Shear thinning materials flow curve

Mathematical models, which can predict the shape of a flow curve of a shear thinning material including lower and upper Newtonian regions, require at least four parameters. The Cross model is one such model ... 

Some shear-thinning materials deform like elastic solids until a certain stress, known as the yield stress, is reached, after which they deform as normal shear-thinning liquids. These materials are described as shear thinning with yield value, and have a consistency curve like curve 2 of Fig. 6.3. Flow ceases when the stress falls below the yield stress. Materials which show this behaviour include toothpaste and muds. These substances also tend to be thixotropic. 

A number of mathematical models have been proposed for yield stress fluids, not all perfectly coherent however. If a shear thinning material is tested with one of several rheometers and the results plotted in terms of shear stress o vs. shear rate y (the so-called flow curve) using linear scales, one is nearly bound to the conclusion that there is a yield stress and that the best manner to model the observed behavior consists in considering the following equality 0 = 0,+ /(y). 

Rheology concerns the study of the deformation and flow of soft materials when they respond to external stress or strain. If the ratio of its shear stress and shear rate is a straight line, the material is termed Newtonian otherwise, it is termed non-Newtonian (Figure 4.3.2(a)). As the slope of the curve is the viscosity rj, a shear-thinning fluid exhibits a reduced viscosity as the shear stress increases, whereas a shear-... 

Many fluids show a decrease in viscosity with increasing shear rate. This behavior is referred to as shear thinning, which means that the resistance of the material to flow decreases and the energy required to sustain flow at high shear rates is reduced. These materials are called pseudoplastic (Fig. 3a and b, curves B). At rest the material forms a network structure, which may be an agglomerate of many molecules attracted to each other or an entangled network of polymer chains. Under shear this structure is broken down, resulting in a shear... 

Under conditions of steady fully developed flow, molten polymers are shear thinning over many orders of magnitude of the shear rate. Like many other materials, they exhibit Newtonian behaviour at very low shear rates however, they also have Newtonian behaviour at very high shear rates as shown in Figure 1.20. The term pseudoplastic is used to describe this type of behaviour. Unfortunately, the same term is frequently used for shear thinning behaviour, that is the falling viscosity part of the full curve for a pseudoplastic material. The whole flow curve can be represented by the Cross model [Cross (1965)] ... 

Figure 6.55 presents the pressure profiles within the material for various melt flow front locations. First of all, we can see that the shear thinning behavior of the polymer has caused the pressure requirement to go down significantly (by a factor of 30). The curves presented in Fig. 6.55 also reveal that the shape of the curves was also affected when compared to the Newtonian profiles. 

If the material to be processed is subject to shear thinning, the linear relationships for the pressure and energy behavior illustrated above no longer apply. With shear thinning, there is a non-linear relationship between the shear rate and shear stress that is reflected in the flow curve (see Chapter 3). As a rule, the zero viscosity and one or two rheological time constants are enough to describe the flow curve with sufficient accuracy. The Carreau equation is often used it contains a dimensionless flow exponent in addition to the zero viscosity and a rheological time constant. 

The rotational speed, which only appeared as a parameter in the linear Eqs. 7.1 and 7.4, forms now an independent dimensionless parameter in the form of the Deborah number n . While the dimensionless pressure generation and dimensionless energy only depend on the kinematic parameter of flow for Newtonian liquids, the dimensionless revolution speed appears as an additional influencing variable for shear thinning. This is plausible if we consider that the rotational speed is a measure of the shear stresses on the material, and thus influences the effective viscosity of the material. It is also to be expected that the interaction will assume a non-linear form since the flow curve is already non-linear. 

Shear thickening materials show an increase in viscosity with increasing shear strain rate. An idealized flow curve is presented in Fig. 6, and the viscosity as a function of shear strain rate is depicted in Fig. 7. The shear thinning region usually extends only over about one decade of shear rate (power law index n > 1) in contrast to shear thinning, which usually covers at least two or three decades. Also, in many cases, shear thickening is preceded by a short phase of shear thinning at low shear strain rates. ° ... 

In some cases the very act of deforming a material can cause rearrangement of its microstructure such that the resistance to flow increases with an increase of shear rate. In other words, the viscosity increases with appHed shear rate and the flow curve can be fitted with the power law. Equation (20.3), but in this case n> 1. The shear thickening regime extends over only about a decade of shear rate. In almost all cases of shear thickening, there is a region of shear thinning at low shear rates. 

Procedmes for extracting valid shear stress versus shear rate data from measurements involving wide gap coaxial cylinder systems (the Brookfield viscometer being an extreme example of wide gap devices) are therefore of considerable interest in making quantitative measurements of the flow properties of non-Newtonian process products. Most of these data-treatment procedures necessarily involve some assumption regarding the functional form of the flow curve of the material. One example is that made in the derivation of data from the Brookfield-type instrument, which assumes that the speed of rotation of the cylinder or spindle is proportional to the shear rate experienced by the fluid. This assumption implies that the flow curve is adequately described by a simple power-law (which for many shear-thinning non-Newtonian fluids may be acceptable), but this assiunption is widely taken to exclude all fluids which display an apparent yield stress and/or non-power law type behaviour. 

Figure 6 Two dimethyl silicone oils. The flow curves show Newtonian behaviour for stress below = 4 kPa. Strong shear thinning effects are seen at stresses above 4 kPA. Heating effects can be expected to be significant only above stresses of 100 kPa. Both materials remain liquid. Deviation from Newtonian properties Increases with degree of polymerization. L/D 54.2 and 5.33, 37.78 C, Pressure s.1 MPa. (11).

When the adhesive is supplied in a tube or container, force is required for application of the material. Viscosity recovery may be an issue. As force is applied and the shear rate increases, the viscosity will probably change (most commonly, it will decrease). After having been sheared, if the material does not recover to a fairly high viscosity, it may not stay where it is put, which can be a problem. A simple two-step flow curve, which only takes two minutes, assesses both the degree of shear thinning behavior and the recovery. 

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