Rates, shear

Corrosion and anti-wear protection Anti-corrosion and anti-wear power High viscosity at high shear rates... 

While the canal viscometer provides absolute viscosities and the effect of the substrate drag can be analyzed theoretically, the shear rate is not constant and the measurement cannot be made at a single film pressure as a gradient is required. Another basic method, more advantageous in these respects, is one that goes back to Plateau... 

The modification of the surface force apparatus (see Fig. VI-4) to measure viscosities between crossed mica cylinders has alleviated concerns about surface roughness. In dynamic mode, a slow, small-amplitude periodic oscillation was imposed on one of the cylinders such that the separation x varied by approximately 10% or less. In the limit of low shear rates, a simple equation defines the viscosity as a function of separation... 

Since emulsion droplets are not rigid spheres, the coefficient of 0 is around 3-6 for many emulsion systems [3-5], More concentrated emulsions are non-Newtonian depends on shear rate and are thixotropic (ri decreasing with... 

In amoriDhous poiymers, tiiis reiation is vaiid for processes tiiat extend over very different iengtii scaies. Modes which invoived a few monomer units as weii as tenninai reiaxation processes, in which tire chains move as a whoie, obey tire superjDosition reiaxation. On tire basis of tiiis finding an empiricai expression for tire temperature dependence of viscosity at a zero shear rate and tiiat of tire mean reiaxation time of a. modes were derived ... 

Flow behaviour of polymer melts is still difficult to predict in detail. Here, we only mention two aspects. The viscosity of a polymer melt decreases with increasing shear rate. This phenomenon is called shear thinning [48]. Another particularity of the flow of non-Newtonian liquids is the appearance of stress nonnal to the shear direction [48]. This type of stress is responsible for the expansion of a polymer melt at the exit of a tube that it was forced tlirough. Shear thinning and nonnal stress are both due to the change of the chain confonnation under large shear. On the one hand, the compressed coil cross section leads to a smaller viscosity. On the other hand, when the stress is released, as for example at the exit of a tube, the coils fold back to their isotropic confonnation and, thus, give rise to the lateral expansion of the melt. 

Colloidal dispersions often display non-Newtonian behaviour, where the proportionality in equation (02.6.2) does not hold. This is particularly important for concentrated dispersions, which tend to be used in practice. Equation (02.6.2) can be used to define an apparent viscosity, happ, at a given shear rate. If q pp decreases witli increasing shear rate, tire dispersion is called shear tliinning (pseudoplastic) if it increases, tliis is known as shear tliickening (dilatant). The latter behaviour is typical of concentrated suspensions. If a finite shear stress has to be applied before tire suspension begins to flow, tliis is known as tire yield stress. The apparent viscosity may also change as a function of time, upon application of a fixed shear rate, related to tire fonnation or breakup of particle networks. Thixotropic dispersions show a decrease in q, pp with time, whereas an increase witli time is called rheopexy. 

Pseudoplastic fluids have no yield stress threshold and in these fluids the ratio of shear stress to the rate of shear generally falls continuously and rapidly with increase in the shear rate. Very low and very high shear regions are the exceptions, where the flow curve is almost horizontal (Figure 1.1). 

A common choice of functional relationship between shear viscosity and shear rate, that u.sually gives a good prediction for the shear thinning region in pseudoplastic fluids, is the power law model proposed by de Waele (1923) and Ostwald (1925). This model is written as the following equation... 

Dilatant fluids (also known as shear thickening fluids) show an increase in viscosity with an increase in shear rate. Such an increase in viscosity may, or may not, be accompanied by a measurable change in the volume of the fluid (Metzener and Whitlock, 1958). Power law-type rheologicaJ equations with n > 1 are usually used to model this type of fluids. 

Incorporation of viscosity variations in non-elastic generalized Newtonian flow models is based on using empirical rheological relationships such as the power law or Carreau equation, described in Chapter 1. In these relationships fluid viscosity is given as a function of shear rate and material parameters. Therefore in the application of finite element schemes to non-Newtonian flow, shear rate at the elemental level should be calculated and used to update the fluid viscosity. The shear rale is defined as the second invariant of the rate of deformation tensor as (Bird et at.., 1977)... 

Figure 5,16. It is assumed that by using an exactly symmetric cone a shear rate distribution, which is very nearly uniform, within the equilibrium (i.e. steady state) flow held can be generated (Tanner, 1985). Therefore in this type of viscometry the applied torque required for the steady rotation of the cone is related to the uniform shearing stress on its surface by a simplihed theoretical equation given as...

In the Couette flow inside a cone-and-plate viscometer the circumferential velocity at any given radial position is approximately a linear function of the vertical coordinate. Therefore the shear rate corresponding to this component is almost constant. The heat generation term in Equation (5.25) is hence nearly constant. Furthermore, in uniform Couette regime the convection term is also zero and all of the heat transfer is due to conduction. For very large conductivity coefficients the heat conduction will be very fast and the temperature profile will... 

Step 3 - using the calculated velocity field, find the shear rate and update viscosity using the power law model. 

Calculate V2(vjlr ) and add this value to the previously calculated value of the shear rate. 

Figure 2.5 Shearing force per unit area versus shear rate. The experimental points are measured for polyethylene, and the labeled lines are drawn according to the relationship indicated. (Data from J. M. McKelvey, Polymer Processing, Wiley, New York, 1962.)...

The power law developed above uses the ratio of the two different shear rates as the variable in terms of which changes in 17 are expressed. Suppose that instead of some reference shear rate, values of 7 were expressed relative to some other rate, something characteristic of the flow process itself. In that case Eq. (2.14) or its equivalent would take on a more fundamental significance. In the model we shall examine, the rate of flow is compared to the rate of a chemical reaction. The latter is characterized by a specific rate constant we shall see that such a constant can also be visualized for the flow process. Accordingly, we anticipate that the molecular theory we develop will replace the variable 7/7. by a similar variable 7/kj, where kj is the rate constant for the flow process. 

The phenomenon under consideration is complicated and the theory developed in the last section is fairly simple-involved, but not really difficult. We have successfully discovered that the transition from Newtonian to pseudoplastic behavior is governed by the product 77, or the relative values of the shear rate and the rate of molecular response. 

Figure 2.9 F /A versus shear rate for natural rubber. The line is drawn according to a two-term version of the Eyring theory. (Redrawn from Ref. 5.)...

Wagner and DUlont have described a low-shear viscometer in which the inside diameter of the outer, stationary cylinder is 30 mm and the outside diameter of the inner, rotating cylinder is 28 mm the rotor is driven by an electromagnet. The device operates at 135°C and was found to be free of wobble and turbulence for shear rates between 3 and 8 sec V The conversion of Eq. (2.7) to Eq. (2.9) shows that F/A = (i7)(dv/dr) (instrument constant) for these instruments Evaluate the instrument constant for this viscometer. 

Shaving products Shaw process Shear breeding Shear energy Shearlings Shearometer Shear plane Shear rate Shear stresses Shear test Shear thinning behavior Shear viscosity Sheath-core fiber... 

Minimization of the elastic behavior of the fluid at high deformation rates that are present when high molecular weight water-soluble polymers are used to obtain cost-efficient viscosities at low shear rates. 

In packed beds of particles possessing small pores, dilute aqueous solutions of hydroly2ed polyacrylamide will sometimes exhibit dilatant behavior iastead of the usual shear thinning behavior seen ia simple shear or Couette flow. In elongational flow, such as flow through porous sandstone, flow resistance can iacrease with flow rate due to iacreases ia elongational viscosity and normal stress differences. The iacrease ia normal stress differences with shear rate is typical of isotropic polymer solutions. Normal stress differences of anisotropic polymers, such as xanthan ia water, are shear rate iadependent (25,26). 

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