Viscometer cone and plate

The cone and plate viscometer measures the dynamic viscosity of modified bituminous binders. Although the test method has been developed for modified bituminous binders, it may also be suitable for other bituminous binders. 

According to CEN EN 13702 (2010), a small sample of bitumen is placed on a plate, a cone is pressed onto the sample, any surplus sample is removed and the system is brought to the test temperature. Then, a stress is applied to the sample by rotation and the torque is measured at the applied shear rate. The dynamic viscosity (q) (in Pa s), which is the ratio of shear stress (t) (in Pa) to shear rate (y) (in s ), is calculated automatically by the apparatus (viscometer) used. More information regarding the test can be found in CEN EN 13702 (2010). 

This is similar to the test described in ASTM D 4287 (2010), which is used to determine the viscosity under high shear conditions, comparable to those encountered during spraying, brushing and so on. It is stated that the high shear cone and plate viscometer test method is suitable for paints and varnishes, whether they are Newtonian in behaviour or not, than for bituminous binders. 

Still another popular type of rotational viscometer is the cone-and-plate, in which the sample is sheared between a flat plate and a broad cone whose apex contacts the plate (Fig. 16.7). For small cone-jplate angles a, this approximates a viscometric flow with (in spherical coordinates) flow in the tangential 6 or 1 direction and the gradient in the azimuthal or 2 direction. Here, the radial 

Example 6. Obtain the expressions for shear rate and shear stress in a cone-and-plate viscometer in terms of the rate of cone rotation co, the measured torque M, and the geometry. 

Solution (see Fig. 16.7). The tangential velocity Ve of a point on the cone relative to the plate is = cor cos oc. Fluid is sheared between that point and the plate over a distance d = ar  

This flow is a viscometric flow when viewed in a spherical coordinate system, and there is only one nonzero component of the velocity. This component is v, which varies with both r and 6 the streamlines are closed circles. If we rotate the plate at an angular velocity 12, the linear velocity on the plate surface at any radial position is Hr. On the cone surface at the same radial position, however, the velocity is zero. If the cone angle is small, we can assume that 

If we integrate the shear stress over the cone surface, we can get an expression for the torque M as follows  

In order to obtain the normal stress functions, we need to solve the equations of motion in spherical coordinates [3]. An examination of the 0 component of this equation shows dp/36 = 0. Thus, p depends on r alone, because derivatives with respect to 4 are zero. Further, because most polymer fluids are fairly viscous, we can neglect inertia and, as a result, the r component of the equation of motion yields the following [3]  

At r = if, equals —p, where p is atmospheric pressiue. Thus, from the 

To make further progress, we examine the equilibrium of the plate and balance forces in the 6 direction (Fig. 14.6b). The result is 

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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. 

In the Couette flow inside a cone-and-plate viscometer the circumferential velocity at any given radial position is approximately a linear function of the vertical coordinate. Therefore the shear rate corresponding to this component is almost constant. The heat generation term in Equation (5.25) is hence nearly constant. Furthermore, in uniform Couette regime the convection term is also zero and all of the heat transfer is due to conduction. For very large conductivity coefficients the heat conduction will be very fast and the temperature profile will... 

Using the described algorithm the flow domain inside the cone-and-plate viscometer is simulated. Tn Figure 5.17 the predicted velocity field in the (r, z) plane (secondary flow regime) established inside a bi-conical rheometer for a non-Newtonian fluid is shown. 

J The viscosity characteristics of a polymer melt are measured using both a capillary rheometer and a cone and plate viscometer at the same temperature. The capillary is 2.0 mm diameter and 32.0 mm long. For volumetric flow rates of 70 x 10 m /s and 200 x 10 m /s, the pressures measured just before the entry to the capillary are 3.9 MN/m and 5.7 MN/m, respectively. 

Data obtained wirh a cone and plate viscometer were ... 

Striking support of this contention is found in recent data of Castro (16) shown in Figure 14. In this experiment, the polymerization (60-156) has been carried out in a cone-and-plate viscometer (Rheometrics Mechanical Spectrometer) and viscosity of the reaction medium monitored continuously as a function of reaction time. As can be seen, the viscosity appears to become infinite at a reaction time corresponding to about 60% conversion. This suggests network formation, but the chemistry precludes non-linear polymerization. Also observed in the same conversion range is very striking transition of the reaction medium from clear to opaque. 

Models based on Eqs. (47)-(50) have been used in the past to describe the disruption of unicellular micro-organisms and mammalian (hybridoma) cells [62]. The extent of cell disruption was measured in terms of loss of cell viability and was found to be dependent on both the level of stress (deformation) and the time of exposure (Fig. 25). All of the experiments were carried out in a cone and plate viscometer under laminar flow conditions by adding dextran to the solution. A critical condition for the rupture of the walls was defined in terms of shear deformation given by Eq. (44). Using micromanipulation techniques data were provided for the critical forces necessary to burst the cells (see Fig. 4)... 

Fig. 25. Total and viable cell concentrations of TB/C3 hybridomas versus duration of shear in a cone and plate viscometer (shear stress 208 Nm ). The error bars indicate the 95% confidence intervals [62]...

Cone-and-plate viscometers have been employed to study shear effects in both suspended (e.g. [138]) and anchorage dependent [122] mammalian cells. These devices have the advantage of requiring only small sample volumes ( lml). However, they are generally inappropriate for plant cell suspensions due to the larger cell and aggregate sizes. 

Fig. 4.2.9 Viscosity versus shear rate obtained using a cone and plate viscometer (a) and MRI ( ) 13 mLs"1, ( ) 22 mL s-. ...

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. 

Assays. Nitrogen assays to determine 1-amidoethylene unit content were done by Kjeldahl method. Limiting viscosity numbers were determined from 4 or more viscosity measurements made on a Cannon-Fenske capillary viscometer at 30°C. Data was extrapolated to 0 g/dL polymer concentration using the Huggins equation(44) for nonionic polymers and the Fuoss equation(45) for polyelectrolytes. Equipment. Viscosities were measured using Cannon-Fenske capillary viscometers and a Brookfield LV Microvis, cone and plate viscometer with a CP-40, 0.8° cone. Capillary viscometers received 10 mL of a sample for testing while the cone and plate viscometer received 0.50 mL. 

There are two main types of viscometer rotary instruments and tubular, often capillary, viscometers. When dealing with non-Newtonian fluids, it is desirable to use a viscometer that subjects the whole of the sample to the same shear rate and two such devices, the cone and plate viscometer and the narrow gap coaxial cylinders viscometer, will be considered first. With other instruments, which impose a non-uniform shear rate, the proper analysis of the measurements is more complicated. 

A schematic representation of a cone and plate viscometer is shown in Figure 3.1. In this case, the viscometer consists of a lower disc and an upper wide-angle cone. The sample fills the gap between the cone and the... 

The rheometer most often used to measure viscosity at low shear rates is the cone and plate viscometer. A schematic of a cone and plate rheometer is found in Fig. 3.24. The device is constructed with a moving cone on the top surface and a stationary plate for the lower surface. The polymer sample is positioned between the surfaces. Two types of experiments can be performed the cone can be rotated at a constant angular velocity, or it can be rotated in a sinusoidal function. The motion of the cone creates a stress on the polymer between the cone and the plate. The stress transferred to the plate provides a torque that is measured using a sensor. The torque is used to determine the stress. The constant angle of the cone to the plate provides an experimental regime such that the shear rate is a constant at all radii in the device. That is, the shear rate is independent of the radial position on the cone, and thus the shear stress is also independent of the position on the cone. 

Various methods are used to examine the viscosity characteristics of metallized gels. Two types that have received extensive application are the cone and plate viscometer and the capillary viscometer. Both instruments can measure rheological characteristics at high shear rates, and the former is useful for low shear rate measurements as well. 

A cone and plate rotational type viscometer is used to obtain rheological data in the low-to-medium shear rate range. It gives a constant rate of shear across a gap, and therefore, equations for this instrument are simple when the angle is small (less than 3°). For this reason the cone and plate viscometer has become a standard tool... 

Figure 2. Consistency curve of 13 vol. % graphite dispersed in a water gel using a cone and plate viscometer...

CONCENTRIC-CYLINDER AND CONE-AND-PLATE VISCOMETERS 4.3a Concentric-Cylinder Viscometers... 

FIG. 4.4 Schematic representation of a cone-and-plate viscometer (the angle is greatly exaggerated). 

As is the case with all differential equations, the boundary conditions of the problem are an important consideration since they determine the fit of the solution. Many problems are set up to have a high level of symmetry and thereby simplify their boundary descriptions. This is the situation in the viscometers that we discussed above and that could be described by cylindrical symmetry. Note that the cone-and-plate viscometer —in which the angle from the axis of rotation had to be considered —is a case for which we skipped the analysis and went straight for the final result, a complicated result at that. Because it is often solved for problems with symmetrical geometry, the equation of motion is frequently encountered in cylindrical and spherical coordinates, which complicates its appearance but simplifies its solution. We base the following discussion on rectangular coordinates, which may not be particularly convenient for problems of interest but are easily visualized. 

Gillespie and Wiley used a cone-and-plate viscometer to measure F/A versus dv/dx for dispersions of silica and cross-linked polystyrene in dioctyl phthalate. At a volume fraction of 0.35 for both solids, the following results were obtained ... 

Yet another geometry is the cone and plate viscometer. This generally operates without a positive hydrostatic pressure and, although often used for plastics melts, is not suitable for rubbers because of excess slipping. 

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... 

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