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of water is not sufficient to ensure satisfactory wojkability. The water
may even separate spontaneously from the system without having to create
In the diagram in Fig. 152, it is assumed that the water penetrating a
particulate system has expelled all the air as a result of complete
wetting. Some of the air, however, always remains trapped in real
systems, somewhat impairing the forming properties of plastic bodies. For
this reason, use is made of vacuum augers, which remove the remaining air
(see the next section).
Particle-size distribution is very significant in ceramic mixture
preparation, since it allows the porosity of dried, green ware to be
controlled. The pores become closed by firing and the ware shrinks as a
whole. The shrinkage is greater for a higher porosity of unfired product.
In technical practice, the shrinkage should be kept as low as possible,
(a) more accurate maintenance of the dimensional tolerances;
(b) more rapid firing (temperature gradients in the ware bring about
stresses which are proportional to shrinkage within the sintering
interval and may result in cracking);
(c) the possibility of manufacturing large products.
The most effective way of attaining low porosity of green ware is by
suitable particle--size distribution. The principle may be demonstrated
on a mixture of two uniformly sized fractions of a solid.
* The so-called lyospheres, transient layers of adsorbed liquid
bound firmly to the surface. Their thickness (with kaolinite of the order
10 nm) and their structure depend on the type of foreign ions present;
structure promoters such as Ca2 + , Mg2 + and Al3+ will result in a
thicker solvated layer being built up around the particle. The properties
of this interparticle water determine the behaviour of the system (cf.
î i î
volume of FIG. 152. Volume relations in the
added water system clay-water-air.
For single-size spherical particles, porosity can be readiJy shown to
be independent of particle radius for a particular arrangement*. For
approximately isometric particles, a porosity of about 40% is obtained in
real systems. When a fine fraction is mixed with a coarse one, then the
fine particles will fill the voids between the coarse particles. In an
optimum case, the minimum porosity amounts to 0.4 x 0.4 x 100 = = 16
vol.% However, such a packing can seldom be accomplished in practice,
because the ratio of particle sizes is not suitably high and the mixing
Volume relations in a two-component system consisting of coarse and fine
The volume relations arising in the mixing of fine and coarse
particles are demonstrated in Fig. 153. The original volumes of the
coarse and fine fractions are designated Ñ and D. The weight substitution
of the coarse fraction by the fine one first affects the total mix volume
as if the respective amount of coarse particles has been removed, since
the fine fraction is completely accommodated in the pores between the
coarse particles. For this reason, in this stage, the volume changes
along the straight line tending towards point E (line CE).
Replacement of the fine by the coarse fraction (the right-hand side
of the diagram) appears at first as the addition of a compact non-porous
solid, since the voids between the large particlcs are completely filled
with the finer fraction. The total volume therefore changes according to
the straight line tending towards the solid phase volume (line DA).
The minimum porosity is attained at the ratio where the voids between
the coarse particles are completely occupied by the finer partices. As
follow's from Fig. 153, this is the case at about 70% of the coarse
fraction. A sharp minimum would be attained at a very high ratio of
particle sizes. In fact, the behaviour of volume moves along the
indicated curve, since the ratio of particle sizes attainable does not
usually exceed 1 : 10 in practice. With binary mixes, it is possible
practically to attain a porosity of 25%, and for ternary mixes, 22%. This
corresponds to a \oIume shrinkage of 22 - 40%, i.e. linear shrinkage 7-
13% for sintered products. Theoretically, it should
* With simple cubic packing, the volume of pores amounts to 48% of
total volume, and for close-packed hexagonal array 26%.
be possible to reduce porosity still further by increasing the number of