Cones, design geometry

Multi-row detector systems are referred to as cone-beam systems. With a moving conveyor they become helical cone-beam systems. The cone-beam designation is in contrast to the fan-beam geometry used in Figures 3 and 4, where the source and detectors are aU in a single plane. 

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. 

As already mentioned in Chapter 1, there are mainly three geometries suitable for the measurement of flow birefringence, viz. those of the concentric cylinder apparatus, the adapted cone-and-plate apparatus and the slit-capillary with a rectangular cross-section. The general principles of the pertinent techniques have been described in the same chapter. The purpose of the present chapter is to give details of the design and construction in order to enable the reader to form a judgement as to the efficiency of the proposed methods, i.e. the relation between information and experimental effort. 

This section describes common steps designed to measure the viscosity of non-Newtonian materials using rotational rheometers. The rheometer fixture that holds the sample is referred to as a geometry. The geometries of shear are the cone and plate, parallel plate, or concentric cylinders (Figure HI. 1.1). The viscosity may be measured as a function of shear stress or shear rate depending upon the type of rheometer used. 

Conventional rheometer geometries such as concentric cylinders, cone and plate and parallel discs are unsuitable, even when the rheometer is designed to allow measurement of normal forces. Many of the disadvantages of such geometries are overcome in the sliding-plate viscometer (Gunasekaran and Ak, 2002). In this instrument (Figure 22.9), the sample (the exact shape and size of which need not be known) is held between a... 

All the major manufacturers of viscometers and rheometers have Internet sites that illustrate and describe their products. In addition, many of the manufecturers are offering seminars on rheometers and rheology. Earlier lists of available models of rheometers and their manufacturers were given by Whorlow (1980), Mitchell (1984), and Ma and Barbosa-Canovas (1995). It is very important to focus on the proper design of a measurement geometry (e.g., cone-plate, concentric cylinder), precision in measurement of strain and/or shear rate, inertia of a measuring system and correction for it, as well as to verify that the assumptions made in deriving the applicable equations of shear rate have been satisfied and to ensure that the results provided by the manufecturer are indeed correct. 

Most mechanical tests developed for fats are empirical in nature and are usually designed for quality control purposes, and they attempt to simulate consumer sensory perception (3, 4). These large-deformation tests measure hardness-related parameters, which are then compared with textural attributes evaluated by a sensory panel (3, 5). These tests include penetrometry using cone, pin, cylinder and several other geometries (3, 6-12), compression (13), extrusion (13, 14), spreadability (15, 16), texture profile analysis (2), shear tests (13), and sectility measurements (14). These methods are usually simple and rapid, and they require relatively inexpensive equipment (3, 4, 17). The majority of these tests are based on the breakdown of structure and usually yield single-parameter measurements such as hardness, yield stress, and spreadability, among others (4, 17-20). The relationship between these mechanical tests and the structure of a fat has, however, not been established. The ultimate aim of any materials science endeavor is to examine the relationship between structure and macroscopic properties. 

Carson (2002) mentions that inserts have been placed within the hopper to expand the size of the active flow channel and/or to relieve pressure at the discharge. Inverted cones and pyramids have been used with hmited success. He suggests a hopper within a hopper so that material flows in the area between the inner and outer hoppers and through the inner hopper if it does not have a cover on it. By proper design of the geometry of the hopper, a uniform velocity profile can be achieved such that there is a minimum amount of particle segregation. Sometimes in-bin blenders have also been used for this purpose. 

The application of the theoretical treatment depends on the ability to measure the extrusion force and rate. Most commercial extruders do not allow for these types of measurement. Normal rheological equipment, such as cup-and-bob or cone-and-plate, do not have a suitable geometry or instrumentation to handle materials of the consistency normally used. A ram extruder is a suitable experimental design. 

The structures and abbreviations used for designating the calix[4]arenes are shown in (5). These calix[4]arenes, have both a wide (upper) and a narrow (lower) rim that can be chemically modified to produce complexants that are selective for particular metal ions. In the simple calixarene framework the wide rim has hydrocarbon functionalities, and the narrow rim phenolic groups. Calixarenes are conformationally mobile, and the extreme structures for the calix[4]arenes have been termed the cone, partial cone, 1,3-alternate, and 1,2-alternate conformations (6). Because of the conical geometry of the calix[4]arene structure, the cavity size of the wide rim is larger than that of the narrow rim. 

---