Shear-free flow measurements

FIGURE 3.25 Extensional rheometer for polymer melts based on the Ballman method. The length of the sample is increased exponentially with time to generate a constant extension rate. 

For both methods the technique for obtaining the extensional viscosity, rj + (e, 1) is similar. With the assumption that the surroundings of the sample are at atmospheric pressure, Pa, the total force per unit area exerted by the load cell and 

FIGURE 3.26 Rheotens apparatus for estimating the uniaxial extensional viscosity. 

VISCOELASTIC RESPONSE OF POLYMERIC FLUIDS AND FIBER SUSPENSIONS 

Obviously, rj is obtained from the values calculated using 

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Flow is generally classified as shear flow and extensional flow [2]. Simple shear flow is further divided into two categories Steady and unsteady shear flow. Extensional flow also could be steady and unsteady however, it is very difficult to measure steady extensional flow. Unsteady flow conditions are quite often measured. Extensional flow differs from both steady and unsteady simple shear flows in that it is a shear free flow. In extensional flow, the volume of a fluid element must remain constant. Extensional flow can be visualized as occurring when a material is longitudinally stretched as, for example, in fibre spinning. When extension occurs in a single direction, the related flow is termed uniaxial extensional flow. Extension of polymers or fibers can occur in two directions simultaneously, and hence the flow is referred as biaxial extensional or planar extensional flow. 

It is known that incompressible newtonian fluids at constant temperature can be characterized by two material constants the density p and the viscosity T. The characterization of a purely viscous nonnewtonian fluid using the power law model (or any of the so-called generalized newtonian models) is relatively straightforward. However, the experimental description of an incompressible viscoelastic nonnewtonian fluid is more complicated. Although the density can be measured, the appropriate expression for r poses considerable difficulty. Furthermore there is some uncertainty as to what other properties need to be measured. In general, for viscoelastic fluids it is known that the viscosity is not constant but depends on shear rate, that the normal stress differences are finite and depend on shear rate, and that the stress may also depend on the preshear history. To characterize a nonnewtonian fluid, it is necessary to measure the material functions (apparent viscosity, normal stress differences, etc.) in a relatively simple or standard flow. Standard flow patterns used in characterizing nonnewtonian fluids are the simple shear flow and shear-free flow. 

Conservation Equations. In the above section, the material functions of nonnewtonian fluids and their measurements were introduced. The material functions are defined under a simple shear flow or a simple shear-free flow condition. The measurements are also performed under or nearly under the same conditions. In most engineering practice the flow is far more complicated, but in general the measured material functions are assumed to hold. Moreover, the conservation principles still apply, that is, the conservation of mass, momentum, and energy principles are still valid. Assuming that the fluid is incompressible and that viscous heating is negligible, the basic conservation equations for newtonian and nonnewtonian fluids under steady flow conditions are given by... 

The material functions tii and rji depend on both t and 8q, and of course on the parameter b that specifies the type of shear-free flow. For elongational flow, with b = 0 and Sq positive, rj becomes rj, the elongational stress growth function. This quantity has been measured for a number of polymer melts. Further information on elongational properties can be found in several extensive... 

It is not the intention here to give an in-depth description of the techniques used in measuring rheological properties of polymer melts as these details can be found elsewhere (Dealy, 1982 Macosko, 1994 Walters, 1975). The goal is to make sure that one is aware of at least the most common methods, how data is manipulated to obtain material functions, and the limitations of various techniques. Methods for measuring shear flow properties are discussed first followed by methods for measuring shear-free flow properties. 

The methods described below outline three dynamic adhesion/aggregation assays used to assess the in vitro and/or ex vivo efficacy of platelet antagonists (1) a viscometric-flow cytometric assay to measure shear-induced platelet-platelet aggregation in the bulk phase, (2) a perfusion chamber coupled with a computerized videomicroscopy system to visualize in real time and quantify (a) the adhesion and subsequent aggregation of platelets flowing over an immobilized substrate (e.g. extracellular matrix protein) and (b) free-flowing monocytic cell adhesion to immobilized platelets. 

Flowability If we re considering particles, powders, and other products that are intended to flow, then this is a very important consideration. These materials need to easily flow from bins, hoppers, and out of boxes for consumer products. Powder flowability is a measure-able characteristic using rotational shear cells (Peschl) or translational shear cells (lenike) in which the powder is consolidated under various normal loads, and then the shear force is measured, enabling a complete yield locus curve to be constructed. This can be done at various powder moistures to create a curve of flowability versus moisture content. Some minimal value is necessary to ensure free flow. Additional information on these devices and this measure can be found in Sec. 21, Sohd-Solid Operations and Processing. ... 

These mixing apparatuses were built to ensure pulse-free flow to obtain a uniform cross-linker concentration throughout the gel. In addition, the mixing devices were connected directly to the viscosity measuring device, so that the gel is continuously sheared from the time of cross-linker injection. Finally, it is recommended that metal content of gels be analytically verified to ensure that the proper amount of cross-linker has been delivered. We have analyzed for titanium with X-ray fluorescence and atomic adsorption spectroscopy. 

Frequency spectra of wall shear stress fluctuations and of velocity fluctuations indicate relative attenuation of the high frequency components (Figure 3). Measurements in boundary-free flows have also usually found that the small-scale components are suppressed relative to the large-scale. 

The above-mentioned boundaries between free-flowing and non-free-flowing are only approximate indicators. They are used because of their simplicity and ease of measurement. However, neither rearrangement compressibility nor the angle of repose are true measures of the flowability of particulate materials. Free-flowing materials are also referred to as non-cohesive materials and non-free-flowing materials as cohesive materials. The shear stress at incipient internal shear deformation in non-cohesive materials can be uniquely related to the normal stress. Consequently, the coefficient of cohesion (see Eq. 6.6) is zero for non-cohesive particulate materials. 

Chapter 3 deals with rheometry which is the method of measurement of the various rheological parameters described in Chapter 2. The rheometers may be of Ae rotational type or the capillary type for shear flows and the shear free t)rpe for extensional flows. 

A free-flowing bulk solid Polypropylene (PP) lens shaped pellet was used. The bulk solid has a friction angle of wall friction angle of (pw = 15°, measured with a ring shear tester and the Jenike shear tester, respectively. The particle size of the bulk solid was about 3 mm. 

The negative electrokinetic zeta potential (C) at the hydrodynamic plane of shear of chloroplasts, measured by free-flow electrophoresis, has a similar temperature optimum as the membrane potential (Fig. 1) and shows a pronounced decline below about 20 C, as is illustrated by Fig. 2. Its light-... 

For reactors with free turbulent flow without dominant boundary layer flows or gas/hquid interfaces (due to rising gas bubbles) such as stirred reactors with bafQes, all used model particle systems and also many biological systems produce similar results, and it may therefore be assumed that these results are also applicable to other particle systems. For stirred tanks in particular, the stress produced by impellers of various types can be predicted with the aid of a geometrical function (Eq. (20)) derived from the results of the measurements. Impellers with a large blade area in relation to the tank dimensions produce less shear, because of their uniform power input, in contrast to small and especially axial-flow impellers, such as propellers, and all kinds of inclined-blade impellers. 

Since pressure driven viscometers employ non-homogeneous flows, they can only measure steady shear functions such as viscosity, 77(7). However, they are widely used because they are relatively inexpensive to build and simple to operate. Despite their simplicity, long capillary viscometers give the most accurate viscosity data available. Another major advantage is that the capillary rheometer has no free surfaces in the test region, unlike other types of rheometers such as the cone and plate rheometers, which we will discuss in the next section. When the strain rate dependent viscosity of polymer melts is measured, capillary rheometers may provide the only satisfactory method of obtaining such data at shear rates... 

Many of the comments in the previous chapter about the selection of grade, additives and mixing before moulding apply equally in preparation for extrusion. It is important of course that the material should be appropriate for the purpose, uniform, dry, and free from contamination. It should be tested for flow and while many tests have been devised for this it is convenient to classify them as either for low or high rates of shear. The main terms used in such testing ( viscosity , shear rate , shear strain , etc.) are defined in words and expressed as formulae in ISO 472, and it is not necessary to repeat them here. Viscosity may be regarded as the resistance to flow or the internal friction in a polymer melt and often will be measured by means of a capillary rheometer, in which shear flow occurs with flow of this type—one of the most important with polymer melts—when shearing force is applied one layer of melt flows over another in a sense that could be described as the relationship between two variables—shear rate and shear stress.1 In the capillary rheometer the relationship between the measurements is true only if certain assumptions are made, the most important of which are ... 

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