The effect of solids in the pulp zone will be determined from measurements of bubble size distribution and gas hold-up. There is little literature on either relevant to flotation systems and that is contradictory. For instance, measurement of bubble size (D_b) in a lab-scale cell by Grau et al. [7] suggested particles (hydrophilic quartz) cause an increase in D_b. Finch et al. [8] inferring from data on sulphide flotation plants concluded particles had little effect, a finding apparent in the visualizations provided Quinn et al. [9] in laboratory column flotation tests on a sulphide ore. Kuan and Finch [10] concluded the presence of solids has little effect provided there is no adsorption of frother by the solid: in the case of talc and a polypropylene frother adsorption was sufficient to eliminate bubble size reduction but this was not the case with talc and alcohol frothers.

The general gas hold-up/gas velocity (E_g-J_g) relationship reflects solution chemistry (e.g. frother concentration) and slurry properties (e.g. percent solids), as illustrated in Figure 1. The relationship found in flotation cells is almost linear over the practical range of J_g [11] [12] . In 2-phase systems increasing frother concentration increases the gas holdup, E_g, reflecting since the impact of frother on reducing bubble size and, consequently, reducing bubble terminal velocity that means the gas residence time is increased [13] . The general observation on adding solids is to decrease E_g [14] . The usual explanation is that solids induce coalescence and the larger bubbles move faster. The tested systems often do not contain surfactant such as frother designed to retard coalescence. Banisi et al. [15] testing a range of solids in the presence of frothers presented data that suggested a de-

crease in gas hold-up can occur without change (increase) in bubble size. They argued that solids increased rise bubble rise velocity and this was the origin of the gas hold-up decrease. Flotation implies that particles are carried by bubbles and this can affect gas hold-up without changing bubble size. Garibay et al. [16] tested the impact of increasing solids content (%solids) in a flotation column where gas hold-up tends to increase up the column reflecting the increase in bubble size (volume) as static head pressure decreases. (The larger volume means higher local gas content, i.e., gas hold-up, and this is more significant than any increase in rise velocity due to increased bubble size and buoyancy [17] . They showed that above ca. 20% solids the gas holdup started to decrease with height now reflecting the slowing down of the bubbles due to the particle load. No independent measure of bubble was made to support the interpretation, however. Kuan and Finch [10] made a similar argument for the increase in gas hold-up in the case of talc and 1-pentanol noting that bubbles in this alcohol are not at terminal velocity and attached solids can slow the bubble rise. In that case it was confirmed by direct measurement that bubble size had not changed. Measurements of both bubble size and gas hold-up make for a powerful combination to interpret observations on the role of solids.

The froth zone has attracted increasing attention in the last decade [18] [19] including the role of solids as summarized in a recent review by Hunter et al., [20] . Froth is an integral part of the flotation system but despite the importance, relatively few studies have been conducted to examine the impact of froth variables (e.g. bubble size, frother type and concentration, liquid/gas/solid content) on the performance of flotation cells [21] - [25] . If the froth phase is not sufficiently stable (i.e., there is excessive bubble coalescence), mineralized bubbles that enter the froth may rupture prematurely causing valuable mineral particles to drop back into the pulp zone. Conversely, too stable froth may cause nonselective entrainment of hydrophilic gangue particles due to excessive water recovery, thereby reducing concentrate grade. Froth stability has been characterized by several methods including: water overflow rate [26] , gas retention time vs. frother concentration [27] , and froth height vs. gas holdup relationship [28] . Much of the work has focused on 2-phase systems. Moyo et al. [26] indicated the strong relationship between water overflow rate (i.e., J_wO) and E_g in 2-phase tests and showed a unique relationship for each frother type. The presence of solids will influence J_wO. The studies by Melo and Laskowski [29] and Kuan and Finch [10] comparing frother types showed that polyglycol frothers produced a higher J_wO than alcohol frothers but that this order reversed in the presence of solids (naturally hydrophobic coal and talc, respectively). As noted in discussion of pulp zone properties the reason appears to be adsorption of some frothers by some solids and thus a change in froth zone stability. It is clear that froth stability is dependent not only on the type and concentration of frothers but also on the solids characteristics (concentration, degree of hydrophobicity, interaction with frother) [10] [20] [25] [30] - [32] . One way to study solids effects on pulp and froth zone properties while free of interaction with frother may be to use salts to replace frothers [33] .

The concentration of frother in the pulp determines the extent of bubble coalescence [37] - [39] . The continued addition of frother has a diminishing effect resulting in bubble size reaching a limiting value at a concentration now referred to as the critical coalescence concentration (CCC) [39] . Although the mechanism by which frothers retard coalescence is still debated, evidence [7] [40] suggests that they might bind water molecules to the bubble surface by hydrogen bonding, thus making it more difficult for the water to drain between approaching bubbles. This phenomenon can be considered the origin of a surface viscosity that is different (higher) than the bulk [41] . Other researchers [34] [42] infer this mechanism also by reference to bubble hydration by frothers.

To help explain this mechanism, consider that frother molecules adsorb on the bubble surface with the hydrophilic (i.e., polar) group oriented to the water-side of the interface (as illustrated in Figure 8). In this orientation H-bonding occurs and increases the stability of the water layer surrounding the bubble (the hydration layer). For bubbles to coalesce this hydrated layer must be disrupted which requires energy.

The so-called gas dispersion parameters have been studied intensively over the last 20 years [43] - [45] . These parameters comprise superficial gas velocity (J_g), gas holdup (E_g), bubble size (D_b) and bubble surface area flux (S_b). Several research groups [5] [43] [46] - [49] have shown that the overall flotation rate constant increases as bubble size is reduced. More commonly today this effect is incorporated in the bubble surface area flux, S_b, which combines the effect of superficial gas velocity (J_g) and Sauter mean bubble size (D₃₂) (S_b = 6 J_g/D₃₂). Figure 2 shows results plotted as rate constant vs. bubble surface area flux giving a close to linear relationship. This figure shows that the effect of frother in controlling bubble size is highly relevant to flotation.

Gas holdup (E_g) in the 2-phase system is readily determined from the hydrostatic pressure difference measured over a set distance in the pulp. In the 3-phase systems E_g measurements can be accomplished using conductivity [45] [50] . Frother concentration influences E_g by controlling bubble size and bubble rise velocity. Azgomi et al. [51] showed that frother type had an effect on gas holdup in addition to its role in controlling bubble size. This was later traced to an effect of frother type on bubble rise velocity [52] [53] . The mechanisms at play the surface of a bubble rising through a frother solution are shown in the Figure 3.

As Figure 3 shows, based on the Frumkin-Levich theory [54] , frother molecules adsorb on the leading surface of bubbles, which are then transported to the rear of the bubble in response to drag from the liquid as the bubble rises. The bubble is said to be mobile. This results in a lowering of surface tension at the bubble rear compared to the front creating a difference in the surface tension with a positive gradient (i.e., a force) directed towards the upper region. This force is in a direction opposite to the flow of liquid and consequently reduces the mobility of the surface. This decrease in mobility makes the bubbles behave more like hollow solid spheres; the surface is said to be more “rigid”.

The decrease in the velocity of an air bubble due to frother is pronounced, as shown in Figure 4 (the frother selected is MIBC and the single bubble diameter was ca. 1.5 mm with measurements at 3 m in a column). The effect of the surface tension gradient force is apparent also in the bubble resisting deformation. There is a relationship between shape and velocity [55] [56] .

As shown in Figure 5, velocity increases with bubble size over the range of interest in flotation (ca. 0.5 to 2.5 mm) [57] . The figure reveals the effect of the frother concentration as the “contaminated water” plot. The combination of bubble size, velocity and frother type/concentration has a profound impact on the gas holdup in the pulp. The same combination also affects shape oscillation [56] with as yet unexplored implications to flotation.

Cappuccitti and Nesset [58] , based on the work of Azgomi et al. [51] and Moyo et al. [26] , explored a possible method to classify frothers using gas holdup (E_g) vs. froth height to try to capture the two frother functions (control of bubble size and froth stability). The relationships readily identify frothers giving more control over froth stability (polyglycols) from those giving more control over gas holdup/bubble size (alcohols).

Finch et al. [47] investigated the relationship between E_g and S_b using data from several sources, proposing that S_b can be determined from gas holdup (S_b ~ 5.5E_g). This implies a consistent relationship between gas holdup and bubble size. The results from Azgomi et al. [51] examined the correspondence of gas holdup with bubble size, an example being Figure 6(a). This shows the relationship is not straightforward: at low concentration while bubble size is decreasing gas holdup remains almost constant while at high concentration bubble size (at least the D₃₂) becomes constant and gas holdup continues to increase. Figure 6(b) offers a possible explanation: at low concentration (e.g. <5 ppm) bubble rise velocity is not decreasing while at high concentration it is continuing to decrease.

Azgomi et al. [51] found a frother type effect: for instance, n-pentanol and F150 could give the same gas holdup but with bubbles in n-pentanol being significantly smaller than F150. This implies bubbles in n-pentanol rise faster than equal-sized bubbles in F150 and this proved to be the case, for bubbles in swarms [53] and for single bubbles [52] . To interpret the effect of solids, the competing influences on bubble size and velocity must be considered.

The froth zone (illustrated in Figure 7) contributes to the flotation process by providing transport to the overflow of the collected (hydrophobic) minerals and rejecting entrained gangue by drainage back to the pulp. Various parameters have been used to describe froth zone behavior among them: target mineral recovery, entrained solids recovery and water recovery [5] . The presence of frother is considered to provide froth stability by retarding bubble coalescence. The mechanisms are those already introduced based on surface tension and surface hydration with an additional one sometimes considered based on bubble surface charge [33] [60] . Mineralized air bubbles also contribute to froth stabilization [20] . The mechanism is mechanical, the particles providing a barrier to coalescence although for nano-sized particles there is evidence of surface tension depression suggestive of a chemical (frother-like) effect [61] .

Analysis of froths has considered thermodynamic aspects [63] and kinetics [64] . According to Shkodin and Tikhomivova [64] at the first stage of froth formation (i.e., at the base of the froth), bubbles are separated by a liquid film in the order of ca. 1 µm. The film is bounded by solvated envelopes (hydrated layers) with properties different from those of the “free” water, as illustrated in Figure 8. On drainage the film thins and the hydrated layers come into contact between neighbouring bubbles. The next stage involves removal of the liquid in the two contacting hydration layers. Depending on the nature of the hydration layer, which reflects the surfactant type, drainage and coalescence can be rapid (e.g. with alcohol frothers) or the film be more persistent (e.g. with some polyglycols, and by common experience soaps and detergents). Gravity and capillary effects in addition to the properties of the hydration layer govern the water drainage. The resultant transition in bubble size as froth ages

(i.e., transition in the vertical direction) is illustrated in Figure 7. This remains the general understanding, at least in the absence of solid particles.

Mechanistic modeling of froths related to flotation systems has accelerated over the last decade. The starting description (e.g. [65] ) sees bubbles in the froth as surrounded by thin lamellae (the hydrated layer) and when three (or more) bubbles meet, a “reservoir” (Plateau border region) is formed at the intersection (Figure 9). Most of the water in froth is contained in the Plateau border region with only a small fraction residing in the lamellae.

Cilliers and co-workers [65] - [67] developed fundamental (i.e., physics-based) models to predict water overflow (J_wO) from foam (2-phase froth). Central to the development was the concept of air recovery, α, the fraction of air entering the foam that leaves as unbroken bubbles. Their analysis resulted in two relationships [65] depending on the air recovery. In terms of the symbols used in this proposal, these relationships are:

where constant k represents the balance between gravity and viscosity, expressed as:

where ρ, µ, g is liquid density (g/cm³), kinetic viscosity (g/cm×s) and the gravitational constant (cm/s²), respec-

tively, and C_pb is the viscous drag coefficient in the Plateau border. To balance the units, the unit of constant k is cm⁻¹∙s⁻¹.

In Equation (1), α < 0.5 represents unstable, shallow froth, which creates an overflow rate that depends closely on α (since more than 50% of the air in froth bubbles is lost to bursting before overflowing). When the froth becomes stable, α > 0.5 (Equation (2)), α bubble bursting can be neglected and the water overflow rate becomes independent of α. Note that the bubble size to calculate J_wO is the mean bubble size flowing over the lip.

Regardless of α, both relationships show J_wO varies with, which is supported by some work [6] [65] . The experimental data of Neethling et al. is shown in Figure 10 on log-log axes. The linear data trend showed the power law and the calculated exponent of 1.97 is close to the predicted value of 2 in Equations (1) & (2). The experimental results of Engelbrecht and Woodburn, [68] and Quinn [69] , however, show that the water overflow rate J_wO increases linearly with the air rate J_g. A recent modification to the theory opens a possible reconciliation with these data [66] . An experimental difficulty is that varying J_g also varies D_bI and likely influences D_bO. Further investigations are required.

Moyo et al. [26] found that water overflow rate correlated against gas holdup in the pulp zone and the trends were unique to frother type. Zhang et al. [70] - [81] introduced a way to estimate bubble surface area flux to overflow (S_bO) given by:

and showed the water overflow rate was vs. S_bO was also unique to frother type. The use of bubble surface area flux will be a feature of the proposed work.