Surface shape factor

The terms av and t s are called volume and surface shape-factors, respectively. Some interesting derivations to which the Hatch-Choate equations may be applied are deducible from these relationships. Let N be the number of particles per unit-weight of material having a density p. Then... 

Now the value of S changes with time. This variable may be related to the weight of the particle at any instant by means of the shape-factors discussed in Chapter 3. Thus pajLz — w and a42 — particle-surface where p is the density of the particle, and a9 and as the volume and surface-shape factors, respectively. Combining these expressions as in Eq (3-47), we obtain... 

Determination of Surface-Shape Factor—The shape-factor is one which, when multiplied by the square of the diameter of a hypothetical particle having an average surface, gives the true surface. The shape-factor is given by Eq (3-41)... 

Table 66—Values of Volume- and Surface-Shape Factors of Various...

The investigations of Gross and Zimmerley were also concerned with surface generated by crushing and grinding. No attempt was made to determine the surface-shape factor, but the modifications of the Martin method merit discussion. 

The constants and fs may be called volume and surface shape factors, respectively. In the expressions for crystal growth rate in section 6.2.1,/v and /s are given the symbols a and / , respectively. These latter symbols are also used in Chapter 8. 

Equation 2.65 defines the useful quantity known as the specific surface area, i.e. the surface area per unit mass of solid. The constant F( = fsjfv = /31a) may be called the overall, surface-volume or specific surface shape factor. For spheres and cubes, F = 6. For other shapes F > 6. For an octahedron fy = J 2) 3,fs = 2 /3 and F = 7.35. Values of F 10 are frequently encountered in comminuted solids, and much higher values may be found for flakes and plate-like crystals. If the particles are elongated or needle-shaped, their volume and surface area may be calculated on the assumption that they are... 

Surface shape factors are much more difficult to measure than volume shape factors and they are subject to greater uncertainty. One method is as follows. A few individual crystals are observed through a low-power microscope fitted with a calibrated eyepiece, and sufficient measurements taken to allow a sketch to be made of a representative geometric shape, e.g. a parallelepipedon, ellipsoid, oblate spheroid, etc. The surface area of the representative solid body may then be calculated. It should be appreciated, of course, that the result of such a calculation will be prone to significant error. 

The particle size enters the equations through the volume equivalent particle diameter, dp, and so-called surface shape factor, /, defined as... 

If the surface shape factor kg is also independent of size, then for each original particle, the new surface created upon reduction is given by the expression ... 

Similarly the surface shape factor is the average surface area of the particle, Sp, divided by the square of the projected diameter, dp... 

The surface shape factor fs relates the external surface area A of a particle to its characteristic dimension L ... 

The specific surface shape factor F is simply the ratio of surface to volume shape factors respectively considered above, i.e. 

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