Cone and plate systems

Fig. 6.6. Cross-section through heart of cone-and-plate system. (C) cone, P) plate, (1F1, IV2) windows, (M) reflection prism, [Z) cover, (F) filling hole, handle, (K) distance piece. Part E and V are explained in the text. AA, axis of rotation LL light propagation (77)...

Several researchers reported viscoelastic behavior of yeast suspensions. Labuza et al. [9] reported shear-thinning behavior of baker s yeast (S. cerevisiae) in the range of 1 to 100 reciprocal seconds at yeast concentrations above 10.5% (w/w). The power law model was successfully applied. More recently, Mancini and Moresi [10] also measured the rheological properties of baker s yeast using different rheometers in the concentration range of 25 to 200 g dm. While the Haake rotational viscometer confirmed Labuza s results on the pseudoplastic character of yeast suspension, the dynamic stress rheometer revealed definitive Newtonian behavior. This discrepancy was attributed to the lower sensitivity of Haake viscometer in the range of viscosity tested (1.5 to 12 mPa s). Speers et al. [11] used a controlled shear-rate rheometer with a cone-and-plate system to measure viscosity of... 

ISO 3219. 1993 (75], covers polyester resins as liquids, emulsions, or dispersions using a rotational viscometer, coaxial cylinder viscometer, and cone and plate system. ISO 2555 (76] refers to the Bookfield viscometer. ASTM D1824 [77] covers the use of this instrument for the measurement of apparent viscosity of plastisols and organisols at low shear rates. For high shear rates. ASTM D1823 (78] describes a method using a Burrell Severs A-120 viscometer. ISO 1628 (79] covers determinations of viscosity number and limiting viscosity for PVC, polyolefins, polycarbonate, thermoplastic polyester, and methyl methacrylate polymers, in parts 2 to 6 respectively. 

Viscometers with cylinder and cone/plate geometries can also be employed. The cylinder viscometers are easier to use and provide more reproducible results. Cone and plate systems can be used to investigate the hardening behavior of paints. The system can easily be cleaned and only a small amount of sample is required. High velocity gradients can be achieved with small cone angles. The potential uses of cone and plate systems are limited for several reasons and they cannot be used with dispersions [9.6], [9.7]. 

Cone and plate systems (Fig. 3.5) allow the build up of a defined constant shear field with only a very small amount of polymer liquid. Because they require high precision motor drives and sensors and because of the high error when wrong distance alignments are used, cone and plate systems are mostly found in expensive rheometers that are capable of more sophisticated kinds of stress fields than the pure shear flow. Nevertheless, they can be used for pure viscosity measurements. 

The cone and plate system according to DIN 53018 and ISO 3219 [27] has a measurement body with a cone like surface and a flat plate. The geometrical measures of the cone are defined by the cone radius R and the cone angle a. The ISO norm recommends a=l° and excludes cone angles of a>4 . In order to avoid any errors due to direct contact of the cone with the plate, the tip of the cone is taken off for several micrometers. Particles of a size that can cause them to be stuck in the slit between the cone and the plate have to be removed before the measurement. If this is not possible, the parallel disc system has to be used instead. 

The (constant) shear stress in a cone and plate system depends on the cone radius R and is given as... 

Other than in a cone and plate system, it is not constant over the radius The mean viscosity is calculated from ... 

Since the surface for the power transmission is big compared to that of the plain cone/plate system, the Mooney/Ewart system is suitable for low viscous liquids. The advantage in comparison to normal cylinder geometries is the avoidance of edge effects at the lower cylinder wall for the smaller sample volume. The Mooney/Ewart system requires a high precision setting of the vertical distance, and is therefore as the cone and plate system mostly used in rheometer systems. 

Fluid shear influences a number of cellular phenomena, including but not limited to vasoconstriction via vascular smooth muscle cells, mechanoreception via plasma membrane receptors or ion channels, and nitric oxide release via endothelial cells. Two main types of systems dominate the apphcation of fluid shear stress parallel plate and cone-and-plate systems. These systems are most useful for studying cell adhesion and engineering vasculature under physiological flow conditions however, the main challenge of these systems is keeping a homogeneous fluid flow to produce uniform shear stress. 

FIGURE 15.5 Cone-and-plate systems apply homogenous laminar shear stress. 

Figure 9 Stacked profile map (A) ofthe fluid velocity across the gap of a 7° cone and plate system containing a semidilute wormlike micelle solution, and shear rate image (B) obtained by taking the derivation of the velooity aoross the gap. Dramatic shear banding effects are apparent. Note the use of an expanded field of view across the gap achieved by using different magnitudes of spatial encoding gradients. Courtesy of MM Britton and the author.

In Chapter 4 the development of axisymmetric models in which the radial and axial components of flow field variables remain constant in the circumferential direction is discussed. In situations where deviation from such a perfect symmetry is small it may still be possible to decouple components of the equation of motion and analyse the flow regime as a combination of one- and two-dimensional systems. To provide an illustrative example for this type of approximation, in this section we consider the modelling of the flow field inside a cone-and-plate viscometer. 

Fig. 2.8.10 (a) Grey scale map of shear taken across gap of 7° cone-and-plate device, for the semi-dilute wormlike micelle system 60 mM cetylpyridinium chloride—100 mM sodium... 

Rheological measurements. Routine viscosity measurements were made with a Wells-Brookfield micro-cone and plate viscometer, or a Brookfield LVT(D) viscometer with UL adapter. Viscosity-temperature profiles were obtained using the latter coupled via an insulated heating jacket to a Haake F3C circulator and PG100 temperature programmer or microcomputer and suitable interface. Signals from the viscometer and a suitably placed thermocouple were recorded on an X-Y recorder, or captured directly by an HP laboratory data system. 

Rheological Properties Measurements. The viscoelastic behavior of the UHMWPE gel-like systems was studied using the Rheometric Mechanical Spectrometer (RMS 705). A cone and plate fixture (radius 1.25 cm cone angle 9.85 x 10" radian) was used for the dynamic frequency sweep, and the steady state shear rate sweep measurements. In order to minimize the error caused by gap thickness change during the temperature sweep, the parallel plates fixture (radius 1.25 cm gap 1.5 mm) was used for the dynamic temperature sweep measurements. 

The flow behaviour of polymeric electrophotographic toner systems containing carbon black varying in surface area and concentration were determined using a cone and plate rheometer [51]. As the concentration of carbon black was increased, the viscosity at low shear rates become unbounded below a critical shear stress. The magnitude of this yield stress depended primarily on the concentration and surface area of the carbon black flller and was independent of the polymer (polystyrene and polybutyl methacrylate) and temperature. It was postulated that at low shear rates the carbon black formed an independent network within the polymer which prevented flow. 

At this point it should be noted that the conclusion drawn from flow birefringence measurements, viz. that p22 — p33 of polymer systems is very small compared with pn — pn is not always supported by other types of measurement. With the aid of pressure measurements in the walls of various rheometers (e.g. cone-and-plate apparatus) results have been obtained by a number of authors (refs. 26, 43, 44), showing that p23 — p33 should be positive and can have values up to 20 per cent of Pn Pta- 1-7 suggests for the investigated polyisobutylene solution... 

Solyom and Ekwall (20) have studied rheology of the various pure liquid crystalline phases in the sodium caprylate-decanol-water system at 20 °C, for which a detailed phase diagram is available. Their experiments using a cone-and-plate viscometer show that, in general, apparent viscosity decreases with increasing shear rate (pseudo-plastic behavior). Values of apparent viscosity were a few poise for the lamellar phase (platelike micelles alternating with thin water layers), 10-20 poise for the reverse hexagonal phase (parallel cylindrical micelles with polar... 

Cone and plate sensor systems are useful when a constant shear rate across the gap is required, when sample sizes must be very small, and when sensor cleaning or sample recovery are problematic. They are less well suited to the study of suspensions of moderately-sized particles which may bridge the gap, causing erroneous readings, and cause wear to the cone and plate surfaces. 

In systems with suspended solids, rheologic measurements are difficult to perform owing to settling in the measurement devices. Conventional methods for measuring rheologic properties (cone-and-plate, concentric cylinder, and rotating-bob viscometers) do not produce accurate and reliable data for some solid suspensions. 

Normally the coordinate system is chosen in such a way that T13 = T31 = T23 = T32 = 0 In general, use is made of normal stress differences, N1 and N2, because they do not include undetermined hydrostatic pressures that are always present but not affect the material properties (as long as they are not too high). In Table 15.1, also the possibilities to determine the normal stress differences or combinations are depicted. In the modem rheogoniometers also normal stress differences can be determined but. They follow from measurements of normal forces, Fn, or normal stresses, T22, as is also depicted in Table 15.1. For the measurements of the normal stresses T22 pressure gauges have to be mounted in the Couette cylinders, in the capillary of the capillary rheometer (in both cases quite difficult to mount) and in the plate of a cone and plate instrument at several distances from the axis (not that difficult). Sometimes use is made of a slit rheometer instead of a capillary rheometer, because pressure gauges are much easier to mount (Te Nijenhuis, 2007, Chap. 9.1.2). 

The cone-and-plate viscometer is an in vitro flow model used to investigate the effects of bulk fluid shear stress on suspended cells. Anticoagulated whole blood specimens (or isolated cell suspensions) are placed between the two platens (both of stainless steel) of the viscometer. Rotation of the upper conical platen causes a well-defined and uniform shearing stress to be applied to the entire fluid medium as described by Konstantopolous et al. (1998). The shear rate (y) in this system can be readily calculated from the cone angle and the speed of the cone using the formula i/ = where y is the shear rate in sec-1, mis the... 

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