Literature Review
2.2 The Rheology of Heavy Medium Suspensions
CHAPTER 2 LITERATURE REVIEW
•
Corrosion Resistance: The occurrence of corrosion is deleterious because corrosion leads to loss of ferrosilicon; The finely divided products of corrosion impair the separation efficiency of the process by increasing the viscosity of the medium; In situ corrosion often leads to the cementing of ferrosilicon particles when they stand in water, caused by the electrochemical oxidation of the ferrosilicon surface to produce non-magnetic iron oxides. Making the start-up of heavy medium processes very difficult after a long shut- down. Rodis .et.al. (1960) have shown that milled ferrosilicon is more susceptible to corrosion than the atomised grade because of its rough, angular shape. For plants operating under abnormal conditions such as high density, high temperature, and acidic or saline water, atomised ferro silicon is the preferred choice.• Costs: The cost of manufacturing atomised ferrosilicon is more than double that of milled ferrosilicon. However, when a choice between the two grades is being made, careful consideration into the overall advantage of each grade must be taken into cognizance.
These include lower consumption due to corrosion; adhesion, and magnetic 'separator losses; greater efficiency of separation; and a smaller bulk concentrate, reducing subsequent treatment costs.
CHAPTER 2 LITERA TURE REVIEW
The particle size distribution and the shape of the particles are the main physical properties in defining rheology, and ferro silicon media are therefore manufactured in a range of grades (or size distributions) and shapes (milled or atomised) [Dunglisonet al. (1999)].
Cf) ,
Cf) , Q)I I -
Ci5
I -ro
Q)
£ (/)
Rate of shear (dv/dx)/S-1
Figure 2.1 Rbeograms for various types of suspensions [Aplan et al. (1964)]
The rheological behaviour of heavy media suspenSIons can either be Newtonian or non- Newtonian. Viscosity may be defined as the resistance to flow of a liquid. Expressed mathematically:
(2.1)
where ~s the shear stress, I! the fluid viscosity, and
r
the shear rate.Fluids which follow Equation 2.1 are called Newtonian fluids, and the slope of the shear curve is the Newtonian viscosity. The rheological behaviour of Newtonian fluids is completely described by their viscosity. From Equation 2.1 it can be seen that a plot of shear-stress versus shear-rate is a straight line through the origin, the slope is constant and the viscosity is independent of the rate of shear. This is illustrated in Figure 2.1
CHAPTER 2 LITERA TIJRE REVIEW
However, dense medium suspensions are rarely that simple, and they fall into three general types of fluids; Bingham plastics, pseudo-plastics, and dilatants. The rheograms of these fluids are shown in Figure 2.1. A brief description of the different types of non-Newtonian behaviour, and the equations governing them is given below [Perry et al. (1997), Eirich (1967)]:
Bingham fluids include those for which a finite stress is required before continuous defonnation occurs; these are called yield-stress materials. The Bingham plastic fluid is the simplest yie1d- stress material, represented by the following equation:
(2.2)
where Q is the fluid yield stress.
Laskowski et al. (1999) define yield stress as the minimum value of shear stress which must be exceeded before a fluid can be made to flow. The occurrence of a yield stress in heavy medium suspensions is caused by inter-particle attractive forces. These forces lead to the fonnation of structural aggregates in the suspension. They also restrict the positional change of volume elements, and the suspension acquires a solid character [Whitmore et al. (1960)]. If external forces lower than the inter-particle forces are applied to the suspension, the suspension will not flow. The aggregate network can only be broken when the externally applied forces become large enough such that they overcome the yield point. This property of Bingham plastic fluids affects the pumping characteristics of the suspension the separation efficiency of dense medium separators.
In practice the curve is noted to bend downward as it nears the stress axis, due to plug flow.
Relatively few materials have been found to exhibit true Bingham plastic behaviour, and this rheological type is important in that it serves as a limiting case for the pseudo-plastic (shear- thinning) type. Typical examples of suspensions of this type are clay slurries, oil-well drilling muds, and cement plant slurries [Perry et al. (1997), Eirich (1967)].
Shear thinning fluids are those for which the ratio of the stress to the rate of shear decreases with the rate of shear. These fluids have been called pseudo-plastic, but this tenninology is outdated and discouraged. They are similar to Bingham Plastic suspensions, but show no yield value. The
CHAPTER 2 LITERATURE REVIEW
line relating the shear stress to the shear rate passes through the origin and is curved convex to the shear-stress axis up to a certain shearing stress, but is approximately linear with shear rate beyond that point [Govier et al. (1957)]. At high shear rates shear-thinning fluids behave like Bingham plastic fluids in that there is a near linear relationship between the shear stress and the shear rate.
They typically obey the following power law model over a range of shear rates:
T=kyn(n<l) (2.3)
The apparent viscosity is,
• n-l
f.J=ky (2.4)
The factor 'k' is the consistency index or the power law coefficient, and 'n' is the power law exponent. The exponent 'n' is dimensionless, while 'k' is in units of kg/ms2.n• This type of flow behaviour is typically exhibited by colloidal solutions such as carboxymethyl cellulose [Perry et al. (1997), Eirich (1967)].
Dilatant, or shear thickening fluids are the opposite situation of pseudo-plastic fluids. They show increasing viscosity with increasing shear rate. Over a limited range of shear rate they may be described by Equations 2.3 and 2.4, with the value of 'n' being greater than one [Perry et al.
(1997)]. Examples of dilatant suspensions are quick-sand, barium sulphate suspensions, aqueous suspensions of starch granules, and mica in water.
The type of non-Newtonian behaviour mentioned thus far have all been time independent.
However, some suspensions have shown a change in rheological properties over a specific period of time whilst operation conditions remained constant. Such rheological time dependency could have an influence on the design of dense media plant circuitry, particularly the residence time of the slurries in each of the process units. The two types of time-dependant flow are thixotropy and rheopexy [Slatter at al (2000)]. Thixotropic behaviour occurs because of the degradation of the structure strength during the shear loading interval, and structure recovery during the unloading interval. Alternatively, thixotropy can be defined as the decrease in yield value of a suspension subj ected to mild vibrations. This type of behaviour is a character of certain types of clay [Eirich (1960)]. Rheopexy is the opposite of thixotropy, with a build up of strength during the load phase,
CHAPTER 2 LITERA TURE REVIEW
and the decomposition of the structure strength during the discharge phase. Although rheopectic behaviour occurs very rarely compared to thixotropy, it is important because to a small degree high concentrated solutions of surfactants sometimes exhibit this type of behaviour
The use of the term viscosity as a measure of the consistency of non-Newtonian fluids is highly misleading and incorrect. As mentioned above, the viscosity of Newtonian fluids is proportional to the ratio between the unit shear-stress and shear-rate. The term viscosity has been applied to this same ratio in the case of non-Newtonian fluids. However, as illustrated in Figure 2.1, the ratio of unit shear-stress and shear-rate for Bingham plastics, pseudo-plastics and dilatants varies, depending upon the shear-rate [Govier et al. (1957)]. Thus, while Newtonian fluids can be characterized by the viscosity, which is independent of the shear-rate, non-Newtonian fluids are described by a series of' apparent viscosities' spanning the range of shear-rate of interest.
For a constant suspension specific gravity, a higher density solid will reduce the viscosity and stability of the suspension by reducing the percentage volume of particles. A spherical medium reduces the viscosity and stability of the suspension by providing more slippage between adjacent solids in the suspension. A coarser medium reduces the viscosity and stability of the suspension by reducing the solid particle surface area, which in turn reduces the apparent solids volume concentration [Collins et al. (1983)].
Although most suspensions show non-Newtonian behaviour, it is usually difficult to predict the type of non-Newtonian behaviour occurring in different systems [Lapsin et al. (1988)]. The type of non-Newtonian behaviour can vary within a single class of systems, especially when the concentration is varied. Some concentrated suspensions can show shear-thinning behaviour at low shear rates, and shear-thickening at higher shear rates. Collins et al. (1974) found that for ferrosilicon suspensions at low shear rates showed shear-thinning behaviour, and shear-thickening behaviour at higher shear rates. The above authors also found that by increasing the degree of contamination of the suspensions, or increasing the suspension specific gravity, the suspensions acquired a yield stress. The figure below shows the effect of suspension density on the viscosity of some common heavy medium suspensions. It can be seen from the figure that the critical density for magnetite suspensions is much lower than that of ferrosilicon suspensions.
CHAPTER 2
(,.'
. . -1
1.:9 ~
LITERATURE REVIEW
• :: CR:TiU .. L CONCENTR;'.T 1 0:1
Figure 2. 2 Effect of pulp density upon apparent viscosity for various suspended medium [Burt (1984)]
Despite the fact that ferrosilicon media are more costly compared to magnetite media, they are still used to maintain suspensions at high specific gravities because of the much higher viscosity and stability problems associated with magnetite suspensions at the same specific gravities. These much higher viscosities reduce the separation efficiency of fine ores and near specific gravity material. The reduction of magnetite suspension viscosities at these high specific gravities can be achieved through the use of coarser magnetite media compared to ferrosilicon media at the same specific gravities [Collins et al. (1983)]. The main problem associated with the use of a coarser medium is the increase in the settling rate of the medium. To alleviate this problem fine media or slimes would have to be used together with the coarse media to reduce the settling rates of the media. Alternatively, the viscosity can be reduced by using dispersants. There are a great variety of dispersants which may be used, such as: alkali phosphates; sodium silicate;
ethylenediaminetetracetic acid; surface active agents, such as lignosulphonates and petroleum sulphonates [Aplan et al. (1964)]. The chemistry and nature of surface active agents will be detailed in a later section.
CHAPTER 2 LITERA TURE REVIEW
Viscosity may be defined as the resistance to flow of a liquid. In the previous section the different types of flow behaviour of fluids were defined. Fluids can either show Newtonian behaviour or non-Newtonian behaviour. Heavy medium suspensions usually show non-Newtonian behaviour;
being either Bingham plastic, shear-thickening, or shear-thickening.
Bevilacqua et al. (1999) did a study on the rheology of low density suspensions in dense medium separation of post-consumer plastics. Although the paper dealt with the separation of plastics, the rheological and performance data obtained were found to be very similar to the dense medium separation of coal. The dense medium solutions were prepared using clays at different size distributions. They found that between a shear rate 0-300 S-1 the rheological behaviour was pseudo-plastic with yield stress (Bingham plastic). As the size distribution varied, suspensions containing a higher percentage of fine material showed higher yield stress values.
As mentioned previously, there are two types of commercial ferrosilicon solids available in industry; milled and atomised ferrosilicon. Ferrara et al. (1986) found that ferrosilicon suspensions behaved like Newtonian fluids at low densities (pseudo-Newtonian behaviour). They also found that by increasing the density and the degree of contamination of the suspensions (e.g.
with clay) the yield stress value increased. Collins et al. (1974) found that ferrosilicon suspensions show pseudo-plastic characteristics at low shear rates, and dilatant characteristics at higher shear rates. An increase in the density of the media resulted in an increase in the dilatant behaviour of the suspensions. This critical value of pulp density for the atomised grades was shown to be much higher than for the milled grades.
Shi et al. (1996) simulated slurry rheology as a function of slurry properties to illustrate the nature of the effects of solids concentration and particle size on rheology. The simulated rheological behaviour tallied well with many observations from industrial grinding slurries. The results showed that at low solids concentration (15 % solids by volume), slurries behave as dilatant fluids. Increasing the fines content leads to an increase in the dilatant trend, and also the development of a yield stress. At intermediate solids concentration (30 % solids by volume), and relatively coarse size, the flow exhibits the characteristics of a classic Bingham plastic. However, at an intermediate density with a high content of fines, the dilatant trend is still present. As the slurry density increases to 45 % solids by volume and the fines content increases, all slurries behave as pseudo-plastic with a yield stress. The higher the fines content of the slurry, the more apparent is the pseudo-plastic trend. The following conclusions were drawn from their study:
CHAPTER 2 LITERATURE REVIEW
• When slurries contain relatively low solids concentration and high contents of fines (typically less than 42 % solids by volume and more than 25-35 % -38JLm e.g. tertiary mill or regrind mill discharge slurries), their rheological character is likely to be dilatant.
• When slurry densities are increased and the amount of fines content is reduced (e.g. 44- 58 % solids by volume and less than 20 % -38JLm), the slurries are likely to exhibit pseudo-plastic characteristics.
• Increasing either fines content or slurry density leads to increased yield stress for both dilatant and pseudo-plastic flows.
Klimpel (1982) also found that many coals and mineral slurries exhibit dilatant character at relatively low slurry densities (less than 40-45 % solids volume for typical size distributions). He also found that increasing the slurry density increases the trend towards pseudo-plastic behaviour.
In some industrial processes ferrosilicon and magnetite are not used separately to make up the medium, but different combinations of the solids are used. The ratio of ferrosilicon to magnetite is largely governed by the medium specific gravity required. For specific gravities greater than 3.0 Ferrosilicon is largely employed on its own. Dilution with magnetite largely takes place at specific gravities below 3.0. Combinations of ferrosilicon and magnetite result in changes in the flow behaviour of the resultant medium compared to that of the individual solid media. Collins et al. (1983) performed experiments on different ratios of ferro silicon and magnetite solutions. They found that pure ferrosilicon solutions showed Newtonian behaviour at low densities and low shear rates, and pseudo-plastic behaviour at high shear rates for either high or low densities. Mixtures of ferrosilicon and magnetite were found to be essentially pseudo-plastic at low magnetite levels (l125 % magnetite), but showed Bingham plastic conditions at higher levels (050 % magnetite). The yield stress of the medium was observed to increase with an increase in the magnetite content. Aplan et al. (1964) attributed this yield stress to the increase in finer material due to the addition of magnetite. They showed through size distribution curves that magnetite media contain about 20 - 30 % more finer material than ferrosilicon media.
Laskowski et al. (1999) stated that the rheological properties of magnetite suspensions are mainly controlled by solid content (medium density), particle size distribution, particle shape, clay
CHAPTER 2 LITERATURE REVIEW
contamination and demagnetization. Magnetite suspensions, even when fine, have been observed to be very unstable. As will be shown later in this section, this poses severe problems for rheological measurements and requires the use of specially designed viscometers. It has been observed that magnetite suspensions display non-Newtonian behaviour. The rheological behaviour of these suspensions is a function of shear rate and exhibits pseudo-plastic characteristics at low shear rates (up to about 300 S·I) and dilatancy at high shear rates [Laskowski et al. (1999)].
Increasing the medium density has a drastic influence on the medium rheology. An increase in medium density results in an increase in the solid content of the medium i.e. an increase in solid volume percentage. This results in an increase in particle-particle interactions (friction and collision), thereby increasing the viscosity of the suspensions. Collins et al. (1983) indicated that on a semi-log plot the relationship between apparent viscosity and magnetite content is linear.
Stability is a property of the suspension considered as a non-homogeneous two-phase system and is related to the rheology of the solid phase in an environment constituted by the liquid phase. The relative movement of the solids in the liquid phase under mass and surface forces determines the suspensions degree of homogeneity, an important medium property in heavy medium separations.
Medium stability determines the density gradient of the medium in the separation zone and thus influences separation efficiency [Bozzato et al. (2000)]. Therefore, it is one of the most important parameters to keep under control.
CHAPTER 2 LITERATURE REVIEW
2.2.1 Effect of particle size / size distribution
Table 2.2 shows the different size distributions of milled and atornised ferrosilicon media used in heavy medium separations.
Table 2.2 Size range consistency of some typical ferro silicon media [Burt (1984)]
Name 650 1000 1500 2700 Normal fine Cyclone 60 cyclone 40 Size pm milled milled milled milled atomized atomized atomized
wt% wt% wt% wt% wt% wt% wt%
+210
-210 +150 2 7
-150+105 5 10 2
-105 +74 12 4 15 5 2
-74 +44 35 30 23 10 10 22 20
-44 45 65 75 90 45 73 90
Ferrosilicon and magnetite media used in the preparation of heavy medium suspensIOns are available in different size distributions. Sizing for quality control is carried out by conventional screening down to 38 p,m and by sub-sieve methods, thereafter by cyc10ning methods to about 5 p,m [Collins et al. (1974)]. The size distributions of the media taken from heavy medium circuits have been found to be well represented by the Rosin-Rammler distribution:
Equation 2.5 can be linearized as follows;
In In _ R W
=
b(ln x -In a) 100Where W R = % mass retained,
x = size (determined by nominal aperture), and a, b = constants.
(2.5)
(2.6)
CHAPTER 2 LITERATURE REVIEW
By plotting In In (WRIlOO) versus In x a straight line is obtained with a gradient equal to 'b'. The characteristic size distribution is generally defined as the size at which x
=
a. This results in W R=
100e-1
=
36.8 % [Wills (1997)]. It is also important to note that for Equation 2.6 to have real roots, the value of x should be greater than that of the constant a.It has been found that for ferrosilicon size distributions, the linear correlation for straight lines fitted in this way is normally close to ideal. The ability ofFeSi size distributions to be represented in this way is extremely useful both for specification purposes, and in the evaluation of research and plant tests [Collins et al. (1974)].
The size distribution of any media chosen for application in heavy medium separations has a direct influence on the viscosity and stability of the media. For a constant dense medium specific gravity, a coarser media type reduces the stability and viscosity of the media. Conversely, using a finer media type increases both the stability and the viscosity of the m~dia. Aplan et al. (1964), using size distribution curves, showed that samples of commercial ferrosilicon contained less fine material than magnetite. The finer media is mown to be more viscous at higher suspension gravities, giving ferrosilicon suspensions an inherent advantage over magnetite suspensions at higher densities. Collins et al. (1983) also found that the viscosity of pure ferrosilicon suspensions is much lower than that of pure magnetite suspensions, or ferrosilicon - magnetite suspensions at constant volume concentrations. They attributed this to the effect of particle shape and size range of the magnetite relative to ferrosilicon. Grobler et al. (2002), using ferrosilicon media, also showed that increasing the amount of fines content in the media resulted in an increase in the viscosity of the ferrosilicon suspensions.
He et al. (1994) performed some experiments to determine the effect of dense medium properties on the separation performance of a dense medium cyclone. They used four magnetite samples, which covered a broad range of particle size distributions. They showed that the separation efficiency was highly dependant on media particle size. They found that viscosity and stability of the suspensions increased as the media size distribution became finer. With coarser magnetite, they found that the stability of the suspensions was too low at low specific gravities, resulting in low separation efficiencies. The stability improved as the specific gravity of the suspensions increased.