Classification, jigging and froth flotation

Classification by settling velocity and equal-settling ratio, dense-medium separation, jigging, froth flotation reagents and the two-product recovery balance.

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Why it matters

Ores, coal and many industrial solids are mixtures of a valuable component and worthless gangue. Classification splits a ground solid by settling velocity (size and density), jigging concentrates heavy minerals by density, and froth flotation separates fine particles by surface chemistry. Together they decide how much of the valuable mineral a plant recovers and how pure the concentrate is.

Key ideas

Classification. Particles are separated according to their settling velocities in a fluid, usually water. Because settling velocity depends on both size and density, a classifier separates a mixture of one density by size, or a mixture of narrow size range by density.

  • Settling (gravity) classifiers — rake, spiral and cone classifiers: fast particles sink to the underflow, slow ones overflow with the liquid.
  • Hydraulic (elutriating) classifiers — a rising water stream of velocity u carries upward every particle whose terminal velocity is below u.
  • Hydrocyclones — the same principle in a centrifugal field (see the cyclone topic). They are the standard classifier in closed-circuit grinding.

Equal-settling particles. A small heavy particle and a larger light particle can have the same terminal velocity. Their diameter ratio, the equal-settling ratio, follows from setting the two terminal velocities equal. It is about the square root of the density-difference ratio in the Stokes region and equal to it in the Newton region, so separation by density is easier for coarse particles. If the size range of the feed is narrower than this ratio, a clean density separation is possible. Hindered settling raises the effective ratio, which is why density separations are run at high solids concentration.

Sink-and-float (dense-medium) separation. The particles are placed in a liquid or suspension (for example finely ground magnetite or ferrosilicon in water) whose density lies between those of the two minerals; the light one floats, the heavy one sinks, independently of size. Used for coal cleaning and pre-concentration of ores.

Jigging. A bed of particles on a screen is subjected to a pulsating vertical water current. On each upstroke the bed is lifted and opened; on the downstroke particles fall back under hindered-settling conditions, and differential initial acceleration and hindered settling make heavy particles move to the bottom and light ones to the top. Heavy concentrate is drawn off through or above the screen and light tailings overflow. Jigs work best on fairly coarse feed (millimetres upward) with a clear density difference.

Froth flotation. Finely ground ore (typically below a few hundred µm) is slurried with water and reagents; air is bubbled through. Particles whose surfaces are hydrophobic attach to bubbles and rise into a froth that is skimmed off; hydrophilic particles stay in the pulp. It separates by surface properties, not density. Reagents:

  • Collectors (e.g. xanthates for sulfide minerals) adsorb on the target mineral and make it hydrophobic.
  • Frothers (e.g. pine oil, MIBC) stabilise a fine-bubble froth.
  • Modifiers: activators, depressants and pH regulators that make the process selective. A larger contact angle between bubble and solid means stronger attachment. Very coarse particles detach from bubbles; very fine ones (slimes) float poorly and unselectively.

Measuring performance. For a two-product separation (concentrate and tailings) with assays f, c and t of the valuable component, a mass balance gives the concentrate yield and the recovery — the fraction of the valuable component in the feed that reports to the concentrate. Grade and recovery trade against each other.

Formulas

Equal-settling ratio: D_a/D_b = [(ρ_b − ρ)/(ρ_a − ρ)]ⁿ, with n = 0.5 (Stokes) and n = 1 (Newton)

  • D_a, D_b: diameters of light particle a and heavy particle b with equal terminal velocity (m); ρ_a, ρ_b: their densities; ρ: fluid density (kg/m³).

Two-product balance: C/F = (f − t)/(c − t) (mass yield of concentrate) R = c·(f − t) / [f·(c − t)] (recovery of valuable component) ratio of concentration = F/C = (c − t)/(f − t); enrichment ratio = c/f

  • F, C: feed and concentrate mass rates (kg/s or t/h); f, c, t: assays (mass fraction or %) of the valuable component in feed, concentrate and tailings; R: recovery (fraction).

Worked examples

Example 1 (standard): equal-settling ratio. Galena (ρ_b = 7500 kg/m³) and quartz (ρ_a = 2650 kg/m³) settle in water (1000 kg/m³). Find the equal-settling diameter ratio in the Stokes and Newton regions.

  1. Density-difference ratio = (7500 − 1000)/(2650 − 1000) = 6500/1650 = 3.94.
  2. Stokes region: D_a/D_b = 3.94^0.5 = 1.98.
  3. Newton region: D_a/D_b = 3.94. So, for coarse particles, a quartz grain must be nearly four times larger than a galena grain to fall as fast; if the feed's size ratio is below this, the two can be separated cleanly by settling.

Example 2 (GATE level): flotation balance. A flotation cell treats 100 t/h of ore assaying 2.5% Cu. The concentrate assays 25% Cu and the tailings 0.2% Cu. Find the concentrate rate, the copper recovery and the ratio of concentration.

  1. C/F = (f − t)/(c − t) = (2.5 − 0.2)/(25 − 0.2) = 2.3/24.8 = 0.0927.
  2. C = 0.0927 × 100 = 9.27 t/h.
  3. R = c(f − t)/[f(c − t)] = 25 × 2.3/(2.5 × 24.8) = 57.5/62.0 = 0.927 (92.7%).
  4. Ratio of concentration = 1/0.0927 = 10.8; enrichment ratio = 25/2.5 = 10. Check: Cu in = 2.5 t/h; Cu in concentrate = 9.27 × 0.25 = 2.32 t/h; Cu in tailings = 90.73 × 0.002 = 0.18 t/h; total 2.50 t/h.

Common mistakes

  • Writing recovery as (c − t)/(f − t). That is the ratio of concentration, which is greater than 1; a recovery above 100% is a sure sign of this error.
  • Using the Stokes exponent 0.5 for coarse particles that settle in the Newton region.
  • Thinking flotation separates by density. It separates by surface hydrophobicity, and dense sulfide minerals float.
  • Confusing collectors (make the mineral hydrophobic) with frothers (stabilise the froth).
  • Forgetting that a dense-medium separation works independent of particle size, while classification does not.

For GATE CH

Expect equal-settling ratio numericals in Stokes and Newton regions, two-product material balances (yield, recovery, ratio of concentration), and conceptual questions on flotation reagents, jigging principles and which separation suits which feed. Practise the two-product formula and always check that recovery lies between 0 and 1.

Quick check

  1. What is the equal-settling ratio exponent in the Newton region?
  2. What does a collector do in froth flotation?
  3. Feed 5% metal, concentrate 20%, tailings 1%: what fraction of the feed mass goes to the concentrate?
  4. Why are density separations run at high solids concentration? Answers: 1. 1. 2. Adsorbs on the target mineral and makes its surface hydrophobic. 3. (5 − 1)/(20 − 1) = 0.21. 4. Hindered settling increases the equal-settling ratio, improving separation.

Interview questions

All Mechanical Operations interview questions

Try answering each one aloud before you open it.

  1. 1.What is classification in the context of mechanical operations?Concept

    Classification in mechanical operations refers to the process of separating particles based on their size, shape, or density. It is commonly used to separate fine particles from coarse ones in a mixture. This process can be achieved using various methods such as screening, hydrocyclones, or classifiers.

  2. 2.Explain the principle of jigging in mineral processing.Concept

    Jigging is a gravity separation technique where particles are separated based on their relative density. The process involves pulsating water currents that cause the particles to stratify, with denser particles settling at the bottom and lighter particles rising to the top. This stratification allows for the separation of different mineral components.

  3. 3.What is froth flotation and how does it work?Concept

    Froth flotation is a process used to separate hydrophobic materials from hydrophilic ones. It involves adding chemicals to a slurry of finely ground ore and water, which causes the desired mineral particles to become hydrophobic. Air bubbles are introduced, and the hydrophobic particles attach to the bubbles and rise to the surface, forming a froth that can be skimmed off.

  4. 4.Why is classification important in mineral processing?Application

    Classification is crucial in mineral processing because it ensures that the subsequent processing steps are efficient. By separating particles based on size or density, classification helps in optimizing the grinding process, improving the efficiency of separation techniques like flotation, and reducing energy consumption.

  5. 5.What happens if the jigging process is not properly controlled?Application

    If the jigging process is not properly controlled, it can lead to poor separation efficiency. This may result in a mixture of particles with varying densities, leading to contamination of the final product. Additionally, improper control can cause excessive wear on equipment and increased operational costs.

  6. 6.In what scenarios would froth flotation be preferred over other separation methods?Application

    Froth flotation is preferred when dealing with fine particles that are difficult to separate using other methods like gravity separation. It is particularly effective for ores where the valuable minerals are hydrophobic and can be selectively separated from hydrophilic gangue materials. This method is widely used in the mining industry for the extraction of metals like copper, lead, and zinc.

  7. 7.How does particle size affect the efficiency of froth flotation?Application

    Particle size significantly affects the efficiency of froth flotation. If particles are too large, they may not attach well to the air bubbles, reducing recovery rates. Conversely, if particles are too fine, they may remain suspended in the water and not attach to the bubbles. Optimal particle size ensures maximum contact with bubbles and efficient separation.

  8. 8.What are the limitations of using froth flotation for mineral separation?Application

    Froth flotation has several limitations, including the requirement for fine particle sizes, which can increase grinding costs. It also requires precise control of chemical reagents and pH levels, which can be challenging. Additionally, it may not be effective for ores with complex mineralogy or those containing minerals with similar surface properties.

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