Adhesion of Irregularly Shaped Particles

Specific Features of Adhesion of Irregularly Shaped Particles. Irregular particles are characterized by three measurements length, width, and height. It is not feasible to compare the adhesion of irregular particles on the basis of these three measurements. Hence it is necessary to reduce the dimensions of irregular particles to a single dimension equivalent to these three. 

These values are valid only for loess particles with a double-mean radius greater than 60 fjim. 

The relationship between adhesive force and sphericity factor, as determined by direct detachment of loess particles with a double-mean radius of 100-160 ixm is illustrated by the following data  

As the sphericity factor increases from 0.4 to 0.9, the adhesive force drops off because of the decrease in the actual contact area for irregularly shaped particles. We also find a greater scatter of values of adhesive force with irregular particles than with spherical particles. For example, in the case of particles with a double-mean radius of 180 juni, the force of adhesion varies over a range of 2.8- 10 to 1.4- 10 dyn. 

Corn [89] noted that the adhesion of fibers with fused spherical ends (see Fig. III.9.b) was greater than that of fibers with ends in other shapes (see Fig. 

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In the general case, the number of contacts in the adhesion of irregularly shaped particles to a rough surface will be proportional to the particle size and inversely proportional to the distance between asperities of the rough surface, i.e.,... 

Dependence of Adhesive Force on Size of Irregularly Shaped Particles. Experiments have been performed [194] to characterize the relationship between the adhesion of irregularly shaped particles and the size of these particles. The equivalent diameter (see Section 14) was taken as a single parameter characterizing the size of irregularly shaped particles. 

Thus we see that, in a liquid medium, the adhesive-force distribution for irregularly shaped particles also follows a log-normal law. This enables us to determine the median force of adhesion and to calculate the average force of adhesion. The values found for the median force of adhesion of irregularly shaped particles are generally greater than those for the equivalent spherical particles. In a liquid medium, in all cases, for particles of different shapes, we find that the adhesive force varies directly with the particle size. 

The relationships found in the adhesion of irregularly shaped particles to painted surfaces, in comparison with the adhesion of spherical particles, have been set forth in Fig. V. 14 (curves 2 and 2 ). The adhesion of irregular particles with diameters larger than 70 jum will be greater than the adhesion of equivalent regularly shaped particles. For particles with diameters smaller than 70 /rm, the reverse relationship can be expected. The characteristic features that we have examined previously for the adhesion of particles to rough surfaces (see Section... 

The velocity Up for detachment of the loess particles is considerably greater than that for the detachment of the spherical particles. These higher values are explained by the increased adhesion of irregularly shaped particles and also by the different distance from the surface to the center of the loess particles in comparison with the spherical particles. 

The author s research has been directed toward analysis of adhesive interactions when roughness and other surface properties are taken into account, the characterization of adhesion of irregularly shaped particles, the relationship between the structure of the boundary layer and the conditions of particle detachment by an air stream, and a number of other questions. 

The concept of the sphericity factor still cannot be used fully in evaluating the specific features of adhesion for irregularly shaped particles since it does not really account for the relationship among the height, length, and width of the particle. This relationship is taken into account more fully in a concept that we have considered previously [162], that of equivalent size of particles, as determined by means of Eqs. (III. 14)-(III. 16). 

We will now compare the forces of adhesion of spherical particles with those of irregularly shaped particles that are equivalent in size to the spherical particles. 

In Fig. V. 13 we show integral curves of adhesion for spherical glass particles with a diameter of 20-40 [xm and for irregularly shaped particles of equivalent size. The distribution of irregularly shaped particles with respect to adhesive force, the same as the spherical particles, follows a log-normal law. 

As can be seen from these data, irregularly shaped particles with an equivalent size (diameter) of 70-110 /zm show an increase in average force of adhesion with increasing particle size the values obtained for the average force of adhesion with irregularly shaped particles are smaller than the values obtained for equivalent spherical particles. As the particle size increases from 70 to 110 fim, the difference in adhesive force between spherical and irregular particles becomes less pronounced. 

Thus we see that the distribution of irregularly shaped particles follows a log-normal law. Those definitions and calculational formulas (see p. 141) that were proposed for use in finding the average force of adhesion of spherical particles can also be used for irregular particles for which the dimensions have been reduced to a single equivalent dimension. 

Relationship between Adhesive Force and Size of Irregularly Shaped Particles. In the general case, when rough, irregularly shaped particles come into contact with a rough surface, the adhesive force will be a function of the equivalent radii of curvature of the contiguous bodies and the number of contacts between them, i.e.,... 

Fig. V.14. Average force of adhesion as a function of equivalent size (diameter) of irregularly shaped particles (1 ) or diameter of spherical particles (l, 2 ) on following surfaces (1,1 ) steel, with Class 5 finish, (2,2 ) painted with chlorinated PVC.

The yield of retained fraction in the case of irregularly shaped particles was found to be 1.3-1.5 times that for particles with a rounded shape. In crushing operations, for example, particles of barite, quartz, feldspar, and magnetite form rounded particles, decreasing their adhesion. The wastes from low grades of asbestos contain irregularly shaped mineral dust particles, which adhere to the drum surface and are separated as the retained fraction [137]. 

The adhesion of irregularly shaped toner particles to the carrier surface is greater than that of regularly shaped particles. With either type of particle, however, the true contact area will be much smaller than the surface area of the carrier particle. 

The number of experiments in which the effect of particle shape on the adhesive forces has been investigated is extremely limited. Table IV.5 presents some results of Fuks et al. on the sliding of irregularly shaped particles, as determined by the inclined-surface method. 

Fig. 1.5 Average adhesive force (1, 2, V, 2 ) and detaching force (3,4) (in dynes) as functions of particle size (1,2) for spherical particles (l, 2 ) for irregularly shaped particles on steel surface (1,1 ) and on chlorinated PVC enameled surface (2,2 ) (3,4) for detaching acceleration of 2 and 4 g-units, respectively.

Thus, the adhesive force for irregularly shaped particles on a rough surface will depend on the relationship between such parameters as the equivalent radius of curvature of the contiguous phases and the number of contacts, which in turn will depend on the particle size and the characteristics of the rough surface. 

When surfaces covered with irregularly shaped particles are placed in an aqueous medium, the force of adhesion is lower than it is in air. The change in median force of adhesion for irregular particles adhering to steel surfaces (Class 5 finish) when the air is replaced with water is illustrated by the following data ... 

The adhesive-force distribution of adherent particles with irregular and spherical shapes is shown in Fig. VI. 16. With respect to equivalent diameter, the adhesive-force distribution of irregular particles also follows a log-normal law. The adhesion of irregular particles in the aqueous medium is greater than that of the equivalent spherical particles. This higher level of adhesion for the irregular particles is observed over the entire range of values of ap. 

In conclusion, we will present comparative data on the median force of adhesion for particles of different shapes and sizes on unpainted and painted metal surfaces (Fig. VI. 17). In all cases, the median force of adhesion for the irregularly shaped particles is greater than the force of adhesion for equivalent spherical particles. 

Fig. VI.17. Median force of adhesion as a function of particle size in aqueous medium on a metal surface painted with chlorinated PVC enamel, V) and on an unpainted surface (2,2 ), for spherical glass particles (1,2) and irregularly shaped particles (1, 2 ).

A lower adhesion of particles to painted surfaces in a liquid medium in comparison with adhesion in air has also been observed for irregularly shaped particles. In air, the median force of adhesion for irregular particles with an equivalent diameter of 70-110 jum was found to vary from 1.3 10 to 3.8 10 dyn in an aqueous medium, the median force for these same particles varied from 1.6 10 to 4.8 10" dyn. The adhesion of particles to paint and varnish coatings in the aqueous medium was 2 orders of magnitude less than in air i.e., the general relationships found previously for adhesive interaction (see Sections 20 and 30) are manifested under these conditions also. 

The application of a paint or varnish coating changes the properties of the original surface, particularly the surface roughness. Hence the adhesive interaction on painted surfaces will differ from the interaction of the same particles on unpainted surfaces. The influence of surface painting on adhesive force can be evaluated in terms of the relative force of adhesion, i.e., the ratio of adhesive force to particle weight. This ratio, for irregularly shaped particles on unpainted and painted steel surfaces (steel surface with a Class 5 finish) was found to be as follows ... 

The relative force of adhesion in air for irregularly shaped particles with a reduced diameter of 70-120 /xm was greater on rough, unpainted steel surfaces than on painted surfaces. 

Figure III.15 shows the adhesive forces measured by the method of direct detachment for loess particles as a function of the sphericity factor. As the sphericity factor rises from 0,4 to 0,9, the adhesive force diminishes as a result of the reduction in the actual contact area of regularly shaped particles. For particles of irregular shape there is a greater spread of adhesive-force values than for spherical particles. Thus, for particles with a double mean radius of 180 M, the adhesive force varies between 2.8 10 and 1,4 10 dyn.

Due to their disperse character and small particle size, silicas are used as flow aids, i.e. they are used to improve the flow behaviour of other materials. The adsorption of the fine silica particles on other type powdered compounds reduces interparticle interactions. Particle adhesion, electrostatic adhesion, Van Der Waals forces and liquid bridge formation is reduced or avoided.33 This allows free-flowing behaviour of strongly interacting or irregularly shaped powdered materials. 

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