Rheometers solids

Bingham-plastic slurries require a shear stress diagram showing shear rate vs. shear stress for the slurry in order to determine the coefficient of rigidity, T], which is the slope of the plot at a particular concentration. This is laboratory data requiring a rheometer. These are usually fine solids at high concentrations. 

The science of the deformation and flow of matter the study of a range of phenomena extending from the plastic flow of solids to the behaviour of fluids under extreme conditions. Rheometer... 

The results of Equation (3.56) are plotted in Figure 3.14. It can be seen that shear thinning will become apparent experimentally at (p > 0.3 and that at values of q> > 0.5 no zero shear viscosity will be accessible. This means that solid-like behaviour should be observed with shear melting of the structure once the yield stress has been exceeded with a stress controlled instrument, or a critical strain if the instrumentation is a controlled strain rheometer. The most recent data24,25 on model systems of nearly hard spheres gives values of maximum packing close to those used in Equation (3.56). 

Dynamic rheometers have been widely used to study the viscoelastic characteristics of liquid, solid, and semi-solid foods. However, to our knowledge, very few studies on the rheological characteristics of potato flesh using dynamic rheometry have been carried out. The dynamic rheological behavior of potato tubers may be helpful to have a quick idea about potato texture and... 

In the food industry it has often been difficult to obtain true viscosity measurements (unithj.j) of complex fluid foods such as coarse fruit suspensions. These are usually non-Newtonian suspensions. Fruit concentrates are dispersions of solid particles (pulp) in aqueous media (serum). Their rheological properties are of interest in practical applications related to processing, storage stability, and sensory properties. Expensive rheometers are often not available in quality control and product development laboratories. However, viscosity is nonetheless an important quality factor of these products. 

The viscoelastic samples to be tested by this method may be in different forms. The simplest to work with is a soft or liquid-like viscoelastic material such as mayonnaise or other food emulsions. These are easy samples to work with terms of sample loading. More solid-like samples such as cheese or food gels are more difficult to load onto the instrument in a consistent matter. The degree of compression of soft samples should ideally be controlled using a normal force measure or force rebalance system. Slippage is also a concern and roughened plates or even adhesives may be needed if slip is an issue. As this protocol is a general one, it is assumed that the sample is already loaded on the rheometer and has achieved equilibrium in terms of temperature and viscoelastic stmcture (time-dependent behavior). 

Specifications for solid of-l,4-polyisoprenes are shown in Table 5 and include analyses for volatile matter, extractables, ash, and Mooney viscosity at 100°C. Standard method ASTM D1416 includes chemical analysis methods for volatile matter, extractables, and total ash, while ASTM D1646 includes Mooney viscosity (82). The Monsanto rheometer data for vulcanizates prepared by a standard recipe may also be specified. This formulation for vulcanizate (ASTM D3403) is mixed in a Banbury mixer in two passes with all but sulfur and accelerator added in first pass ... 

The polymer-gas solution to be tested is prepared separately, and is loaded into the rheometer barrel as a well-mixed, equilibrated sample. The loading method depends on whether the polymer itself is a liquid or a solid at room temperature. For liquid polymers such as PDMS, Gerhard (1994) developed a sealed module that attached to the top of the rheometer barrel, with a side valve though which an equilibrated liquid polymer-gas sample is injected. For solid polymers such as polystyrene, Kwag (1998) found that the diffusion of gas from solid pellets at room temperature was sufficiently slow to allow direct loading of the sample as solid pellets pre-... 

The chemical microstructures of cis-polyisoprene (HR) vulcanised with sulfur and N-t-butyl-2-benzothiazole sulfenamide (TBBS) accelerator were studied as a function of extent of cure and accelerator to sulfur ratio in the formulations by solid-state 13C NMR spectroscopy at 75.5 MHz [29]. Conventional (TBBS/Sulfur=0.75/2.38), semi-efficient (SEV=1.50/1.50) and efficient (EV=3.00/1.08) vulcanisation formulations were prepared, which were cured to different cure states according to the magnitude of increase in rheometer torque. The order and types of the sulfurisation products formed are constant in all the formulation systems with different accelerator to sulfur ratios. However, the amount of sulfurisation has been found to vary directly with the concentration of elemental sulfur. 

Figure 10.8 The density of network junctions as a function of the volume fraction of paraffinic oil in EPDM/oil vulcanisates [74], The solid line represents the result of a linear regression analysis of the dependence (intercept = 453 5 mmol/kg slope = -6.2 0.0.3 mmol/kg the correlation coefficient = 0.996). Maximum torque in the rheometer curve for the vulcanisates is shown on the right ordinate...

Rheometers can be divided into two broad types viscometers, used to measure the rheological properties of liquids, and solids rheometers, used to measure the rheological properties of solids. Viscometers and solids rheometers are not mutually exclusive in application some viscometer geometries can be used for testing solids, while some solids rheometer geometries can be used for testing (viscous) liquids. 

Solids Rheometers and the Measurement of Fundamental Elastic Properties... 

Solids rheometers are instruments in which solid samples of regular shape are subjected to well-defined deformations, and the forces required to do this are measured. 

The most common solids rheometers are of the universal testing machine (UTM) type (Gunasekaran and Ak, 2002). Such an instrument comprises a horizontal stationary base-plate and a crosshead, above the base-plate, that can move up or down vertically at a variable constant speed (Figure 22.8). The crosshead incorporates a load cell for measuring and recording force. The crosshead speed, position and direction of movement relative to the base-plate are accurately controlled and recorded. 

Figure 22.8. Schematic diagram of a universal testing machine (UTM)-type solids rheometer. (Reproduced with permission from Gunasekaran and Ak, 2002.)...

Modern solids rheometers are fully computerized. The test parameters (crosshead speed, direction of travel, rate of collection of force-distance data pairs, etc) can be set up on the instrument s computer. The computer then initiates and controls the mechanical action of the instrument and records the measured data. 

Details of solids rheometer design, operation and data analysis can be found in Whorlow (1992), Collyer and Clegg (1998) and Gunasekaran and Ak (2002). 

The most common dynamic method is oscillatory testing, in which the sample is subjected to a sinusoidal oscillatory strain, and the resulting oscillatory stress measured. The more sophisticated rotational viscometers have the additional capability of dynamically testing liquid-like materials using small angle oscillatory shear. A parallel disc viscometer can be set up for testing solid-like materials (e.g., butter), in oscillatory shear. Some UTM-type solids rheometers, in which the moving crosshead can be made to reciprocate sinusoidally, can be used to test solid-like materials in oscillatory deformation in compression, tension or shear. 

A number of highly sophisticated commercial rheometers, rather different in design from the traditional UTM, are now available in which dynamic and static tests on solids in compression, tension, shear and bending can all be carried out using the same instrument. 

In the most suitable test configuration for foods, the sample initially completely fills the gap between two coaxial horizontal discs, one attached to the base and the other to the crosshead, of a UTM-type solids rheometer. Lubrication between the sample and disc surfaces is achieved by Teflon coating the surfaces and/or deliberately lubricating the surfaces with a suitable liquid of very low viscosity. 

Compression testing in a UTM-type solids rheometer, especially in the form of the TPA test, is the most common mode of Theologically testing cheeses of which self-supporting cylindrical samples can be prepared sample preparation is straightforward, the test itself is simple, and valuable information about texture-related attributes is obtained (IDF, 1991 P. Watkin-son, personal communication). TPA testing in penetration mode is used for semi-solid cheeses (P. Watkinson, personal communication). 

The shear dependency of the viscosity of ceramic suspensions at low to intermediate shear rates can be measured with common rheometers. The results for a ceramic suspension with a high volume fraction of solids and a ceramic ink are shown in Fig. 6. 

This instrument operates by applying an oscillatory, sinusoidal stress and records the strain (Figure 17.16). The solid line corresponds to the applied stress, controlled by the instrument, and the sample s response strain appears as the dotted line. The rheometer measures the variation in strain as a function of applied stress and reports... 

The maximum strain rate (e < Is1) for either extensional rheometer is often very slow compared with those of fabrication. Fortunately, time-temperature superposition approaches work well for SAN copolymers, and permit the elevation of the reduced strain rates kaj to those comparable to fabrication. Typical extensional rheology data for a SAN copolymer (h>an = 0.264, Mw = 7 kg/mol,Mw/Mn = 2.8) are illustrated in Figure 13.5 after time-temperature superposition to a reference temperature of 170°C [63]. The tensile stress growth coefficient rj (k, t) was measured at discrete times t during the startup of uniaxial extensional flow. Data points are marked with individual symbols (o) and terminate at the tensile break point at longest time t. Isothermal data points are connected by solid curves. Data were collected at selected k between 0.0167 and 0.0840 s-1 and at temperatures between 130 and 180 °C. Also illustrated in Figure 13.5 (dashed line) is a shear flow curve from a dynamic experiment displayed in a special format (3 versus or1) as suggested by Trouton [64]. The superposition of the low-strain rate data from two types (shear and extensional flow) of rheometers is an important validation of the reliability of both data sets. 

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