Effect of ore particle size on flotation process

In the flotation process, the attachment of the ore particles to the bubbles is the basic behavior of the flotation process. The adhesion of the ore particles to the bubbles is firm or not, although it is related to the hydrophobicity of the ore particles, but the size of the mineral particles is also in the bubbles of the ore particles. The degree of adhesion on the top has a great relationship, so the flotation granularity has a great relationship with the selection index. The smaller the floatability of the ore particles, the smaller the particle size (but should be greater than 5-10 microns), the faster and firmer the adhesion; the larger the particle size, the slower the adhesion and the less stable. Therefore, the flotation process has certain requirements on the particle size of the suspended ore, that is, the floating ore particles must be smaller than the upper limit of the mineral floating particle size. The upper limit of the particle size of the general froth flotation: 0.25 ~ 0.3 mm of sulfide minerals; 0.5 ~ 1 mm of natural sulfur .
The force of the mineral on the bubble is shown in the figure below. When the ore particles adhere to the bubbles without falling off, the forces that work in this system are:

The gravity of the ore particles in the water F 1 :
F1=d 3 (δ-⊿)g
Where d is the side length of the ore, in centimeters;
Δ——the density of the ore particles, gram/(cm) 3 ;
⊿ - the density of the liquid, gram / (cm) 3 ;
g - gravity acceleration, cm / sec 2 .
The downward direction of F 1 is the force that causes the ore particles to escape from the bubbles.
a component force F2 acting in the vertical direction on the surface tension of the three-phase wetted periphery;
F2=2 rσ gas-liquid sin θ
Where r is the radius of the attachment surface, cm;
σ gas-liquid-surface tension at the gas-liquid interface, Newton/cm;
θ - contact angle, degree.
The direction of F 2 is upward, which is the force that keeps the particles attached to the bubbles.
The pressure F 3 of the gas molecules in the bubble on the attachment surface:

Where R - bubble radius, cm.
The downward direction of F 3 is the force that causes the ore particles to detach from the bubbles.
When the ore particles adhere to the bubble and are in a condition close to falling off, the balance of the above three forces is:
F 2 =F 1 +F 3
After finishing, you can get:

The above formula expresses the relationship between the contact angle and the surface tension, the weight of the ore, the radius of the attachment surface, and the radius of the bubble when the ore and the bubble are relatively stationary. But in fact, the flotation process is in a violent relative movement, and the force is much more complicated. But still get some inspiration from the above formula:
If the contact angle of the floating mineral is large, the particle size of the ore may be coarser; if the radius of the bubble is increased, the contact angle of the floating mineral may be smaller, and the ore particle may be coarser.

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