This document summarizes research on improving the flotation of ultrafine particles smaller than 0.08mm. It proposes using smaller air bubbles in turbulent flow to increase collision probability between particles and bubbles. A mathematical model is described showing that concentration of particles decreases exponentially with flow distance as particles coagulate with bubbles. Experimental results show a new flotation machine using this approach concentrates over 90% of lead in under 1m3/h, demonstrating effectiveness for extracting ultrafine particles.

1. JournalofMiningScience, Vol.34, No. 5, 1998
FLOTATION OF FINE PARTICLES AND INTERGROWTHS BY
SMALL AIR BUBBLES
Yu. M. Filippov UDC 622.765
Practical experience in flotation and many special studies have demonstrated that the flotability of materials depends
on the particle size. Serious difficulties are encountered in the extraction of particles smaller than 0.02 mm, and even more
so with particles smaller than 0.01 mm. Such fine particles account for almost all of the metal that is lost to the tailings dump;
also, these particles raise the level of contamination of the concentrates with associated materials.
The low efficiency of flotation of such particles is due primarily to the low probability of their collision with air
bubbles; another factor is the disruption of the balance of hydrodynamic and surface forces acting on fine particles, lowering
the selectivity of the process.
In a number of studies, relationships have been obtained between the flotability of fine and ultrafine particles and the
size of the air bubbles [1-3]. It has been found that the extraction of particles is increased significantly as the air bubble
diameter is reduced. Hence it is of interest to obtain some sort of mathematical model for the process of flotation of ultrafine
particles by air bubbles no larger than 0.08 mm.
I. Dispersion of Air Bubbles in Turbulent Liquid Flows
N. N. Kolmogorov [4] obtained equations for the radius of a bubble formed in a turbulent flow and for a bubble formed
at the wall.
aer=L2/3LKf'P J V6/5LRI)
await ~ V- Iny / o"0'
where L is the dimension of the large-scale pulsations of the turbulent flow; Kf is a numerical coefficient; V is the flow
velocity; cr is the surface tension; % is the magnitude of the boundary layer; p and Pl are the respective densities of the air
and the liquid.
It can be seen from (1) and (2) that an effective dispersion process requires a high-velocity turbulent flow with strongly
developed small-scale pulsations.
In an actual flotation process, the air consumption Qa ~ Qp, the bubble dispersion must be sequential in turbulent flows
with a varying form, in which the velocities and the pulsation dimension are variables.
A method and a dispersing device for obtaining air bubbles smaller than 0.08 mm were described in [5]. The method
is based on successive breakup of bubbles in turbulent flows: a) In a pipe; b) in a pipe with flow around a cylinder; c) in a
plane turbulent jet successively striking a solid wall. In this last case, the jet velocity is increased in each successive impact.
Mining Institute, Siberian Branch of the Russian Academy of Sciences, Novosibirsk. Translated from Fiziko-
Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 5, pp. 114-119, September-October, 1998. Original article
submitted May 12, 1998.
466 1062-7391/98/3405-0466520.00 9 Kluwer Academic/Plenum Publishers

2. 2. Coagulation of Ultrafine Particles with Air Bubbles in a Turbulent Flow in the Course of Flotation
It is fully evident that the probability of collision of ultrafine particles and intergrowths with 1.0-2.0 mm bubbles is
negligibly small. Moreover, air bubbles of this size are unaffected by small-scale pulsations of the flow; and in relation to
ultrafine particles, the bubbles as an immobile solid body. A different mechanism is necessary for coagulation of the bubbles
with the particles.
According to [6], air bubbles smaller than 0.08 mm have the property of being involved with pulsations smaller than
the bubble dimension, these pulsations playing a primary role in the mechanism of particle/bubble encounter. Then, the process
of particle coagulation with a bubble is described by the equation of turbulent diffusion [7, 6]:
0C
0t + V(grad C) = div(D grad C) - N. C, (3)
N R.v. Re3/2
,~3 . Co~ (4)
where N is the flux of particles to the surface of a sphere of radius...*
Pulsating motion of the particles and bubbles can be described by a certain turbulence coefficient Dturb characterizing
the transport of mass by a chaotic turbulent motion D = v0,/~)2, where ~, is the dimension of the small-scale flow pulsation;
r/is the distance between particles; v is the liquid viscosity; R is the bubble dimension.
Let us examine the simplest form of turbulent flow of a liquid in a pipe with circular or rectangular cross section.
Assuming that the particle/bubble coagulation process is steady-state with respect to time, and as a consequence of the small
concentration gradient with respect to y, we fred that the equation describing the particle/bubble coagulation process in a flow
with a rectangular cross section and constant velocity will assume the form
The boundary conditions are
uOC 0 (D OC)-N.C.
C=Co at x=0.
C---~0 at x.---~oo.
(5)
(6)
We will take the turbulent diffusion coefficient in the form of the function Dx = a/(x + 1)D0, where DO is the
coefficient of turbulent diffusion in the initial section of the channel; c~ is a coefficient accounting for particle shape and
properties and the reagent quantity and quality.
The general solution of Eq. (5) with boundary conditions (6) is
C = Coexp[-E(x)] x3/2,
l u R3vRe3/2 )
~(x)= + xj/3_ u x,;2,
ado L2 aDo
(7)
where L is the dimension of the flow pulsations. It can be seen from Eq. (7) that with increasing flow velocity and increasing
coordinate x, the particle concentration decreases exponentially.
3. Determination of Detachment Forces Acting on a Particle Adhering to an Air Bubble in a Liquid Flow
Let us examine a bubble and attached particles in a turbulent liquid flow. Stability of the bubble/particle aggregate,
the same as in any thermodynamic system, corresponds to the maximum of its potential energy. The probability of existence
of an aggregate is determined by the ratio of forces acting upon it (2):
*As in Russian original; apparent omission - Translator.
467

3. TABLE 1
Feed
Concentrate
Chamber
product
Feed
Concentrate
Chamber:
product
Product iYield,%1 Content, % Recovery, % Degree of Selectivity
[ [ Pb I Zn [ Cu Pb [ Zn [ Cu enrichment ,index
First series of experiments
100,0 1.6 4,5 25,9 100 100 100
4,9 5,7 8.4 24,0 19,7 9,3 4,6 3,5 2,26
95.1 1,2 4,3 26,0 80,3 90,7 95,4
Second series of experiments
100.0 3,4 3,6 25,6 100 100 100
5.4 17,8 8,6 16,7 28,1 13,0 3,5
94,6 2,6 3,3 26,1 71,9 87,0 96,5 5,18 3,26
TABLE 2
Class
+0,44
-0,044+ 0,022
-0,022 +0,011
-0,011 +0,005
-0,005
Total
MFP-30M
First series Second series
of expts, of expts.
18,6 35,2
14,0 28,4
12,7 22,3
6,4 8,1
3,1 3,6
3,5 5,18
Laboratory
flotation
machine
7,8
7,2
5,6
4,5
2,4
2,98
FMR-10
6,5
6,02
3,49
3,20
2,07
2,12
1.2
2errat_g sinO=rcr3q(po--Po)+rc--ffCrl.g +Fd~t ; (8)
1 2 (9)
Fdet = ~-K/ p U0So,
where Kf is the drag coefficient; so is the cross-sectional area of a sphere with a radius equal to that of a sphere having a
volume equal to the sum of the bubble and particle volumes; u0 is the relative velocity of the aggregate; r and R are the
dimensions of the particle and bubble; at_g is the surface tension at the liquid/gas boundary; 0 is the angle formed by the
liquid/gas interface with the horizontal at the contact perimeter.
In [2], on the basis of an analysis of Eqs. (8) and (9), it was shown that air bubbles with a size similar to the particle
size have higher selectivities in comparison with bubbles of the size normally used in flotation.
Thus, for effective flotation of ultrafine particles and intergrowths, it is necessary to obtain a spectrum of air bubbles
in which the overwhelming majority of the bubbles have dimensions in the 0.03-0.05 nun interval. Of course, along with the
bubble size, the flow regime is important.
It is evident that for each type of flotated particles, the form and parameters of the flow must be determined.
The flotation process proceeds in the following manner: "Fine" air bubbles collide with particles, and an aggregate
is formed; if the aggregate is stable, then it is obvious that the coagulation process will proceed very rapidly. Among
themselves, bubble/particle aggregates begin to merge, forming stable floccules. These are captured by the larger bubbles (0.6-
1.0 mm) and carried out into the froth layer.
Thus, we are proposing a mathematical model of the process of flotation of ultraf'me and fine particles and intergrowths
by air bubbles smaller than 0.08 mm. To the system of equations (1)-(3) and (8), equations are added to describe the liquid
flow in a specific flotation chamber.
From the above discussion, it follows that for effective flotation of ultraf'me particles, a completely different type of
flotation machine is required.
Using the proposed model of the process, a single-chamber pneumohydraulic flotation machine has been developed
at the Mining Institute of the Siberian Branch of the Russian Academy of Sciences; also, the form of the turbulent flows and
their parameters that are required for effective flotation of fine particles have been determined.
468

4. TABLE 3
Size class
+0,063
-0,063+0,045
-0,045+0,032
-0,032+0,020
-0,020
Total
+0,063
-0,063+0.045
-0,045+0,032
-0,032+0,020
-0,020
Total
yi•eld• Concentrate Zn reco- Degree of IChamber product
ntent, yield, Zncontent;Ivery, % yield, Zn content,enrichmeni'
1% 1%. % % % ~o
First series of ex~eriments
14 0,57 29,5 1,91 3,35 11,5
8,3 0.21 6,1 0,66 3,14 I1,0
11.3 0,32 9,0 0,53 1,66 15,4
26,5 0,21 32,8 0,48 2,3 28,1
40 0,40 22,8 0,60 1,65 34,0
100,0 0,30 100,0 0,70 1,9 100,0
0,59
0,20
0,35
0,19
0,38
0,31
Seconl
16,3
7,8
12,8
22,1
42,1
100,0
series of ex:
3,24
0,72
1,82
0,87
3,83
2,1
71,0
2~,3
26,4
41,0
19,0
31,0
~eriments
75,5
58,8
62,0
55,0
66,1
62,0
5,5
3,6
5,2
4,7
10,1
6,6
14,7
8.3
13,0
15,7
40,0
100,0
0,21
0,16
0,20
0,25
0,36
0,26
12,1 0,21
9,6 0,09
13,3 0,14
29,7 o,11
35.5 0,14
100,0 0,13
An experimental model of the flotation machine MFP-30M with a capacity up to 1 m3/h was installed in an ore-
dressing plant of the Zyryanovskii Lead Combine in a scheme for selection of copper-lead concentrate after the second
control flotation [8]. It should be noted that 91% of the lead was concentrated in the class -0.011 mm, with 75% of the total
lead in the class -0.005 mm; it is known that such material is extremely difficult to upgrade.
The flotation experiments were performed in two stages. In the first stage, the operating conditions of the disperser
were such that in the spectrum of air bubbles, the averaged dimension of the small bubbles was 0.12 mm; in the second stage,
this was reduced to 0.08 mm.
It can be seen from Table 1 that the technological indexes of flotation were considerably better in the second series
of experiments than in the first.
In Table 2 we show the relationship between the degree of enrichment and particle size for two series of experiments
in the MFP-30M, a laboratory mechanical machine, and an FMR-10 flotation machine.
It can be seen from Table 2 that the degree of enrichment in flotation in the MFP-30M is almost 30 units greater for
the +0.044 class than in the FMR-10; as the particle size is reduced, this difference decreases, amounting to 1.2 for particles
in the -0.005 mm class. These data provide firm confirmation of the selectivity of the small bubbles.
There is great interest in the flotation of hatergrowths with a degree of surface exposure greater than 15%. In order
to test the hypothesis that have been advanced, we performed experiments on the flotation of intergrowths. A modernized
pneumatic flotation machine MFP-0.01, equipped with two pneumohydraulic dispersers, was installed in the Berezovskii
Oredressing Plant of the Irtysh Polymetal Combine. The feed came from the tailings dump of a flotation repartitioning process,
as the chamber product from a control zinc flotation. Mineralogical analysis of the feed to the flotation machine showed that
in the -0.060+0.044 mm class, more than 70% of the sphalerite was present in intergrowths, with about 30% in the
-0.044+0.020 mm class. Thus, the zinc in this material is concentrated mainly in the fine classes or in intergrowths. It was
difficult to carry out the finish-flotation of zinc from these classes under the plant conditions in mechanical type flotation
machines.
In the course of testing the experimental flotation machine, two series of experiments were performed. In the first
series, the jet velocities in the preliminary and main dispersers were fairly low, and hence no more than 15-20% of the air
bubbles were smaller than 0.08 mm. As a result, the technological indexes of flotation were comparatively low (Table 3).
In the second series of experiments, the jet velocities were increased in both dispersers, giving a substantial change
in the spectrum of air bubbles; also changed was the hydroaerodynamic regime of the flows moving in the flotation chamber.
The flotation indexes in the second series of experiments were incomparably better than in the first (Table 3). This difference
is particularly evident in the flotation results obtained on the -0.020 mm class particles. As indicated above, it is precisely
in the +0.020 mm class that all of the intergrowths are concentrated; this provides an explanation for the lower technological
indexes of flotation of these particles in comparison with the -0.020 mm class.
469

5. The results from these and subsequent studies performed in experimental-commercial flotation machines of the MFP
type, under actual plant conditions, have repeatedly confirmed the possibility that extremely small bubbles will flotate fine
particles effectively.
Similar results on such a classof particles were obtained in the flotation of tailings dump material from nickel flotation
at the Norilsk Oredressing Plant.
Thus, effective flotation of ultrafine particles and intergrowths depends on having air bubbles with a spectrum in which
the overwhelming majority consists of 0.03-0.05 mm bubbles; it also depends on having hydroaerodynamicflows in the volume
of the flotation chamber such that the probability of particle/bubble collision will be sufficiently high, while at the same time
the force of particle detachment from the bubble is optimal for each material being processed by flotation.
REFERENCES
l.
2.
3.
4.
5.
6.
7.
.
V. I. Melik-Chaikyazyan, N. P. Emel'yanova, and V. T. Pronin, "Possibility of separation of fine mineral particles
by flotation with small bubbles," Tsvetn. Met., No. 5 (1994).
Yu. M. Filippov, "Selectivity of small bubbles in flotation process," Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No.
2 (1994).
"New flotation process," Austral. Min., 86, No. 11 (1996).
A. M. Kolmogorov, "Drop breakup in a turbulent liquid flow," Dokl. Akad. Nauk SSSR, No. 6 (1949).
Yu. M. Filippov and S. A. Kondrat'ev, "Dispersion of air bubbles in a turbulent jet with a high exit velocity, upon
impact on a solid surface," Obogashch. Rud, No. 2 (1983).
V. G. Levich, Physicochemical Hydrodynamics, Prentice-Hall, Englewood Cliffs, N.J. (1962).
Yu. M. Filippov, "Coagulation of particles by air bubbles in a liquid flow in the process of flotation with Re >> 1,"
in: Intensification of Processes for Concentrating Minerals [in Russian], Mining Institute, Siberian Branch of the
Academy of Sciences of the USSR, Novosibirsk (1982).
G. R. Bochkarev, Yu. P. Grigor'ev, and Yu. M. Filippov, "Commercial tests on experimental pneumatic machine,"
Tsvetn. Met., No. 8 (1983).
470