Couette flow viscometer

It is evident that by adding particles in a flow the amount of energy dissipated will be increased, since the work done by the shearing stresses is increased because of the addition of the solid boundaries associated with the particles. The particles plus liquid, which we term the suspension phase, might therefore be looked upon as a Newtonian fluid but with a coefficient of viscosity larger than that of the pure liquid. To understand the relation between the particle and fluid characteristics, Einstein (1956) set himself the problem of a dilute suspension in a simple Couette flow viscometer and asked what would be the measured viscosity. 

Rotating cone viscometers are among the most commonly used rheometry devices. These instruments essentially consist of a steel cone which rotates in a chamber filled with the fluid generating a Couette flow regime. Based on the same fundamental concept various types of single and double cone devices are developed. The schematic diagram of a double cone viscometer is shown in... 

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... 

Cottrell equation Cottrell unit Couchman equation Couette flow Couette viscometers Cough drops Coughlozenges... 

The variability of physical properties widens both the dimensional x- and the dimensionless pi-space. The process is not determined by the original material quantity x, but by its dimensionless reproduction. (Pawlowski [27] has clearly demonstrated this situation by the mathematical formulation of the steady-state heat transfer in an concentric cylinder viscometer exhibiting Couette flow). It is therefore important to carry out the dimensional-analytical reproduction of the material function uniformly in order to discover possibly existing, but under circumstances concealed, similarity in the behavior of different substances. This can be achieved only by the standard representation of the material function [5, 27]. 

Serum is a good but undefined shear protectant. It promotes better cell growth in agitated and/or aerated cultures in a dose-dependent fashion up to 10% (v/v) (Papoutsakis, 1991b). Several studies employing bioreactors and well-defined Couette flows in a viscometer have shown that the protective effect of serum is... 

It should, however, be noted that there exist some hints that bicontinuous microemulsions behave elastically. This has been assumed to be due to the differences observed in measuring viscosities once in a Couette flow and in the other case by a capillary viscometer. Here it was observed that the values obtained with the capillary viscometer are markedly higher. It has been suggested that in capillary flow a component of elongational flow is observed and that in this type of flow elastic components can be observed much earlier than in shear flow [106,107]. 

The apparent viscosity of dilute polymer solutions can be represented by the power-law model over a wide range of shear rates [3,4]. For such fluids, the shear rate depends on, among other factors, the power-law index. The shear rate for a power-law fluid in a co-axial rotational viscometer (Couette flow) is ... 

Among the different possible ways to measure viscosities in rotating viscometers, the coaxial cylinder apparatus is the most commonly used in practice. The measured liquid intersperses the annular gap between the stationary inner cylinder (bob) and the rotating outer cylinder (cup). Therefore a velocity gradient builds between the inner and outer cylinders (Couette flow). The momentum, which is transferred by this downward gradient to the inner cylinder, is directly proportional to the viscosity. Deflection is compensated by a torsion bar and the equilibrium deflection is measured electrically. The measurement of the angular velocity of the cup and the angular deflection of the bob makes it possible to determine the viscosity [4, 11]. 

A model used to demonstrate laminar shear mixing is Couette flow [16, 17], the principle used in the Couette Viscometer ... 

Couette Flow n Shear flow in the annulus between two concentric cylinders, one of which is usually stationary while the other turns. By measuring the relative rotational velocity and the torque required to maintain steady flow, one can infer the viscosity of the liquid. See Rotational Viscometer. Flow in the metering section of a single-screw extruder resembles Couette flow, modified by the presence of the flight and, normally, by the pressure rise along the screw. 

Obviously, the analysis above is not valid in the area beneath the bob at the bottom of the viscometer. This is best taken into account by making measurements with two fluid depths, the lower being well above the bottom of the bob, and using the differences between the torques and depths in (16,28), thereby subtracting out the effects of non-Couette flow. Another approach is illustrated in Example 7. 

The study of flow and elasticity dates to antiquity. Practical rheology existed for centuries before Hooke and Newton proposed the basic laws of elastic response and simple viscous flow, respectively, in the seventeenth century. Further advances in understanding came in the mid-nineteenth century with models for viscous flow in round tubes. The introduction of the first practical rotational viscometer by Couette in 1890 (1,2) was another milestone. 

Figure 11 shows the reference floe diameter for viscometers as a function of shear stress and also the comparison with the results for stirred tanks. The stress was determined in the case of viscosimeters from Eq. (13) and impeller systems from Eqs. (2) and (4) using the maximum energy density according to Eq. (20). For r > 1 N/m (Ta > 2000), the disintegration performance produced by the flow in the viscosimeter with laminar flow of Taylor eddies is less than that in the turbulent flow of stirred tanks. Whereas in the stirred tank according to Eq. (4) and (16b) the particle diameter is inversely affected by the turbulent stress dp l/T, in viscosimeters it was found for r > 1.5 N/m, independently of the type (Searle or Couette), the dependency dp l/ pi (see Fig. 11). 

Fig. 8. Sustained damage in Daucus carota suspensions, as a function of total energy expended, under laminar flow conditions in a Couette viscometer. Redrawn from Dunlop et al. (1994) Effect of fluid shear forces on plant cell suspensions. Chem Eng Sci 49 2263 - 2276, with permission of Elsevier Science...

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-... 

Subsequent falling-ball experiments performed with suspended rods (Graham et al., 1987 Milliken et al., 1989) replacing the spheres revealed significant and systematic differences between quiescent values of the suspension viscosity and those derived from Couette and capillary viscometer flow measurements. This is attributed by Graham, Mondy, and co-workers to fundamental differences in the distributions of rod orientations characterizing the quiescent and sheared suspensions. 

In order to model the flow behavior of molten silicate suspensions such as magmas and slags, the rheological behavior must be known as a function of the concentration of suspended crystals, melt composition, and external conditions. We have determined the viscosity and crystallization sequence for a Kilauea Iki basalt between 1250°C and 1149°C at 100 kPa total pressure and f02 corresponding to the quartz-fayalite-magnetite buffer in an iron-saturated Pt30Rh rotating cup. viscometer of the Couette type. The apparent viscosity varies from 9 to 879 Pa.s. The concentration of suspended crystals varies from 18 volume percent at 1250°C to 59 volume percent at 1149 C. The molten silicate suspension shows power-law behavior ... 

Two common methods for measuring viscosity are the cup and bob (Couette) and the tube flow (Poiseuille) viscometers. 

A nearly identical flow pattern exists in the annular space between two concentric cylinders, one rotating and the other stationary, provided the width of the annulus, B, is small compared to the diameters of the cylinders. A device that makes use of this is the Couette viscometer. By measuring the torque required to rotate one cylinder at a known speed, the viscosity may be readily calculated from Eq. (5.70). 

Merrill EW, Smith KA, Shin H, Mickley HS (1966) Study of turbulent flows of dilute polymer solutions in a couette viscometer. Trans Soc Rheol 10 335-351... 

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