When magnetite, hematite and quartz are ground by a ball mill, their grinding products follow the Gaudin-Schuhmann size distribution formula
y=100 (
x/k)
a, where
y is the cumulative weight percent [%] finer than size
x[μ],
k is the size modulus [μ] and α is the distribution modulus [-]. The grinding products which follow the G-S size distribution formula were rolled into green balls, and the capillary pressure in the balls is expressed by the following equation;
Zα=
A (0.45 cos θ)(
F(α)/
k){(1-ε)/ε}.(a) where
Zα[g/cm
2] is the capillary pressure determined, θ is the contact angle [deg], ε is the porosity [-],
k/F(α) [cm] is the average size of the grinding Products following the G-S equation, And A corresponds to the ratio of the rise of the liquid in the actual capillaries to that in idealized ones with circular cross sections of a uniform diameter.
From the measurement of the crushing strength of the green balls, it is found that the maximum crushing strength
T [g/cm
2] is proportional to the capillary pressure
Z [g/cm
2] which is calculated on the assumption that
A=1 and cos θ=1 in the equation (α).
Assuming that
T=
Za,
T/Z equals to
A. The value of
A is 1.3 for magnetite and quavtz, and 0.6 for hematite, respertively.
The capillary pressure in the balls rolled by the sized particles is expressed by the following equation;
Zα=A (0.45 cos
θ)(1/χ
αv){(1-ε)/ε}(b) where
χαv is the average size.
Using the value of
Zα obtained by the measurement of capillary rise or the maximum crushing strength of balls,
A is estimated to be 1.3-1.5 for magnetite, hematite and quartz from the equation (b).
From the above results, it is noticeable that the value of
A is considerably less than 1 of hematite.
Probably, the behavior of finer Particles, in respect of ther Plugging in the voids of coarser particles, will be particular in the grinding products of hematite
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