Internal friction angle

Geldart a group Powder Average particle size, (, )J.m Particle density, p, kg/m Angles Internal friction, deg of Repose, deg Sphericity, f... 

Fig. 3. Complex-plane diagram showing vector relationships among stress, strain, = complex modulus, = Mreal = storage modulus, M2 = M maginary modulus, and (j) = loss angle = internal friction. Adapted from Nowick and Berry.

Rock Porosity Cohesion c in MPa Angle Internal Friction tp Range of Confining Pressure in MPa... 

Internal angle of friction deg deg ( 0 Applied axial stress kg/cm psf... 

Here, [L is the coefficient of internal friction, ( ) is the internal angle of friction, andc is the shear strength of the powder in the absence of any applied normal load. The yield locus of a powder may be determined from a shear cell, which typically consists of a cell composed of an upper and lower ring. The normal load is applied to the powder vertically while shear stresses are measured while the lower half of the cell is either translated or rotated [Carson Marinelli, loc. cit.]. Over-... 

In addition to the physical properties just described there are those properties which affect the flowability of the material. Specifically, these properties are the material s angle of repose, angle of internal friction, and the angle of slide. 

The angle of internal friction, a, is defined as the equilibrium angle between flowing particles and bulk or stationary solids in a bin. Figure 4 illustrates the definition. The angle of internal friction is greater than the angle of repose. 

Angle of Internal Friction—a. Angle of internal friction, or angle of shear, is the angle of solid against solid. It is the angle at which a catalyst will flow on itself in the nonfluidized state. For an FCC catalyst, this is about 80°. 

Note that for completeness, the nondimensional particle size distribution, sphericity and the internal angle of friction (for slugging and spouting beds) should also be matched between the two beds. 

The internal friction angle is also important for slugging beds (Zenz and Othmer, 1960). DiFelice et al. (1992 a, b) did not report their values it could be that the disagreement they found in their slugging bed tests was due to mismatches of the internal friction angle. 

Figure 33. Dimensionless spoutdiametersasafunctionof dimensionless height for small columns. Case A test case Case B all dimensionless parameters matched, bed diameter halved Case C particle Reynolds number mismatched Case D Froude number mismatched Case E density ratio, Reynolds number mismatched Case F bed Reynolds number mismatched Case G internal friction angle, loose packed voidage mismatched. (From He et al., 1995.)...

If the fluid stream is a gas, the last term in the above equation is essentially unity. Unless the cyclone itself is rotating or, for example, located on another planet, g can be taken as 32.2. If the bulk solids angle of internal friction is unknown, then taking an average value of 62 degrees, the equation reduces to ... 

The influence of consolidation load on the flowability of sucrose is shown in Fig. 8. For this material, the effective angle of internal friction is nearly constant yet the shear index is seen to change with state of consolidation. Apparently, for sucrose, increased consolidation results in a somewhat more free flowing although still cohesive material. As such, sucrose can be considered a complex powder [49] with perhaps somewhat better flow characteristics when consolidated (as might occur in a hopper). 

Podczeck, F., Miah, Y. The influence of particle size and shape on the angle of internal friction and the flow factor of unlubricated and lubricated powders. Int. J. Pharm., 144, 1996, 187-194. 

Figure 10 Mass flow/funnel flow design chart for a conical hopper handling a bulk material with a 40 effective angle of internal friction.

The angle of repose of a powder blend, effective angle of internal friction (EAIF) from shear cell measurements, and the mean time to avalanche (MTA) in powder cohesivity tests are useful for assessing the flow of a tableting mixture at various scales (15 18). 

At very low solvent viscosity, when f is small compared with the internal friction factors, the chain molecules must behave like "frozen molecules. In this case, the initial slope of the extinction angle curve becomes again a linear function of the solvent viscosity. The slope of this straight line, however, is considerably higher than (J eRj2)(M ri jRT). Its intercept with the ordinate axis is equal to zero. This behaviour is schematically shown in Fig. 5.10 (3). 

As the results of Schwander and Cerf (188) and of Leray (180,181), which were obtained on samples of DNA from calf thymus, have been reproduced already in several review articles (1,3), the present discussion can be kept rather short. When the viscosity of the solvent (1.0 molar aquous solution of sodium chloride) is increased by replacing part of the water by glycerol, the behaviour of the initial slope of the extinction angle curve follows the qualitative pattern, as given by Fig. 5.10. At low solvent viscosities the molecules seem to behave like frozen molecules, at high solvent viscosities they seem to become flexible coils exhibiting internal friction. These results have been considered to prove the correctness of Cerf s theoretical model. 

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