D5 · Publication Volume 21

Physical Separation

gravity, magnetic, dense-media separation and sorting

Learning objectives

By the end of this lesson, the learner should be able to match a physical-separation method to a measured property contrast; distinguish gravity, magnetic, dense-media and sensor-based sorting responses; explain liberation and size constraints; interpret partition, recovery and upgrading curves; calculate simple separation metrics; recognise misplaced material and bypass; and design a staged preconcentration assessment without assuming that a visible contrast is economically useful.

Start from a property contrast

Physical separation succeeds when particles differ in a property that can be measured or acted upon at the operating scale. Relevant contrasts include density, magnetic susceptibility, electrical conductivity, optical or spectral response, radiometric response, surface or shape characteristics and size. The first question is not “which machine?” but “which particle property differs, how large is the contrast, at what size is it expressed, and how stable is it across domains?”

Distinguish mineral property from particle property. A dense target mineral embedded in a low-density gangue particle produces a composite density. A magnetic inclusion may change a particle response without making it a clean product. A sensor sees a surface or transmitted signal that may not represent the interior. Property distributions overlap, so separators produce probabilistic partitions rather than perfect binary decisions.

Gravity separation and settling response

Gravity methods use differences in particle motion under gravity, acceleration and fluid resistance. Density contrast is central, but size, shape, viscosity, turbulence, bed structure and hindered settling also matter. In a simplified low-inertia regime for an isolated sphere, terminal velocity can be expressed as

$v_t=\frac{(\rho_p-\rho_f)g d^2}{18\mu},$

where particle density is \rho_p, fluid density is \rho_f, diameter is d and dynamic viscosity is \mu. This relation illustrates coupled effects; it is not a design equation for all separators.

Equal-settling effects mean a small dense particle can behave like a larger light particle. Narrow size fractions can therefore improve selectivity. Fine particles may be dominated by drag and surface effects, while coarse particles may be insufficiently liberated. Test gravity response by size and mineral, record water and solids conditions, and distinguish true density separation from classification by size.

Dense-media separation

Dense-media separation places particles in a fluid or suspension with a controlled effective density. Particles with effective density above the cut tend to sink; lighter particles tend to float, subject to size, shape, residence and medium stability. It is often considered for coarse preconcentration where waste can be rejected before fine grinding, but only if valuable-mineral loss and product handling remain acceptable.

A partition curve plots the probability of reporting to one product against particle density or a suitable proxy. The density at 50% partition locates an effective cut, while the curve width describes imperfection. Near-density material is intrinsically difficult to separate. Measure feed density distribution, partition by density and size, medium density, contamination, misplaced fractions and sampling uncertainty. A single float-sink point cannot describe the operating window.

Magnetic and electrical separation

Magnetic response depends on mineral susceptibility, field and gradient, particle size, liberation, orientation and competing forces. Strongly responsive phases may separate at lower intensity, while weakly responsive minerals require higher gradients and careful control. Weathering or fine coatings can alter response. A “magnetic fraction” is a test-defined product, not a mineralogical identification; analyse what actually reports to it.

Electrical methods exploit conductivity, charge acquisition or dielectric behaviour. Moisture, surface condition, temperature, particle contact and feed presentation can dominate. As with magnetic separation, response distributions overlap. Test under controlled conditioning, include non-target phases and quantify recovery, mass pull, product quality and stability across replicates and domains.

Sensor-based sorting

Sensor-based sorting measures individual rocks or particle groups and applies an ejection decision. The signal might represent colour, spectrum, transmission, density proxy or another observable. Performance depends on presentation, particle size and spacing, surface condition, calibration population, detection depth, decision threshold and actuator timing. A classification metric alone is not a process result because mass, value and particle-size distributions are unequal.

Build a labelled test set from representative particles and preserve each particle's mass, source, measurements and reference classification. Evaluate confusion by mass and contained component, not only by count. Test false rejection of valuable material, false acceptance of waste, unclassifiable particles, throughput effects and drift. If calibration and evaluation particles are not independent, apparent accuracy is optimistic.

Quantitative performance and partition

For a separated product p, mass yield is Y_p=M_p/M_f and component recovery is R_{p,j}=M_p g_{p,j}/(M_f g_{f,j}). Waste rejection is 1-Y_p for a retained-product convention, but must be paired with valuable-component loss to reject. Separation efficiency can be expressed in several ways; always define the formula and desired products because labels such as “efficiency” are not universal.

A size, density or sensor-score partition curve estimates P(p\mid x), the probability a particle with property x reports to product p. Confidence intervals should reflect sample counts and mass distribution. Examine curves by geological domain and size. An apparently sharp aggregate curve can be created by mixing subpopulations with different cut points, and then fail when feed proportions change.

Testwork and scale progression

Begin with characterisation and amenability tests: property measurements, liberation, size distribution and theoretical or laboratory separations. Next run variability tests with controlled preparation, then continuous or larger-scale tests if material and decision warrant. Integrated work must include feed presentation, steady state, start-up exclusions, water or medium quality, recycles and product dewatering.

Preconcentration changes downstream feed. Rejecting mass may upgrade grade and reduce energy, but can also remove water-bearing or buffering minerals, concentrate hardness, shift clay, alter sulfur distribution or make residues environmentally different. Characterise both retained and rejected streams. Allocate the energy, water, equipment and sampling needed for the separation itself.

Uncertainty and common failure modes

Failure modes include selecting a method from mineral names rather than measured response; testing hand-picked coarse pieces; ignoring fines and unclassifiable material; using particle count instead of mass; reporting ideal float-sink data as plant performance; treating a magnetic fraction as one mineral; and optimising waste rejection without a valuable-loss constraint. Moisture, coatings, feed overlap and calibration drift are frequent hidden variables.

Represent property distributions and partition uncertainty, not just means. Track selection bias in test particles, measurement error in reference labels, and scale differences in presentation and residence time. A promising test remains conditional if adverse domains are sparse or if the rejected stream lacks environmental and handling characterisation.

Interfaces and transferable data

Geology supplies domains, mineralogy, texture, oxidation, particle-size implications and spatial variability. Physical-separation testwork returns property distributions, partition curves, products, losses and conditions. The resource or scheduling model may receive a preconcentration response only after mass conservation, support and applicability are defined. Do not attach a binary sortable/not-sortable flag to blocks from a few selected rocks.

Data records should preserve parent samples, particle or fraction identifiers, sensor raw values, reference measurements, threshold version, product destination and rejected material. When a classifier is recalibrated, old results retain their original version. Model feedback distinguishes inherent rock attributes from response variables generated by a particular preparation and separator.

Integration checkpoint

Reconcile feed, retained, middling and rejected streams; then inspect performance by size and domain. A preconcentration claim advances only if the property contrast, partition, valuable loss, downstream benefit and reject consequence are all supported on the same material population.

Synthetic worked example

A synthetic coarse feed contains 100 dry mass units at 0.80% component X. A density test produces 35 units of sinks at 1.90% X and 65 units of floats at 0.208% X. Contained X is 0.800 units in feed, 0.665 in sinks and approximately 0.135 in floats, so the retained-product recovery is about 83.1% with 65% mass rejection. Replicate uncertainty and rounding are recorded.

The attractive mass rejection is conditional. Domain South contributes disproportionate valuable loss because weathered composite particles have lower effective density. The next gate tests narrower size fractions and a three-product option, characterises the reject for sulfur and clay, and evaluates whether the downstream energy reduction exceeds separation costs. No plant performance is claimed; all values are synthetic.

Conceptual figure

Physical separation maps overlapping particle-property distributions through a partition curve into retained, middling and rejected streams.
Physical separation maps overlapping particle-property distributions through a partition curve into retained, middling and rejected streams.

Practice and decision record

Create a synthetic feed with two size classes and overlapping density distributions. Calculate product yields and component recoveries at two cut points, then explain why one aggregate result could conceal poor performance in a domain. Draft a decision record with property hypothesis, material selection, reference method, partition evidence, losses, downstream effects, residue boundary and next test.

The record fails if hand selection substitutes for representative sampling, a theoretical cut is reported as operating recovery, count accuracy replaces mass and value metrics, or rejected material disappears from the system boundary.

Sources