Flow models viscosity, rheological measurements

Many materials are conveyed within a process facility by means of pumping and flow in a circular pipe. From a conceptual standpoint, such a flow offers an excellent opportunity for rheological measurement. In pipe flow, the velocity profile for a fluid that shows shear thinning behavior deviates dramatically from that found for a Newtonian fluid, which is characterized by a single shear viscosity. This is easily illustrated for a power-law fluid, which is a simple model for shear thinning [1]. The relationship between the shear stress, a, and the shear rate, y, of such a fluid is characterized by two parameters, a power-law exponent, n, and a constant, m, through... 

Abstract. The viscosity is a physical parameter which controls not only the melting and fining of melts, but also the stress relaxation and the nucleation and crystallization phenomena. Here the basis of viscous flow is presented and discussed. Rheological models and some measurement methods fiber extension, beam bending and indentation are described. 

RhGOlogy. Flow properties of latices are important during processing and in many latex applications such as dipped goods, paint, and fabric coatings. Rheology is used to characterize the stability of latices (45). For dilute, nonionic latices, the relative latex viscosity is a power-law expansion of the particle volume fraction. The terms in the expansion account for flow aroimd the particles and particle-particle interactions. For ionic latices, electrostatic contributions to the flow around the diffuse double layer and enhanced particle-particle interactions must be considered (46). A relative viscosity relationship for concentrated latices was first presented in 1972 (47). A review of empirical relative viscosity models is available (46). In practice, latex viscosity measurements are carried out with rotational viscometers (see Rheological Measurements). 

During the experiments, the solid concentration was increased to 20% by volume. Except for suspensions with plastic particles, the suspensions showed a Newtonian behavior up to volume contents of 15 %. Suspensions with glass beads and s = 0.2 as well as all examined suspensions with plastic particles showed a shear thinning behavior. Considering the non-Newtonian behavior of these suspensions in the calculation of the time steady flow based on Eqs. (5.9-5.21), the viscosity of the suspension had to be described by a model depending on the deformation speed y. A Carreau-Yasuda model according to Eq. (5.52) fitted well to measurements carried out with a Couette system. The parameters Hq, a, n, and X were determined by the rheological measurements. 

Flow curves - Melt rheological properties of PES were evaluated on a capillary instrument attached to a Shimadzu Universal Materials Testing Machine model AG-IOTA. Viscosity curves measured at 315, 330 and 350°C and for shear rates ranging from 10 to 10000 1/s are presented in Figure 1. A typical pseudo-plastic behavior can be seen. That is, the melt viscosities of PES decrease with the increase of apparent shear rates. 

The sample is subjected to compression by moving the crosshead downwards at a constant speed. The sample is extruded from between the two discs, undergoing elongational or biaxial flow the sample is stretched radially and azimuthally as it flows outwards between the approaching discs. Lubrication ensures that shear flow cannot occur. Elongational viscosity is calculated directly from the measured force-distance data, disc radius and crosshead speed no rheological model is required (Campanella and Peleg, 2002). 

We can see that Eqs. (2 101) (2-104) are sufficient to calculate the continuum-level stress a given the strain-rate and vorticity tensors E and SI. As such, this is a complete constitutive model for the dilute solution/suspension. The rheological properties predicted for steady and time-dependent linear flows of the type (2-99), with T = I t), have been studied quite thoroughly (see, e g., Larson34). Of course, we should note that the contribution of the particles/macromolecules to the stress is actually quite small. Because the solution/suspension is assumed to be dilute, the volume fraction is very small, (p 1. Nevertheless, the qualitative nature of the particle contribution to the stress is found to be quite similar to that measured (at larger concentrations) for many polymeric liquids and other complex fluids. For example, the apparent viscosity in a simple shear flow is found to shear thin (i.e., to decrease with increase of shear rate). These qualitative similarities are indicative of the generic nature of viscoelasticity in a variety of complex fluids. So far as we are aware, however, the full model has not been used for flow predictions in a fluid mechanics context. This is because the model is too complex, even for this simplest of viscoelastic fluids. The primary problem is that calculation of the stress requires solution of the full two-dimensional (2D) convection-diffusion equation, (2-102), at each point in the flow domain where we want to know the stress. 

While various methods and equipment can be used to measure viscosity, the most common uses the Brookfield viscometer (Fig. 7.1). ASTM D2196, Rheological Properties of Non-Newtonian Materials by Rotational (Brookfield) Viscometer, covers this method for Model LVF and Model RVF viscometers. Brookfield LV viscometers are used for low-viscosity materials, RV for medium-viscosity formulations, and HV for high-viscosity formulations. Test Method ASTM D2556, Apparent Viscosity of Adhesives HavingShear-Rate Dependent Flow Properties also specifies... 

Most polymer processes are dominated by the shear strain rate. Consequently, the viscosity used to characterize the fluid is based on shear deformation measurement devices. The rheological models that are used for these types of flows are usually termed Generalized Newtonian Fluids (GNF). In a GNF model, the stress in a fluid is dependent on the second invariant of the stain rate tensor, which is approximated by the shear rate in most shear dominated flows. The temperature dependence of GNF fluids is generally included in the coefficients of the viscosity model. Various models are currently being used to represent the temperature and strain rate dependence of the viscosity. 

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