Regularly shaped particles

Today s massive efforts in nanotechnology will certainly provide more well-defined, regular-shaped particles in the submicron range, and mini fixed-bed technology wiU profit from that. 

The three most important characteristics of an individual particle are its composition, its size and its shape. Composition determines such properties as density and conductivity, provided that the particle is completely uniform. In many cases, however, the particle is porous or it may consist of a continuous matrix in which small particles of a second material are distributed. Particle size is important in that this affects properties such as the surface per unit volume and the rate at which a particle will settle in a fluid. A particle shape may be regular, such as spherical or cubic, or it may be irregular as, for example, with a piece of broken glass. Regular shapes are capable of precise definition by mathematical equations. Irregular shapes are not and the properties of irregular particles are usually expressed in terms of some particular characteristics of a regular shaped particle. 

For non-spherical particles, values of sphericity lie in the range 0 < < 1. Thus, the effective particle diameter for fluidization purposes is the product of the surface-volume mean diameter and the sphericity (Kunii and Levenspiel, 1991). The sphericity of regular-shaped particles can be deduced by geometry whilst the sphericity of irregular-shaped... 

Similar to other raw materials, e.g., metals, it is principally possible to vary the properties of macromolecular substances by mixing two or more different polymers. Though, one has to pay attention to the fact that in most cases phase-separated, i.e., heterogeneous products are obtained by mixing macromolecules. These polymer blends consist of a continuous phase (matrix) in which a discontinuous (dispersed) phase in the form of more or less regularly shaped particles is included. This phenomenon can be explained thermodynamically ... 

Features of Adhesion of Cylindrical Particles and Other Regularly Shaped Particles. As in air, particle adhesion in liquid media has a number of special features when the particles are not spherical. First, let us consider the adhesion of particles to a glass surface in an aqueous medium when the particles are cylinders with a diameter of 40 fim and a length within the range of 100-600 jLim. The distribution of adherent particles with respect to adhesive force in a liquid medium, the same as in air (see Fig. V.l 1), follows a log-normal law [194]. 

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... 

Cylindrical particles and other regularly shaped particles also show greater forces of adhesion on an oily surface than on the original painted surface. For cylindrical glass particles adhering to an oily surface, we also find a log-normal distribution of particles with respect to adhesive force. Hence we can find the median force of adhesion [194], which is listed below for different particle lengths (oil layer density 0.1 mg/cm ) ... 

Thus we see that for regularly shaped particles (spherical, cylindrical, and rectangular, prismoidal), the forces of particle adhesion to oily surfaces are much greater than the forces of adhesion to painted surfaces that do not have any oil layer. 

An adherent layer of particles with a regular shape (with flat faces) is detached more rapidly than a layer of irregular particles. With an air velocity of 30 m/sec, within 0.25 sec from the moment at which the air stream starts to act, approximately 60% of an adherent layer of regularly shaped particles is detached, but only 20% are detached if the particles are irregularly shaped. The denudation rate can be calculated ... 

Fig. X.9. Velocity of denudation of dust deposits on surface covered with Grade 0 emergy paper as a function of parameter (Fautp) r for adherent layer of regularly shaped particles (2) or irregularly shaped particles (1) dimensions of dust deposit 17.8 X 5.1 X 0.6 cm.

Under these conditions, the irregular particles were removed by the stream to shorter distances from the site of particle detachment, in comparison with regularly shaped particles of equivalent size. 

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. 

Today the dry adsorbed emulsions are obtained from a W/O emulsion containing a hydrosoluble active ingredient, effective in small do.ses and characterized by a short or a long half-life. Each phase of the emulsion is fixed on a compatible polarity adsorbent so that a fluid powder with regularly shaped particles and a. sustained release effect of drug is obtained. 

Regular-shaped particles can be accurately described by giving the shape and a number of dimensions. Examples are given in Table 1.1. 

The cosolvent effect on the dimensions and shape of the particles is due to the formation of a layer around the monomer droplets and this layer controls the transfer of the monomer molecules from inside the droplets to the surrounding aqueous phase and can absorb the monomer molecules that are dispersed in the solvent e.g. in the presence of toluene, the size of the drop limits the dimension of the particle and also reduces the probability of collision, responsible of the coalescence. Moreover, the cosolvent acts as a hydrophobic layer and reduces the potential energy of the interface, leading to an overall stabilization of the emulsion and hence to regularly shaped particles a high polydispersity and irregular particle shapes were found for those samples prepared in the absence of toluene, while very low polydispersity and a regular round shape were found for the others this behavior is consistent with the study of Tanrisever et al. [284] on the polymerization kinetics of PMMA. 

Maximum packing concentration of solids Concentration by weight of the solid particles in percent Diameter of a sphere with a surface area equal to the surface area of the ir regularly shaped particle flLpp Apparent particle diameter... 

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.

In order to test the measuring system and verify the measuring principle, measurements were initially conducted using steel balls and then with non-spherical, but regularly-shaped particles. The measurements with the steel balls allow an assessment of whether the three optical sub-systems operate to an absolutely equivalent standard. From the results, one can also assess the highest attainable measuring reproducibility, the accuracy and resolution of such a system (i.e. in the absence of any shape influence). 

The regularly-shaped particles (cube, cuboid, cylinder, cone etc.) were individually made in the size range of between 1 mm and 6 mm. Regular bodies allow the average projected area and volume to be calculated from their linear dimensions. In the case of the average projected area, this can either be calculated numerically by a computer or with the aid of the Cauchy theorem ... 

In Eq. 3.4, /, Vi, and di are the beam length across the sample (the sample chamber thickness), the volume, and the diameter of particle i, respectively. A correction factor can be added for non-spherical but regularly shaped particles [14]. Sample concentration can also be estimated because it is inversely... 

Table 6.1, Theoretical models for electrophoretic mobility of regularly shaped particles...

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