Rotating cone-plate

Fig. 7 Reprinted with permission from [111], copyright (2004), Institute of Physics Publishing. Confocal images (yz, 75p.mx56gm, 512x512 pixels-) of a colloidal fluid at various shear conditions taken in a counter-rotating cone-plate shear cell [111] see Sect. 2.3. The applied shear rates are 1.67,3.36 and 8.39 s (fop to bottom)-, the ratios ofthe applied cone to plate rotation speeds are 84, 129 and 175 (left to right). Graphs (a) and (b) show displacement profiles, y(z). measured from these images via cross-correlation of scanned lines. The appropriate profile is overlaid on each image (white curves). The velocity profiles (dy/dz) calculated from these displacement profiles are shown in the graphs (c) and (d). The particle diameter is 1.50 pm...

Cone—Plate Viscometer. In a cone—plate viscometer (Fig. 28), alow angle (<3°) cone rotates against a flat plate with the fluid sample between them. The cone—plate instmment is a simple, straightforward device that is easy to use and extremely easy to clean. It is well suited to routine work because measurements are rapid and no tedious calculations are necessary. With careful caUbration and good temperature control it can also be used for research. Heated instmments can be used for melt viscosity measurements. 

In most rotational viscometers the rate of shear varies with the distance from a wall or the axis of rotation. However, in a cone—plate viscometer the rate of shear across the conical gap is essentially constant because the linear velocity and the gap between the cone and the plate both increase with increasing distance from the axis. No tedious correction calculations are required for non-Newtonian fluids. The relevant equations for viscosity, shear stress, and shear rate at small angles a of Newtonian fluids are equations 29, 30, and 31, respectively, where M is the torque, R the radius of the cone, v the linear velocity, and rthe distance from the axis. 

Dyna.mic Viscometer. A dynamic viscometer is a special type of rotational viscometer used for characterising viscoelastic fluids. It measures elastic as weU as viscous behavior by determining the response to both steady-state and oscillatory shear. The geometry may be cone—plate, parallel plates, or concentric cylinders parallel plates have several advantages, as noted above. 

The Nametre Rotary B rotational viscometer measures torque in terms of the current needed to drive the d-c motor at a given speed while a material is under test. The standard sensors are coaxial cylinders or Brookfield disk-type spindles, but a cone—plate system is also available. The viscosity range for the coaxial cylinder sensors is 5 to 5 x 1(T mPa-s, and the maximum shear rate is 200. ... 

Two main types of viscometers are suitable for the determination of the viscosity of a polymer melt The rotation viscometer (Couette viscometer, cone-plate viscometer) and the capillary viscometer or capillary extrusiometer. The latter are especially suitable for laboratory use since they are relatively easy to handle and are also applicable in the case of high shear rates. With the capillary extrusiometer the measure of fluidity is not expressed in terms of the melt viscosity q but as the amount of material extruded in a given time (10 min). The amount of ex-trudate per unit of time is called the melt index or melt flow index i (MFI). It is also necessary to specify the temperature and the shearing stress or load. Thus MFI/2 (190 °C)=9.2 g/10 min means that at 190 °C and 2 kg load, 9.2 g of poly-... 

Union, NJ). A considerable variation in shear rates can be applied in a number of different geometries including rotating cone and plate between which a thin layer of sample is inserted. 

Fig. 1. Schematic layout of the operating unit of the Weissen-berg rheogoniometer 1 - the liquid studied 2 — rotating cone of the operating unit 3 — round plate ( plane ) 4 — torsion beam 5 — bar which displaces upon torsion twisting 6 — induction translation transducer 7 — opening camera with a thermostated furnace...

Example 3.2 Cone-and-Plate Flow Rheometry The cone-and-plate flow apparatus is shown schematically in Fig. E3.2a. The polymer melt flows in the space formed by the rotating cone and stationary plate. 

The velocity field between the cone and the plate is visualized as that of liquid cones described by 0-constant planes, rotating rigidly about the cone axis with an angular velocity that increases from zero at the stationary plate to 0 at the rotating cone surface (23). The resulting flow is a unidirectional shear flow. Moreover, because of the very small i//0 (about 1°—4°), locally (at fixed r) the flow can be considered to be like a torsional flow between parallel plates (i.e., the liquid cones become disks). Thus... 

Full characterization of the flow behaviour, therefore, requires the determination of the apparent viscosity over a broad range of ror of 7. For low rates of shear q can be measured with a cylindrical or a cone-plate rotation viscometer. For higher rates of shear (from about 1 sec-1) capillary viscometers can be applied. 

A Brookfield Engineering Rheometer, Model DV-III fitted with a Cone/Plate spindle CP-40 was used to measure the viscosity of the polymer samples. The CP-40 was chosen for its relatively small sample volume requirements (0.5 ml). The sample was measured and delivered with a syringe, allowed to equilibrate at temperature for 15 minutes and then rotational force was applied. Data was collected using Brookfield Engineering software... 

Solution viscosities for 2 to 14% (w/w) concentrations of cellulose in TFA-CH2CI2 (70 30 v/v) at three different cone rotation speeds (or shear rates) in the cone/plate viscometer are shown in Table VI and Figure 1. 

Some rotational viscometers employ a rotating disc, bar, paddle or pin at a constant speed (or series of constant speeds). It is extremely difficult to obtain tme shear stress, and the shear rate usually varies from point to point in the rotating member. In particular, the velocity field of a rotating disc geometry can be considerably distorted in viscoelastic fluids. Nevertheless, because they are simple to operate and give results easily, and their cost is low, they are widely used in the food industry. While they may be useful for quality control purposes, especially Newtonian foods, the reliability of their values should be verified by comparison with data obtained with well defined geometries (capillary/tube, concentric cylinder, and cone-plate). 

Consider a viscoelastic material under torsion in a cone-plate configuration (Fig. P5.4.1). How much should we modify the base of the cone to have a rotation angle, under the same torque, twice as large at the same time and temperature ... 

In the last decade of the nineteenth century, Maurice Couette invented the concentric cylinder viscometer. This instrument was probably the first rotating device used to measure viscosities. Besides the coaxial cylinders (Couette geometry), other rotating viscometers with cone-plate and plate-plate geometries are used. Most of the viscometers used nowadays to determine apparent viscosities and other important rheological functions as a function of the shear rate are rotating devices. 

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