Geometry, cone-and-plate

Gel formation was monitored using a controlled-stress rheometer (Carri-Med CS 50, TA Instruments, Guyancourt, France) with cone-and-plate geometry (cone diameter 4 cm, angle 3°58 ). The bottom plate was fitted with a Peltier temperature controller that... 

Deviation from laminar shear flow [88,89],by calculating the material functions r =f( y),x12=f( Y),x11-x22=f( y),is assumed to be of a laminar type and this assumption is applied to Newtonian as well as viscoelastic fluids. Deviations from laminar flow conditions are often described as turbulent, as flow irregularities or flow instabilities. However, deviation from laminar flow conditions in cone-and-plate geometries have been observed and analysed for Newtonian and viscoelastic liquids in numerous investigations [90-95]. Theories have been derived for predicting the onset of the deviation of laminar flow between a cone and plate for Newtonian liquids [91-93] and in experiments reasonable agreements were found [95]. 

Flow irregularities at gap angles of 30° were observed in viscoelastic liquids [94]. It has been indicated in theoretical treatments that the possibility of secondary flows [96,97] in rotational devices is to be expected if the gap angle is much greater than 5°. For viscoelastic fluids deviations from laminar flow have only been reported in cone-and-plate geometries with gap angles above 10°. 

In the Couette cell the shear stress varies signficantly with radial position across the gap as r2. Should a more uniform stress environment be required then the cone-and-plate geometry may be used [17]. An example apparatus is shown in Figure 2.8.7. 

We begin with a brief discussion of Newton s law of viscosity and follow this with a discussion of Newtonian flow (i.e., the flow of liquids that follow Newton s law) in a few standard configurations (e.g., cone-and-plate geometry, concentric cylinders, and capillaries) under certain specific boundary conditions. These configurations are commonly used in viscometers designed to measure viscosity of fluids. 

On the other hand, the principles of some additional rheological measurements needed for comparison, will briefly be reviewed in this section. The cone-and-plate geometry has already been mentioned above. With such an arrangement the apex of a rather flat cone rests on a flat... 

As has already been pointed out in Sections 1.3 and 1.5, the slit-geometry is interesting for two reasons. First, it enables the measurement of flow birefringence in the 1—3 plane. Second, it furnishes the possibility to investigate polymer melts at high shear rates, where the cone-and-plate geometry fails. In the present section it remains to give a short description of the apparatus. 

With rubbers a similar situation is met, but now with the aid of a rotation viscometer. The Mooney viscosity is measured as the torque needed to rotate two parallel plates, between which the rubber mass is present, with respect to each other. This provides a rough indication of the viscosity, and thus of the molar mass. This measurement can also be used to characterize the vulcanization behaviour under vulcanization conditions the increase of the Mooney viscosity indicates the onset of network formation. When the network develops further, a continuous rotation can, of course, no longer be applied because the viscosity increases unlimitedly therefore an oscillation method is mostly used with a cone-and-plate geometry. Initially, the viscosity is being measured, and later on the build-up of the E-modulus of the network. Another characterization of the viscosity of unvulcanized rubbers is the Hoekstra method. The rubber is present between two parallel plates, which are moved towards each other with a certain speed the force needed to do so is an indication of the viscosity. 

Model RMS-7200 In steady shear mode with cone and plate geometry. 

Using the cone and plate geometry, stress growth experiments have also been performed using different temperatures and different shear rates. Correct tangential (X+(t,Y) Tj+(t,Y)) and normal stress (Ni(t,Y) Vi(t,Y)) data were... 

In contrast to a cone and plate geometry to be discussed next, the shear rate of non-Newtonian foods cannot be determined from a simple expression involving the angular velocity and often one must use a suitable relationship between rotational speed and shear stress to correct for non-Newtonian behavior. More complex equations are needed to describe the flow of non-Newtonian fluids in concentric cylinder geometry. For example, for fluids that can be described by the power law model, an expression presented by Krieger and Elrod (Van Wazer et al., 1963) has been used extensively in the literature ... 

Figure 3-7 Schematic Diagram of a Cone and Plate Geometry.

Problem 1.1 and Worked Example 1.2, just after this chapter, explore the degree of uniformity of the shear rate in the circular Couette and cone-and-plate geometries. 

Problem 1.2 (Worked Example) Compute the shear-rate profile in a cone-and-plate geometry. For a cone angle a of 0.1 radians, what percentage increase occurs in shear rate as one migrates from the plate to the cone Hint Look at the component of the momentum balance equation in spherical coordinates.)... 

When applied to geometries with moving boundaries, such as the cone-and-plate geometry, the Helfrich argument suggests that the flow should be concentrated in thin zones of width proportional to mesh size, and hence there should be apparent slip. 

Figure 4 Images (a) and shear rate profiles (h) from a cetylpyridinium chloride sodium salicylate solution of wormlike micelles at different imposed average shear rates in the cone-and-plate geometry. The dark and bright hands show regions of fast moving approaching and receding regions of fluid (from ref 57)...

A cone and plate geometry is illustrated in Fig. 17. The plate remains stationary, while the cone rotates, or vice versa. The angle between the cone and plate surfaces is usually less than 5°. For larger angles, the analysis of the results obtained from non-Newtonian materials would be complex or even impossible. For the small angles, sample ejection is less pronounced and temperature control can be easily achieved. ° ... 

Fig. 17 Cone and plate geometry R = radius of the cone and plate, d — gap between cone and plate at the perimeter of the geometry,

The rheological experiments were performed on a Rheometrics Mechanical Spectrometer RMS 705F. Cone and plate geometry was used in order to generate a homogeneous shear history throughout the sample, a prerequisite in order to analyse transient behaviour. All experiments have been performed at 293K. 

A study, relevant to recirculation behaviour in a RRIM machine, of polyol and polyol slurry rheology at shear rates in the range 0-103 s 1. This study is based on viscometry with modified cone and plate geometry. 

A more sensitive rheological techniques for following the stability of multiple emulsions is to use oscillatory techniques. In this case, a sinusoidal strain or stress is applied to the sample, which is placed in the gap of the concentric cylinder or cone-and-plate geometry the resulting stress or strain sine wave is followed at the same time. For a viscoelastic system, as is the case with multiple emulsions, the stress and strain sine waves oscillate with the same frequency, but out of phase. 

A constant stress a is applied on the system (that may be placed in the gap between two concentric cylinders or a cone and plate geometry) and the strain (relative deformation) y or compliance J =Y/ff, Pa" ) is followed as a function of time for a period of t. At t = t, the stress is removed and the strain y or compliance J is followed for another period t [1]. 

One very important point that must be considered in any rheological measurement is the possibility of slip during the measurements. This is particularly the case with highly concentrated dispersions, whereby the flocculated system may form a plug in the gap of the platens, leaving a thin liquid film at the walls of the concentric cylinder or cone-and-plate geometry. This behaviour is caused by some syneresis of the formulation in the gap of the concentric cylinder or cone and plate. In order to reduce sHp, roughened walls should be used for the platens an alternative method would be to use a vane rheometer. 

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