Torque scale

Two Brookfield viscometers were used to collect the data necessary for rheologic property studies of wet grains a Brookfield RVDV III viscometer with a cone-and-plate spindle and a Brookfield HBDV III viscometer with a double helical ribbon impeller attachment. The Brookfield RVDV III had a full-scale torque of 7187 dyn-cm, and the HBDV III had a full-scale torque of 57,496 dyn-cm. Each viscometer had a maximum rotational speed of 250 rpm. Both viscometers had accuracy limits of 5% full-scale torque. 

Howeever, inaccuracies were apparent for non-Newtonian calibration fluids and distiller s grain slurries up to 10% of the full-scale torque. Therefore, only measurements above 10% and below 90% torque were utilized for guar gum solutions and distiller s grain slurries. The experiments were conducted at a constant temperature of 25 0.1°C. 

Figures 2-4 show that no experimental data were recorded at low impeller shear rates. Experimental data began at y = 8.53 s4 for 21% solids, 5.15 s 1 for 23% solids, and 3.43 s 1 for 25% solids. The reason for the missing data is that the helical impeller viscometer has limitations. Owing to possible viscometer error, data were not recorded until the impeller torque was >10% of the full-scale torque. Therefore, no experimental data were recorded at low impeller rotational speeds. The lack of experimental data at low shear rates made comparison of rheologic models at low shear rates and the prediction of yield stress impossible.

The shear stress measurement range of the YR-1 (in Pascals) is determined by the size and shape of the vane spindle and the full scale torque range of the calibrated spring. 

The Z-concept permits scale-up between sinulat centrifuges solely on the basis of sedimentation performance. Other criteria and limitations, however, should also be investigated. Scale-up analysis for a specified sohds concentration, for instance, requires knowledge of sohds residence time, permissible accumulation of sohds in the bowl, G level, sohds conveyabihty, flowabihty, compressibihty, limitations of torque, and sohds loading. Extrapolation of data from one size centrifuge to another calls for the apphcation of specific scale-up mechanisms for the particular type of centrifuge and performance requirement. 

FIGURE 26.28 Side force coefficient and self-aligning torque of a radial ply tire 175 R 14 on two wet road surfaces of different friction coefficient, at three slip angles and loads as function of the quantity c (Equation 26.17c) aU on log scales. The sohd hnes correspond to the brush model. (From Schallamach, A. and Grosch, K.A., Mechanics of Pneumatic Tires, S.K. Clark (ed.). The US Department of Transportation, National Highway Safety Administration, Washington DV.)... 

Two other features of the classical mechanics are illustrated in Fig. 3. The first is that the torque responsible for the angular deflection at low k comes from points close to r = 0 in the scaled form of Eq. (2), around which the quartic term can be ignored. Thus... 

POMs are also employed in plumbing and irrigation because they resist scale accumulation, and have good thread strength, torque retention, and creep resistance. POMs are also... 

Analyzing the significance of the scale-up exponent for liquid motion shows that the similar results are obtained when equal tip speed (fluid velocity) of torque per volume is applied to geometrically similar agitation system... 

It is important to note that the small-scale agitator operations may be described in terms of impeller diameter and agitator speed, while manufacturing process equipment is more conveniently specified by horsepower and fluid velocity. For most standard turbine configurations, power number correlations are available to convert impeller diameter and agitator speed into a horsepower value for given fluid properties. Most laboratory bench equipment is designed to provide a torque measurement that can be readily converted to horsepower directly from the conditions of the pilot batches. 

With reliable instrumentation available, a stress relaxation procedure was eventually standardized as ISO 289-467. The normal Mooney apparatus has, in addition, to be capable of being stopped within 0.1 s, resetting zero torque for a static rotor and recording the torque every 0.2 s. The decay of torque with time is plotted on a log-log scale and the slope of the resulting line taken as the Mooney stress relaxation rate. The British standard, BS ISO 289-4 is identical and ASTM D164640 has the same procedure. 

The torque rheometer with a twin-screw extruder is considered a scaled-down continuous compounder. It allows the compounding engineer to develop polymer compounds and alloys. It also permits the formulation engineer to assure that the formulation is optimum. 

The fiber is suspended in the liquid, which means that due to small time scales given by the pure viscous nature of the flow, the hydrodynamic force and torque on the particle are approximately zero [26,51]. Numerically, this means that the velocity and traction fields on the particle are unknown, which differs from the previous examples where the velocity field was fixed and the integral equations were reduced to a system of linear equations in which velocities or tractions were unknown, depending on the boundary conditions of the problem. Although computationally expensive, direct integral formulations are an effective way to find the velocity and traction fields for suspended particles using a simple iterative procedure. Here, the initial tractions are assumed and then corrected, until the hydrodynamic force and torque are zero. 

The molecular theory of Doi [63,166] has been successfully applied to the description of many nonlinear rheological phenomena in PLCs. This theory assumes an un-textured monodomain and describes the molecular scale orientation of rigid rod molecules subject to the combined influence of hydrodynamic and Brownian torques, along with a potential of interaction (a Maier-Saupe potential is used) to account for the tendency for nematic alignment of the molecules. This theory is able to predict shear thinning viscosity, as well as predictions of the Leslie viscosity coefficients used in the LE theory. The original calculations by Doi for this model employed a preaveraging approximation that was later... 

As discussed before ( 5.2), a molten polymer shows also elastic behaviour, particularly on a short time-scale the fluid is visco-elastic. This can, in a simple experiment, be demonstrated in two ways. When we let a bar rotate around its axis in a viscoelastic fluid, then, after removal of the driving torque, it will rotate back over a certain angle. Moreover the fluid will, during rotation, creep upward along the bar, which indicates the existence of normal stresses next to shear stresses. 

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