Shear viscosity function, effect

The shear thinning behavior, as generally observed with polymer systems, is a typical nonlinear viscoelastic effect, so that by combining the Carreau-Yasuda and the Arrhenius equations a general model for the shear viscosity function can be written as follows ... 

Typical effects of carbon blacks on the shear viscosity function are illustrated in Figure 5.2, drawn using data published by Montes et al. Three types... 

Effects of carbon black on the shear viscosity function. (Data from S. Montes, J.L. White, N. Nakajima, /. Non-Newtonian Fluid Mech., 28,183-212,1988.)... 

Effect of carbon black loading in the shear viscosity function of LDPE and PS melts. (Drawn using data by M. Lobe, J.L. White, Polym. Eng. Sci., 19,617-624.)... 

There is however an aspect which is qualitatively common to all filler-thermoplastic systems the linear viscoelastic behavior exhibited by most pure polymers at sufficiently low strain or low rate of deformation disappear above a sufficient filler level. For instance, the so-called Newtonian plateau on the shear viscosity function is no longer observed, the d5mamic modulus is strongly strain dependent and the terminal region in the elastic modulus function disappears and is replaced by a low frequency plateau. As we have seen, such typical effects are also observed with filled rubber compounds. 

The above discussion easily motivates the notion that reorientation times will become long as the liquid is cooled towards the glass transition, but it does not explain the shape of the observed relaxation function. Part of the shear viscosity in fluids is due to coupling to molecular reorientation. This effect has been studied in detail in alkane liquids26,27. At low viscosities the shear modulus can be described by... 

Figure 10 Shear viscosity as a function of shear rate for water layers of various thickness, D, compared to bulk NEMD simulation and experiment. For D<0.92 the effective viscosity of the confined water is comparable in magnitude to that of the bulk at all shear rates studied. Reprinted figure with permission from 441. Copyright 2005 by the American Physical Society...

Steady state shear stress a-shear rate y measurements This requires the use of a shear rate-controlled instrument, and the results obtained can be fitted to models to obtain the yield value Up and the viscosity as a function of shear rate. Time effects (thixotropy) can also be investigated. 

The measurement of yield stress at low shear rates may be necessary for highly filled resins. Doraiswamy et al. (1991) developed the modified Cox-Merz rule and a viscosity model for concentrated suspensions and other materials that exhibit yield stresses. Barnes and Camali (1990) measured yield stress in a Carboxymethylcellulose (CMC) solution and a clay suspension via the use of a vane rheometer, which is treated as a cylindrical bob to monitor steady-shear stress as a function of shear rate. The effects of yield stresses on the rheology of filled polymer systems have been discussed in detail by Metzner (1985) and Malkin and Kulichikin (1991). The appearance of yield stresses in filled thermosets has not been studied extensively. A summary of yield-stress measurements is included in Table 4.6. 

Both liquid fabric softeners exhibit time-dependent shear effects as shown in step shear rate measurements at room temperature. Figure 4.27 summarizes the steady shear viscosity as a function of time at shear rates of 0.1,0.5,1, and 5 sec-1. Each shear rate is held for a period of 30 sec. 

The zero-shear viscosity rip is defined as the melt viscosity in the limit of y=0, and is a function of T and Mw. It is important to keep in mind, however, that rp) is very often not measured directly, but extrapolated from measurements at low shear rates. Such extrapolations can introduce an error in the value of r o if the range of shear rates used in the extrapolation is sufficiently high for non-Newtonian effects to begin manifesting themselves. 

The effect of overall molecular weight or the number of blocks on rheological properties for the samples from the second fractionation can be illustrated as a plot of reduced viscosity vs. a function proportional to the principal molecular relaxation time (Figure 2). This function includes the variables of zero shear viscosity, shear rate, y, and absolute temperature, T, in addition to molecular weight, and allows the data to be expressed as a single master curve (10). All but one of the fractions from the copolymer containing 50% polystyrene fall on this... 

An integration over all orientations of the vector R has been effected in these equations. The first term arises from momentum transport from mass motion and can be neglected in comparison with the second term. The indicated integration of Eq. 42 has been carried out numerically. That of Eq. 43 proved to be too sensitive to variation in the radial distribution function g0(2) to yield reliable results. In order to obtain the shear viscosity r), it is now necessary to evaluate the frictional coefficient f. A solution in series was obtained by Kirkwood25 but its numerical evaluation is too unwieldy for practical calculations. The analysis, however, stiggests the following estimate for the frictional coefficient ... 

In this case it is no longer sufficient for one to use the constant viscosity of Newtonian fluid ( Newtonian viscosity ), r = x/y = dx/dy, as a single characteristic of the system. The so-called effective viscosity, r ef, along with the differential viscosity, dx/dy (which in this case is also the function of y), are thus introduced. At low strain rate (low shear stress) the effective viscosity is maximal. When the applied stress is increased further, the effective viscosity decreases to some minimal value and then remains unchanged with... 

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