Jan Svoboda. Magnetic Techniques for the Treatment of Materials
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440 CHAPTER 5. PRACTICAL ASPECTS OF MAGNETIC METHODS
chemicals. At the production rate of 82 c/h of 0.035 T fluid, which can be
diluted to 143 c/h of 0.02 T fluid, the 1983 cost of the 0.02 T ferrofluid would
be less than US$1.00/c.
A batch pilot-plant with capacity of 6 c/h was constructed in 1998 at De
Beers Consolidated Mines (Pty.) Ltd. (South Africa) to evaluate the process
scale-up for the manufacture of kerosene-based ferrofluid. The raw material cost
for 1 litre of 0.04 T ferrofluid was, in 2002, US$1.25 [K23]. The manufacturing
cost of this fluid, at the production rate of 6 c/h, was approximately US$2.50 for
the 0.04 T fluid or US$1.35 per litre for the 0.02 T fluid. Further cost reduction
was obtained in the automated continuous plant with a capacity of 10 c/h, as a
result of cheaper chemicals and lower labour costs [V7].
5.6.2 Ferrohydrostatic separation
As has been discussed in Sections 3.8 and 4.8, the e!ciency and selectivity of
separation in a ferrofluid depends upon the pattern of the magnetic field in the
working gap of a magnet. This pattern is determined by the shape of the pole
tips. If the gradient of the magnetic field is not constant along the vertical axis
of the system (see Figs. 4.51 and 4.54), the apparent density of the fluid along
the vertical will also vary and several density fractions can be obtained, as is
shown in Fig. 4.53. Such an approach to material separation is acceptable only
if the density dierential between the components of a mixture is large and the
required accuracy of separation is limited.
For accurate separation into two well-defined density fractions the field gra-
dient must be constant along the vertical. Such a pattern of the field gradient
can be achieved using hyperbolic shapes for the pole tips, as shown in Section
4.8.2.
The fundamental relationship that defines the required field gradient is given
by eq. (2.9). For the required range of apparent densities, and for the range
of saturation polarizations of available ferrofluids, the field gradient can be de-
termined from eq. (2.9). Once the gradient of the magnetic field has been
determined, the shape of the pole tips can be designed using the procedure
outlined in Section 4.8.3.
A typical relationship between the apparent density, magnetic field strength
(or the electrical current in the coil) and the physical density of the ferrofluid
is shown in Fig. 5.106. It can be seen that, in this specific case, the apparent
density ranges from 2500 kg/m
3
to 5500 kg/m
3
, depending on the density (and
magnetization) of the ferrofluid. The lower limit of the apparent density that
can be obtained in FHS, for a given shape of the pole tips, is determined by
the magnetization of the ferrofluid that can still be held in the separation gap
of the magnet. The upper limit of the apparent density is given either by the
maximum magnetization of the ferrofluid and/or by the acceptable viscosity of
the ferrofluid The eects of the ferrofluid polarization and of the field gradient
on the apparent density, are shown in Figs. 5.107, and 5.108, respectively.
It can be seen, therefore, that for a given shape of the pole tips only a
relatively narrow range of apparent densities can be generated. In order to
5.6. SEPARATION IN MAGNETIC FLUIDS 441
Figure 5.106: The apparent density of the ferrofluid as a function of the electrical
current, for various physical densities of the ferrofluid and for a
particular shape of the pole tips.
achieve higher (or lower) apparent densities, the shape of the pole tips has to
be re-designed, as described in Section 4.8.3. To obtain low apparent densities,
at which the ferrofluid is too weakly magnetic to remain in the working gap of
the separator, special measures must be introduced to restrain the fluid in the
separation space. In principle, it is essentially impossible to design a separator
operating e!ciently over the entire range of apparent densities [G4].
Optimization of the pole-tip profile
A simplified approach to the pole-tip design required that the vertical compo-
nent of the field gradient be constant (eq. (4.60)). As has been discussed earlier,
most ferrofluids are not likely to be saturated at the magnetic field usually used
in ferrohydrostatic separators, (as shown in Fig. 5.98). In order to obtain the
shape of a pole tip that would ensure truly constant apparent density of the
ferrofluid along the vertical, it follows from eq. (2.9) that the product M
i
uE
must be constant, at the working magnetic induction of the ferrohydrostatic
separator:
M
i
uE = frqvw= (5.28)
It is obvious that the shape of the pole tips thus obtained will ensure a
constant apparent density only for a ferrofluid of a specific density with known
details of its magnetization curve.
442 CHAPTER 5. PRACTICAL ASPECTS OF MAGNETIC METHODS
Figure 5.107: The eect of polarization of the ferrofluid (
0
= 1000 kg/m
3
)on
its apparent density when exposed to the field gradient of 2 T/m.
Figure 5.108: The eect of magnetic field gradient on the apparent density of
ferrofluid (M = 0.02 T,
0
= 1000 kg/m
3
).
5.6. SEPARATION IN MAGNETIC FLUIDS 443
A well optimized shape of pole tips will generate an apparent density that
will be constant along a limited region along the vertical, at the centre of the
separation gap, as is shown in Fig. 4.57.
Feed preparation
Magnetic scalping In order to prevent blockage of the separation chamber,
strongly magnetic components must be removed from the feed by magnetic
scalping using, for instance, a permanent magnet roll. Selection of the type of
the magnet in the roll and of the operating conditions, is determined mainly by
the magnetic field strength generated by the ferrohydrostatic separator. FHS
units operating at high densities, or high-throughput separators, in which the
gap between the pole pieces is large, usually generate a magnetic field of the
order of 0.5 T or higher and an RE magnet roll should be used. Smaller units,
with throughputs up to 100 kg/h, usually use a magnetic field as low as 0.2 T
to 0.3 T, and scalping using a strontium ferrite roll is su!cient. Material with
a magnetic susceptibility as high as 6×10
6
m
3
/kg (500×10
6
cm
3
/g) can be
fed into such a FHS machine without any problems.
As has been discussed in Section 3.8.4, materials with non-zero magnetic
susceptibilities, immersed in a ferrofluid, exhibit an eective density that is
greater than their physical density. This density dierence, given by eq. (3.159),
increases with increasing magnetic susceptibility and external magnetic field, as
shown in Fig. 3.59. In those applications where accurate density separation
of materials, which dier in their magnetic properties, is required, accurate
magnetic scalping should be carried out. On the other hand, density dierential
as a result of dierences in magnetic susceptibilities can be advantageously used
to separate materials with similar physical densities. Using magnetic tracers,
the cut-point magnetic susceptibilities can be set quite accurately. Cut-point
magnetic susceptibilities down to 10×10
7
m
3
/kg can be set with strontium
ferrite rolls, while an NdFeB roll can remove materials with susceptibilities as
low as 2.5×10
7
m
3
/kg.
The eect of moisture The presence of moisture has an eect on the ef-
ficiency of separation and the degree of this influence depends on the type of
ferrofluid used, and on the size, wettability and porosity of particles to be sep-
arated. When a kerosene-based ferrofluid is used, the presence of moisture
reduces the eective density of the material, which is reflected in a decreasing
amount of material reporting into the sink fraction, as can be seen in Fig. 5.109.
For highly selective separation of relative fine materials with close densities, it
is important, therefore, to feed the material into the FHS separator in a dry
form. However, a mixture of coarse materials, particularly with a large density
dierential, can be treated wet.
444 CHAPTER 5. PRACTICAL ASPECTS OF MAGNETIC METHODS
Figure 5.109: The eect of moisture on the FHS recovery of materials into the
sink fraction. Apparent densities for kimberlite,
d
= 3500 kg/m
3
,
and for ferrochrome slag,
d
= 5700 kg/m
3
[S8, D16].
Separation chambers
Numerous designs of separation chambers have been used over the years and
their description can be found in a review article by Fujita [F8]. More recent
ferrohydrostatic separators usually use an open-ended stainless steel trough po-
sitioned between the hyperbolic pole tips of the magnet, as is shown in Figs.
2.103 and 4.56. Such a separation chamber shown in Fig. 5.110, is usually in-
clined at a small angle to facilitate movement of particles through the fluid. The
chamber can also be vibrated to assist in propelling particles into usually two
discharge outlets, where the float and sink fractions are collected. A splitter is
often installed to separate the sink and float fractions, and its judicious position
is important for accuracy of separation.
The most frequently employed separation chambers use a solid bottom, as
shown in Fig. 5.111, while the front end of the chamber is opened to allow con-
tinuous removal of the separation products. Although the bottomless chamber,
shown also in Fig. 5.111, allows simple removal of the sink fraction, the dis-
advantage is often a considerable sagging of the ferrofluid outside the working
space of the separator. Gubarevich [G4, G17] showed that, in equilibrium, the
balance of forces acting on the ferrofluid placed in a non-homogeneous magnetic
field is expressed by
i
jc =
1
0
Z
E(|
2
)
E(|
1
)
MgE (5.29)
5.6. SEPARATION IN MAGNETIC FLUIDS 445
Figure 5.110: Separation chamber of a ferrohydrostatic separator.
y
S N S
N
y
1
y
2
Suspended fluid in a
bottomless chamber
Chamber with
solid bottom
y
Figure 5.111: Designs of separation chambers in FHS.
446 CHAPTER 5. PRACTICAL ASPECTS OF MAGNETIC METHODS
Figure 5.112: Graphical determination of the equilibrium length of the fer-
rofluid column. The slope of the straight line is given by: wj =
0
i
j@M
v
(after [G4]).
where c is the length of the column of the ferrofluid,
i
and M its density and
polarization, respectively. E(|
l
) is the magnetic induction at position |
l
(l =1,
2) as shown in Fig. 5.111. While an analytical solution of the above equation is
di!cult, it is fairly easy to develop a graphical technique to solve the equation
and to determine the length of the ferrofluid column that can be held within
the magnetic field of the separator.
Figure 5.112 depicts a pattern of the magnetic induction along the vertical
axis | with the origin at the lower edge of the pole pieces. If we assume that the
polarization is independent of the magnetic induction and thus M = M
v
, then eq.
(5.29) can be re-written
E
c
=
0
i
j
M
v
(5.30)
where E = E(|
2
) E(|
1
).
The tangent of the straight line in Fig. 5.112 is thus given by the right-
hand side of eq. (5.30) and intersections of the straight line E = |
0
i
j@M
v
with curve E = E(|) determine the coordinates |
1
and |
2
of the end points of
the ferrofluid column. By shifting this line along the | axis it is then possible
to determine the sagging of the ferrofluid, for a given length of the ferrofluid
column.
It is clear that only a limited length of the ferrofluid column can be retained
in a bottomless chamber before the fluid starts running out of the chamber.
Several methods have been proposed to address this problem. A layer of a
5.6. SEPARATION IN MAGNETIC FLUIDS 447
Figure 5.113: Retention of a ferrofluid in a separation chamber by a more
strongly magnetic ferrofluid.
strongly magnetic ferrofluid based on a carrier liquid (e.g. kerosene) that is
immiscible with the working fluid (water) can be introduced into the separation
chamber [G4]. As can be seen in Fig. 5.113, such a strongly magnetic fluid
will form a "liquid bottom" that will support a su!ciently high column of the
working fluid. Discharge of the sink fraction through the supporting layer is
facilitated by the fact that it is positioned in a zone with an inverted magnetic
field gradient, below the point at which uE = 0, as can be seen in Fig. 4.57.
An alternative technique to prevent sagging of the ferrofluid is the applica-
tion of a water column as shown in Fig. 5.114. This technique is particularly
suitable for the separation of materials of low density where a relatively feebly
magnetic ferrofluid is placed in a low-gradient magnetic field. The height c
z
of the hydraulic support column, for a given ferrohydrostatic separator, can be
determined from a relationship
c
z
=(
1
0
Z
E
2
E
1
MgE +
i
jc
i
)@
z
j (5.31)
where
z
is the density of the supporting liquid.
Themodeoffeeding
It is well established that the way in which the particles are fed into the ferrofluid
aects significantly the results of separation. Particles can be dropped into
448 CHAPTER 5. PRACTICAL ASPECTS OF MAGNETIC METHODS
l
w
l
f
N
S
B
2
B
1
g
rad B = 0
Figure 5.114: Schematic diagram of a hydraulic support of a ferrofluid column
in FHS (adapted from [G17]).
the ferrofluid directly from a certain height or introduced indirectly into the
ferrofluid at essentially zero initial velocity from a ramp that determines the level
of the ferrofluid in the chamber. In the direct method, shown in Fig. 5.115, the
selectivity of separation is strongly dependent on the drop height, particle size
and on the depth of the ferrofluid pool, particularly for materials with small
density dierentials. Introduction of particles into the ferrofluid at non-zero
velocity, on the other hand, improves considerably the wetting of the particles
with ferrofluid, and partially eliminates the eect of surface tension, which is of
importance in the separation of fine particles or particles of large aspect ratio.
In the indirect mode, the eect of particle size is less pronounced, particu-
larly when the depth of the ferrofluid pool is su!cient. However, the adverse
eect of surface tension of the ferrofluid does not allow selective separation of
fine particles, particularly with a small density dierential. The e!ciency of
separation, when the direct and indirect modes of feeding material onto the up-
per level of the ferrofluid are employed, is impaired by considerable interparticle
interactions within the pool of the ferrofluid, particularly when high feedrates
are used.
A comparison of trajectories of particles that were introduced directly into
the ferrofluid from a height of 10 mm and from essentially zero height (2 mm)
is given in Fig. 5.116. It can be seen that for a small drop height (2 mm),
a particle with density of 3500 kg/m
3
will hover within the fluid of apparent
density of 3500 kg/m
3
, while a particle with density of 3400 kg/m
3
dropped
into the fluid from 10 mm will sink.
Disadvantages of feeding material onto the top of the ferrofluid can be re-
duced by introducing the feed horizontally and directly into the centre of the
pool of the fluid. Such an approach was employed in the early AVCO, NASA
5.6. SEPARATION IN MAGNETIC FLUIDS 449
Figure 5.115: Direct mode of feeding material into ferrofluid. Drop height: 40
mm [K23].
Figure 5.116: Comparison of trajectories of particles introduced in FHS from
dierent heights. Apparent density: 3500 kg/m
3
=