Torque, suspensions

Continuous clarifiers generally are employed with dilute suspensions, principally industrial process streams and domestic municipal wastes, and their primary purpose is to produce a relatively clear overflow. They are basically identical to thickeners in design and layout except that they employ a mechanism of hghter construction and a drive head with a lower torque capability. These differences are permitted in clarification applications because the thickened pulp produced is smaller in volume and appreciably lower in suspended solids concentration, owing in part to the large percentage of relatively fine (smaller than 10 Im) solids. The installed cost of a clarifier, therefore, is approximately 5 to 10 percent less than that of a thickener of equal tank size, as given in Fig. 18-94. 

The tool features a spline assembly that transmits high torque loads to the bit through its outer tube, while the inner assembly absorbs vibration through a series of steel-disc springs. The spring system works in both suspension and compression. 

Viscosity A 16 ml sample of the suspension removed after remixing was used for torque measurements using a Brookfield viscometer (Model LVTD) with a UL adapter. Initial torque readings were used for estimating viscosity in order to avoid problems arising from any settling of the kaolinite in the viscometer during the measurements. 

Few details of the apparatus are given in ISO 4663, it is simply stated that means shall be provided to measure frequency to 1% ( 5% in a transition region), amplitude to 1% and, for method C, the supplied energy to 2%. It is suggested that a moment of inertia of about 0.03 gm is suitable for the inertia member which may be a disc or rod. For methods B and C the torsion wire should be of such dimensions that its restoring torque is not more than 25% of the total restoring torque due to the test piece and suspension. BS 903 (equivalent to method B of ISO 4663) suggests that moments of inertia between 50 and 500 g cm are suitable and states that the tensile strain on the test piece should be between 0 and 5%. The British... 

Finally, the distribution of solid particles across the gap may not be uniform if the fibers separated out of the suspension. Therefore, based on the previous reasoning, it is concluded that the stress method does not offer a reliable and accurate way to measure yield stress in filamentous suspensions. Figure 5 shows the typical torque-time relationship obtained with the helical impeller method for corn stover suspensions. 

The helical impeller technique is better suited to measure yield stress in a greater variety of fluids, including filamentous suspensions. The helical impeller technique is also less sensitive to initial undesired torque deflections in the measuring spring. The undesired initial torque, introduced at the moment the helical impeller is submerged into the liquid, can easily be... 

Newtonian and non-Newtonian calibration fluids were used to determine the necessary calibration constants for the impeller method. It has been previously determined that the impeller method is only valid for a Reynolds number (Re) <10. Impeller rotational speed and torque data from Newtonian calibration fluids of known viscosity were employed to determine the Newtonian calibration constant, c. Cone-and plate-viscometer data from non-Newtonian calibration fluids were used to determine a viscosity vs shear rate relationship. Impeller rotational speed and torque data of the non-Newtonian calibration fluids combined with a determined viscosity vs shear rate correlation were utilized to calculate the shear rate constant, k. The impeller method calibration constants allow the calculation of viscosity, shear rate, and shear stress data of non-Newtonian suspensions. Metz et al. (2) have thoroughly discussed the equations utilized in the impeller method. 

Viscosity, shear stress, and shear rate can be calculated for any non-Newtonian suspension using the impeller method calibration constants. Viscosity is determined using Eq. 4. The shear stress can be calculated for any impeller speed and measured torque ... 

Consider a single, freely suspended axisymmetric particle in a homogeneous shear flow held of an incompressible Newtonian liquid. The free suspension condition implies that the net instantaneous force and torque on the particle vanish. There is, however, a finite net force along the axis that one half of the particle exerts on the other, as shown schematically in Fig. 7.25. 

Wiedmann et al. (1980) have compared the mixing of nonaerated liquids, aerated liquids, and slurries in a turbulent flow. They found that the torque required for stirred, aerated liquids is lower than that for nonaerated stirred liquids because of the decrease in the density of the gas-liquid mixture. The concentration distribution of the particles in aerated suspension becomes more uniform with increasing impeller speed, whereby the torque is higher than that for aerated liquids but lower than that for nonaerated slurries. For gas-liquid-solid systems, very limited data on dispersion of solids and gas phase are available, and further studies are necessary with different designs and for systems with different physical properties. The available literature has been reviewed by Stiegel et al. (1978), Shah et al. (1982), and Shah and Sharma (1986). 

This generic formula permits averages to be calculated for any pertinent suspension property /. When time-independent external forces F(e) and torques N(e) act on each of the suspended particles, Eq. (7.14), together with the net force- and torque-free conditions characterizing the neutrally buoyant... 

Available results pertinent to the hydrodynamics of fractal suspensions are sparse thus far, encompassing only three physical situations. Gilbert and Adler (1986) determined the Stokes rotation-resistance dyadic for spheres arranged in a Leibniz packing [Fig. 7(a)], With the gap between any two spheres assumed small compared with their radii, lubrication-type approximations suffice. In this analysis, the inner spheres are assumed to rotate freely, whereas external torques T( (i = 1, 2, 3) are applied to the three other spheres. For Stokes flow, these torques are linearly related to the sphere angular velocities by the expression... 

FIGURE 12.10 Reduced torque versus strain following flow reversal for hard sphere suspension of various concentrations. Polystyrene spheres 45 pm in diameter in silicone oil. Taken from Gadala-Maria and Acrivos [34]. 

The melt is stirred with an agitator running at 30 rpm to keep the catalyst in suspension. The torque on the agitator is monitored to determine the level of inorganic impurities and carbon residues that have accumulated. At a preset torque level the polymer melt is completely pyrolyzed and the carbon residues and impurities are then evacuated from the chamber using an auger positioned in the base of the vessel. Char removal is only activated when the vessel is cooled. 

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