Shear viscosity, extensional flow

It is well known that LCB has a pronounced effect on the flow behavior of polymers under shear and extensional flow. Increasing LCB will increase elasticity and the shear rate sensitivity of the melt viscosity ( ). Environmental stress cracking and low-temperature brittleness can be strongly influenced by the LCB. Thus, the ability to measure long chain branching and its molecular weight distribution is critical in order to tailor product performance. 

Oscillatory shear experiments are the preferred method to study the rheological behavior due to particle interactions because they directly probe these interactions without the influence of the external flow field as encountered in steady shear experiments. However, phenomena that arise due to the external flow, such as shear thickening, can only be investigated in steady shear experiments. Additionally, the analysis is complicated by the different response of the material to shear and extensional flow. For example, very strong deviations from Trouton s ratio (extensional viscosity is three times the shear viscosity) were found for suspensions [113]. 

Figure 9.14 Droplet deformation as a function of the duration of deformation for different flow fields (ratio of shear and extensional flow) for a viscosity ratio of X = 3 the larger a, the larger the ratio of extensional flow a=0 corresponds to pure shear flow...

Patzold (1980) compared the viscosities of suspensions of spheres in simple shear and extensional flows and obtained significant differences, which were qualitatively explained by invoking various flow-dependent sphere arrangements. Goto and Kuno (1982) measured the apparent relative viscosities of carefully controlled bidisperse particle mixtures. The larger particles, however, possessed a diameter nearly one-fourth that of the tube through which they flowed, suggesting the inadvertant intrusion of unwanted wall effects. 

Gibson and Williamson (1985b, 1985a) examined the shear and extensional flow of BMC materials in injection moulding. Extensional and shear viscosities are found to be important in injection moulding, and here they use the following power-law relationships ... 

Kennedy, J.C., Meadows, J. and Williams, PA. (1995) Shear and extensional viscosity characteristics of a series of hydrophobically associating polyelectrolytes. /. Chem. Soc. Faraday Trans., 91,911-916. Andrews, N.C., McHugh, A.J. and Schieber, J.D. (1998) Polyelectrolytes in shear and extensional flows conformation and rheology. /. Polym. Sei., PartB Poly. Phys., 36,1401-1417. 

The important rheological properties which need to be studied and measured in order to be able to characterize suspensions are the same as those which have already been indicated in Chapter 2. However, only the viscous flow behavior in shear and extensional flow will be discussed in this chapter. In particular, shear viscosity will be dealt with in sufficient detail because of the wealth of information that exists on it. 

Figure 7.19 shows the time dependent viscosities derived from Eqs. (7.143) and (7.154) for both simple shear and extensional flow. For simplicity a single exponential relaxation with a relaxation time r is assumed for The... 

Fig. 7.19. Time dependent viscosities for shear and extensional flow, and as predicted by Lodge s equation of state. Calculations are performed for different Hencky strain rates en, assuming a single exponential relaxation modulus G(t) exp — t/r...

The influence of deformation rate, type of flow, and viscosity ratio on the deformation of droplets in shear and extensional flow. At high deformation rates (right-hand shapes) drop breakup can occur. Adapted from Rum-scheidt and Mason fl961). 

In addition to investigations on elasticity, also the dynamics of droplets consisting of shear thinning or yield stress fluids has received some attention. Both for shear and extensional flow, it has been found that shear thinning of the droplet fluid reduces the deformation as compared to that of a Newtonian droplet with the same viscosity at the applied shear rate [84,85]. Desse et al. [86] showed that the dependence of the critical Cfl-number on viscosity ratio for a starch suspension droplet with a yield stress deviates substantially from that of Newtonian droplets. In conclusion, the precise relations between the rheological constitutive parameters of droplet and matrix fluid and the droplet dynamics for materials with a complex rheology are far from fully revealed. 

Figure 9.21 shows the time-dependent viscosities derived from Eqs. (9.178) and (9.189) for both simple shear and extensional flow. For simplicity a single exponential relaxation with a relaxation time t is assumed for G t"). The dotted line represents the time-dependent viscosity for simple shear, which is independent of 7. A qualitatively different result is found for the extensional flow. As we can see, the time-dependent extensional viscosity ff t) increases with ch and for en > 0.5t a strain hardening arises. 

First, we examine the results from the rheology experiments performed on the two PHA samples. We report on both shear and extensional flow experiments. Figure 3 displays the dynamic oscillatory shear results for the two PHA samples. It can be observed that Sample II has a higher zero-shear viscosity. This difference can be explained by the greater molecular weight of Sample II. 

Extensional flow describes the situation where the large molecules in the fluid are being stretched without rotation or shearing [5]. Figure 4.3.3(b) illustrates a hypothetical situation where a polymer material is being stretched uniaxially with a velocity of v at both ends. Given the extensional strain rate e (= 2v/L0) for this configuration, the instantaneous extensional viscosity r e is related to the extensional stress difference (oxx-OyY), as... 

Fig. 22. Radius of drops produced by capillary breakup (solid lines) and binary breakup (dotted lines) in a hyperbolic extensional flow for different viscosity ratios (p) and scaled shear rate (p,cylo) (Janssen and Meijer, 1993). The initial amplitude of the surface disturbances is ao = 10 9 m. Note that significantly smaller drops are produced by capillary breakup for high viscosity ratios.

However, this expression assumes that the total resistance to flow is due to the shear deformation of the fluid, as in a uniform pipe. In reality the resistance is a result of both shear and stretching (extensional) deformation as the fluid moves through the nonuniform converging-diverging flow cross section within the pores. The stretching resistance is the product of the extension (stretch) rate and the extensional viscosity. The extension rate in porous media is of the same order as the shear rate, and the extensional viscosity for a Newtonian fluid is three times the shear viscosity. Thus, in practice a value of 150-180 instead of 72 is in closer agreement with observations at low Reynolds numbers, i.e.,... 

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