been covered as well as a brief treatment of the equivalent elastic problem. The method of the equivalent elastic problem is of major assistance to designers of plastic products since, by knowing the elastic solution to a problem, the viscoelastic solution can be readily deduced by simply replacing elastic physical constants with viscoelastic constants. 

Fano columns are most easily formed in viscoelastic solutions where extensional viscosities exceed shear viscosities by several orders of magnitude. 

Figure 3.10 Example of the "Weissenberg Effect" for a viscoelastic solution. Stirrer is rotated (n=200 s 1) in a glass beaker containing aqueous PEO solution (c=1wt.-%. Polyox WSR 301). The solution climbs up the stirrer shaft due to normal stress effects...

Figure 3.21 Pouring a viscoelastic solution with high extensional viscosity (open siphon effect).

As a consequence of their tendency to form lamellar phases or rod shaped micelles at low concentration, cationic surfactants are frequently employed as the primary surfactants to thicken high salt formulas [72,73]. The viscoelastic nature of certain cationic surfactant solutions has been employed in a novel way to allow for a solution of sodium hypochlorite not to be easily diluted and therefore to remain at a higher concentration for the purpose of oxidizing clogs of human hair which form in drains [73 ]. Low concentrations of cetyl trimethyl ammonium chloride in combination with two hydro tropes form viscoelastic solutions with the values of viscosity and Tau/Go shown in Table 6.6. 

The gas-liquid mass-transfer coefficient for non-Newtonian and viscoelastic solutions has been extensively studied by Yagi and Yoshida (1975). The... 

Finally we comment briefly on weakly elastic fluids. (See [26] and section 3.2.) We assume that the given Newtonian solution v satisfies ] v i < (ciRe), where Ci is some constant depending only on the domain of the flow this condition ensures that v is asymptotically Liapunov stable. (See e.g., [67].) Then, the viscoelastic solution (v ,Tt) close to (v, 0) is linearly (asymptotically) stable for c > 0 small enough. 

We note that elastic and viscoelastic solutions have the same formal structure. For a step temperature input, the inverse Laplace of Eq. (P16.5.12) is given by... 

For a sinusoidal steady excitation and small deflections, the elastic and viscoelastic solutions are formally similar, as the separation of variables methodology outlined above suggests. Thus, in this case, the viscoelastic response is dependent on only the specific material properties of the sample under study. Moreover, on the basis of one of the hypotheses mentioned above, the thermoviscoelastic problem can be reduced to a thermoelastic one. Therefore, in the present context only the elastic solution of the problem will be discussed. 

The simplest mechanical model which can describe a viscoelastic solution is called Maxwell element. It consists of a spring and a viscous element (dashpot) connected in series. The spring corresponds to a shear modulus Gq and the dashpot to a viscosity r). The behavior of the Maxwell element under harmonic oscillations can be obtained from the following equations ... 

The use of a rheology modifier such as HEC or xanthan gum that produces a viscoelastic solution which prevents not only creaming or sedimentation but also entrapment of the oil droplets in between the suspension particles, or the suspension particles in between the emulsion droplets. 

Viscoelastic stress analysis of two component systems shows that a broadening of the dispersion zone is to be expected 166,167), even if the disperse phase (filler) is purely elastic 166) and it is not necessary to ascribe different molecular properties to the continuous phase. The simplest way to visualize this mechanical interaction is by the use of phenomenological mechanically equivalent models. The model of Takayanagi (/68) is illustrated in Fig. 16. The elastic solution for this model is easily derived from elementary considerations. By the correspondence principle of viscoelastic stress analysis 169), the viscoelastic solution is obtained simply by substituting complex moduli in place of purely elastic moduli... 

Linear viscoelastic solutions from stress analysis handbooks Relatively quick. Small strain effects only. Simple, accepted material laws. Standard geometries only. Some material testing may be required. 

The deformability of the viscoelastic drops in Newtonian matrix was studied in the convergent slit flow. Both, the experimental observations and the boundary element method computations were carried out. It was reported that deformation of the Boger fluid drop, was quite low —about 1/3 of that recorded for the deformability of a strongly shear-thinning, viscoelastic solution. The latter drops showed deformability similar to these observed for Newtonian drops of similar viscosities. 

Interpreting the results of flow visualization and measurement takes theory, and theory requires flow properties viscosities as functions of shear and extension rates, peculiar viscoelastic parameters if the coating liquid is mildly viscoelastic solution, surface tension... 

Whitsitt, N. F., Harrington, L. J., and Crawford, H. R., Effect of waU shear stress on drag reduction of viscoelastic solutions, in Proceedings of the Symposium on Viscous Drag Reduction, DaUas, TX, WeUs, C. S., Ed., Plenum Press, New York, 1969, pp. 265-280. 

Naidu, B. V. K., Sairam, M., Raju, K. V. S. N., and Aminabhavi, T. M. 2005. Thermal, viscoelastic, solution and membrane properties of sodium alginate/ hydroxyethylcellulose blends. Carbohydrate Polymers 61 52-60. 

On the other hand, the Tr of the viscoelastic solutions at low concentrations, for ejample, in a 3 wt% surfactant system, first increases promptly with increasing temperature, reaches the maximum value at -20 °C, and then decreases. When the surfactant concentration increases from 3 to 5 wt% and above, the trend remains essentially the same, but the position of the Tr maximum slowly moves to lower temperature. At higher concentrations of surfactant (e.g., at 10 and 15 wt%), the Tr maxima are around 5 °C. No maximum is seen at 25 wt% surfactant concentration, but Tr starts decreasing from 5°C. However, judging from the trends of the Tr—T curves, the Tr maxima for these concentrations is expected to... 

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