Concentric cylinders geometry

Fig.4.5.7 (a) Chemical shift imaging pulse sequence and (b) schematic drawing of CSI data for a given pixel of an oil-in-water emulsion inside the horizontal concentric cylinders geometry. 

Flow effects on non-neutrally buoyant emulsions and suspensions can be studied in various geometries. For example, flow in rotating cylinder and narrow gap concentric cylinder geometries in both horizontal and vertical orientations can be studied. Flow instabilities in settling suspensions in a horizontal rotating cylinder have recently been reported [84], Measurements of velocity fields have not been reported in the literature, but can be performed by using the methods presented in this work. 

Figure 3-1 Schematic Diagram of a Concentric Cylinder Geometry.

In a concentric cylinder geometry, the shear stress can be determined from the total torque (A/) ... 

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 ... 

Table 3-1 Values of Shear Rate Correction Factors for Concentric Cylinder Geometry...

Other expressions for concentric cylinder geometry include that for Bingham plastic fluids where the yield stress must be taken into account which leads to the Reiner-Riwlin equation ... 

Figure 3-3 Schematic of a Concentric Cylinder Geometry Air Bubble to Minimize Shear at the Bottom of a Rotating Cylinder.

Figure 3-5 Double Concentric Cylinder Geometry for Low-Viscosity Fluids.

The apex of a cone is brought into close proximity, but not in to contact, of a horizontal plate (Figure 3-7). Often, the apex is truncated slightly to eliminate a sharp point. The minimum gap between the cone and plate is usually of the order of 50 xm so that this geometry may not be suitable for dispersions containing larger diameter solids. The test fluid fills the gap between the cone and the plate, and because the gap is small, only a small volume (typically, 1-5 mL) of fluid is needed. The cone is rotated and the torque is measured at various speeds of rotation. A cone and plate viscometer can be used to obtain shear stress-shear rate curves and shear-stress versus time at constant shear rate curves as described above for concentric cylinder geometry. The... 

A sphere vibrating at a specific frequency can be used to obtain magnitudes of G and G" at a specific frequency. Such an instrument was used to follow sol-gel transition of 5,7, and 10% starch dispersions (Hansen et ah, 1990). However, such instruments seem to have a limited range of oscillation frequencies (e.g., 676-680 Hz). In addition, the reliability of the data obtained in comparison to data from dynamic rheological tests in which cone-plate, parallel plate, and concentric cylinder geometries have been used needs to be established. 

While the concentric cylinder geometry is relatively easy to use in rheological studies, some of its limitations should be recognized as shown in Figure 3-44. 

Campanella and Peleg (1987) presented stress growth and decay data on mayonnaise at shear rates of 1.8, 5.4,9.9, and 14.4s with a controlled shear rate viscometer and a concentric cylinder geometry. They modeled the data by a three-constant model that was a modification of Larson s (1985) model that was successfully employed for polyethylene melts with a wide distribution of molecular weights. The model employed by Campanella and Peleg was ... 

---