Rotational Geometries

The test geometries listed in Table 2-2 are those commonly used for instruments that can apply rotary motion, either in the form of a controlled torque or a controlled amount of rotation. The listed examples can as a set handle samples from stiff viscoelastic solids to freely flowing liquids. All are 

Flex tests on rotational equipment can be mn on the geometry indicated in Table 2-2. While this fixture may not be provided with commercial instruments, it is easy to build. The remarkable aspect of this geometry for flex testing is that the length of the sample enters only to the first power instead of the third power of the usual flex test. This means that one can be a bit less fastidious about the length and still get good results. The sample s width and thickness still enter in the same fashion, however. 

Links to representative suppliers of commercial equipment, both axial and rotational are listed at www.rheology.org.7 

Calculate the weight needed to bring about a 0.40-cm shearing displacement AX, of a viscoelastic cube 2 cm on a side after 10 4, 10 2, 10°, 104, and 106 seconds. The time-dependent shear compliance is 

Calculate the stress at time t longer than 2t, in a body with a relaxation modulus given by 

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Mechanical rheometry requires a measurement of both stress and strain (or strain rate) and is thus usually performed in a simple rotating geometry configuration. Typical examples are the cone-and-plate and cylindrical Couette devices [1,14]. In stress-controlled rheometric measurements one applies a known stress and measures the deformational response of the material. In strain-controlled rheometry one applies a deformation flow and measures the stress. Stress-controlled rheometry requires the use of specialized torque transducers in conjunction with low friction air-bearing drive in which the control of torque and the measurement of strain is integrated. By contrast, strain-controlled rheometry is generally performed with a motor drive to rotate one surface of the cell and a separate torque transducer to measure the resultant torque on the other surface. 

A. M. Corbett, R. J. Phillips, R. J. Kauten, K. L. McCarthy 1995, Magnetic resonance imaging of concentration and velocity profiles of pure fluids and solid suspensions in rotating geometries),/. Rheol. 39, 907. 

For a nonlinear molecule, there are three moments of inertia that are perpendicular to each other. We use the convention that h < h < h- The rotational geometry of a molecule belongs to one of three types, which are shown in figures 4.8 and 4.9. 

No invariance by rotation geometry estimated from ii. configurations interaction... 

The obvious difference between the co- and counterrotating extruder is that in the co-rotating geometry both screws rotate in the same direction, either clockwise or coimter clockwise. In the counter-rotating geometry, they rotate in opposite directions. In addition to geometry, this simple difference impacts the way the two screws interact. 

Historically, the co-rotating geometry has been preferred by the plastics industry, as having more even distribution of stresses, providing easier control of compounding, and operating at higher... 

Similar relations apply to other rotational geometries, differing only in the instrument constant K. For the cone-plate geometry, with radius R and cone angle 0,... 

Re2X4(LL)2]PF, 3 LL = dppe [bis(diphenylphosphino)ethane], or arphos [1-diphenylphosphino-2-diphenylarsinoethane] X = Cl, Br, I. LL bridges the two metal center thereby conferring a staggered rotational geometry. 78... 

For creep of viscoelastic liquids, one of the rotational geometries is usually chosen. A constant torque is suddenly applied (actually, within a small time interval t ) and after lapse of a period somewhat longer than ti the angular displacement is followed as a function of time. After steady-state flow has been achieved, it is desirable to remove the torque and follow the creep recovery as described in Chapter 1, Section E. Absence of perceptible friction is essential. For temperature control, which is important because of the strong dependence of viscoelastic properties on temperature, there must be no heat leakage through the device used to apply the torque connecting members of low thermal conductivity are useful. 

Other eccentric rotating geometries (a) tilted rotating hemispheres (also called balance rheometer), (b) eccentric rotating cylinders, and (c) tilted rotating cone and plate. 

Methyl chloride has Raman-active vibrations belonging to A and the doubly degenerate E, syimnetry species. The E-vibrations are non-totally synunetric and contain contributions from compensatory molecular rotation. Geometry parameters, definition of synunetry coordinates and the orientation of the molecule in Cartesian space are given in Table 3.8 and Fig. 3.7. The equilibrium molecular polarizability tensor of CH3CI employed in the calculations has the following form [289] ... 

Solution. Consider a rotational geometry with outside radius R, inside radius kR, and angular velocity of the inside cylinder, W. The velocity profile, vg, of the fluid in the gap for isothermal laminar flow with no gravitational and centrifugal forces and with no slip at the walls is given in Problem 2B.6. The shear rate is given (Table 2.10) by... 

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