Single particle size equivalent dimensions

However, it is not easy to evaluate the particle size of a powder. For a large lump, it is possible to measure it in three dimensions. But if the substance is milled, the resulting particles are irregular with different numbers of faces and it would be difficult or impracticable to determine more than a single dimension.For this reason, a solid particle is often considered to approximate to a sphere characterized by a diameter. The measurement is thus based on a hypothetical sphere that represents only an approximation to the true shape of the particle. The dimension is thus referred to as the equivalent diameter of the particle. 

Sometimes the height of irregularly shaped particles is neglected in this case, the particle length / and width b are determined, these dimensions are then reduced to a single dimension. The concept of equivalent shape and size of particles [107] is used for this purpose. The edge of a cube is such an equivalent dimension for irregularly shaped particles. For particles with projections close to a circle or square (/ Z = 1 1 or 1 2), the equivalent dimension is... 

Thus, is the dimensions of cylindrical particles are reduced to a single equivalent dimension, we then find, as in the case of adhesion of spherical particles in an aqueous medium, that the adhesive foce varies directly with particle size. 

Derived diameters are determined by measuring size-dependent properties of particles and relating them to single linear dimensions. The most widely used of these are the equivalent spherical diameters. Thus, a unit cube has the same volume as a sphere of diameter 1.24 units hence this is the derived volume diameter. The diameter therefore depends upon the measured property. Consider a cube of side 1 cm its volume V = 1 cm and its superficial surface area S = 6 cm, is the diameter of a sphere having the same volume as the cube and d is the diameter of a sphere having the same surface area. 

A comparison of the relationship between adhesive force and size of cylindrical particles can be made if the cyUndrical particle dimensions can be reduced to a single dimension. For this purpose it is necessary to find the equivalent diameter of spherical particles such that their adhesive interaction would be equivalent to the interaction of the cylindrical particles. In this connection we will make use of the concept of disjoining pressure (see Section 26), which is determined by means of Eq. (VI. 8). 

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