Angle of difference

The difference between the angle of repose and the angle of fall gives an indication of the potential floodability of materials. The greater the angle of difference the better the flowability, fluidisability and floodability. 

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As early as 1669 the Danish crystallographer Steno made a detailed study of ideal and distorted quartz crystals (Figure 9-5). He traced their outlines on paper and found that the corresponding angles of different sections were always the same regardless of the actual sizes and shapes of the sections. Thus, all quartz crystals, however much distorted from the ideal, could result from the same fundamental mode of growth and, accordingly, corresponded to the same inner structure. 

Fig. 12 Water contact angles ( ) of different substrates. The block copolymer films of POEGMA-l)-PMPS- -POEGMA and POEGMA-lr-PS-f>-POEGMA selectively delaminate only from the substrates with a hydrophilic surface upon immersion in H20. Reproduced with permission from [75] Popescu et al., (2004) Macromolecules 37 3431-3437. American Chemical Society...

Other classification systems are used less frequently. Carr " also devised a system to classify materials as to their floodability. He defines the floodability of a material as its tendency to flow like a liquid because of the natural fluidization of a mass of particles by air. In order to so classify a material, the flowability is determined utilizing the method just described. This value is equivalent to a measurement Carr calls the angle of fall, angle of difference, and dispersibility. Though referred to in any of the papers mentioned here, this system is much less utilized then the flowability measurements. Geldart reported on a characterization system of powders according to their ability to aerate and later Molerus modified this system. In a more recent symposium this method of powder classification was examined. ... 

According to Table 3,1) amide of fatty alcohols and alkyl quaternary ammonium salt ratio of 2 1, surface tension when compared with 1 1 is slightly higher, but the effect of the contact Angle of three kinds of coal sample decreased, better effect than 4 1 and for the most appropriate ratio formula is amide of fatty alcohols and alkyl quaternary ammonium salt ratio of 2 1. 2) For JFC and Triton X-100 in addition to the 1 1 ratio, the surface tension of the solution are rising with other proportion. The contact Angle of different coal sample has the tendency of increase, with the rest of the proportion is not suitable for carrying out the test. 3) The compound formula was finally determined ... 

Figure 3.2 Catenation angle of different arylene rings.

Gj, 9, 9vj 9i, 92 equilibrium, Cassie-Baxter, fractal, and Wenzel contact angles and contact angles of different surface types 9q equilibrium angle Qiji, bond angle formed by atoms ij, k K reaction rate X linear dimension Xj) Debye length... 

Figure 1.9 Apparatus for the measurement of angle of repose, angle of fall and angle of difference (Carr 1965a).

Test A - Measurement of Carr angle of repose Test B - Measurement of Carr angle of fall Test C - Calculation of Carr angle of difference Test D - Measurement of Carr loose bulk density Test E - Measurement of Carr packed bulk density Test F - Calculation of Carr compressibility Test G - Measurement of Carr cohesion Test H - Measurement of Carr uniformity Test I - Measurement of Carr angle of spatula Test J - Measurement of Carr dispersibility... 

When powders flow, they do so either in a steady controlled fashion (as in the case of dry sand), or in an uncontrolled gushing manner (as would damp sand, for which the entire bulk tries to move in a solid mass). This latter condition is termed floodable flow, and is most characteristic of the flow of cohesive, sticky powders. The floodability of a powder is determined by its overall flowability (the determination of which has just been described), the angle of fall (obtained as the new repose angle when the powder cone is mechanically shocked), the dispersibility (ability of a given powder to become fluidized), and the angle of difference (obtained as the numerical difference between the angle of fall and angle of repose). 

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