Bubbles and particles for fun and profit

This article develops the Antoine M. Gaudin Award presentation delivered at the Mineral & Metallurgical Processing Division (MPD) Awards Plenary Session on Feb. 23, 2026 during the MINEXCHANGE 2026 SME Annual Conference & Expo in Salt Lake City, UT. It reviews selected research undertaken at the Royal School of Mines, Imperial College London over approximately two decades. The work spans physically based modeling of flotation froths, the use of air recovery for flotation optimization, positron emission particle tracking (PEPT), the redesign of hydrocyclone geometry and electrostatic traveling waves for dry particle transport and separation. Although the topics differ, they share a common method: identify the governing physical mechanisms, construct a model or measurement that exposes them, and use the resulting understanding to improve process operation or equipment design. The examples show the industrial value of fundamental models, direct observation in opaque systems, rapid prototyping and careful attention to unexpected experimental results. Introduction The title “Bubbles and Particles for Fun and Profit” is deliberately light-hearted, but the subject is economically important. Mineral processing depends on controlling the interactions among particles, bubbles and liquids. Small changes in these interactions can produce large changes in recovery, concentrate grade, energy use and circuit capacity. This is necessarily a selective account. It draws on work by many doctoral students, researchers, academic colleagues and industrial collaborators, and it builds on the ideas of earlier leaders in mineral processing. I was fortunate to learn from Peter King, Len Austin and Ted Woodburn. King’s modeling philosophy, Austin’s disciplined approach to particulate systems and Woodburn’s seminal work on flotation froths all influenced the research described here. Figure 1: The effect of operating a bank of flotation cells at the peak air recovery on the grade-recovery curve. Four topics are considered. The first is the development of physically based models of flotation froths and the use of air recovery as an operating variable. The second is the direct measurement of particle motion using positron emission particle tracking (PEPT) and the application of these measurements to flotation-cell design. The third is the redesign of hydrocyclones through computational fluid dynamics (CFD), 3D printing and rapid experimentation. The final topic is the electrostatic traveling wave, an emerging technique for transporting and separating fine dry particles. Flotation froth models and control The flotation froth is often treated as a product-transport layer above the pulp, but it is more properly understood as a second separation zone. Valuable particles collected in the pulp may be lost after entering the froth through detachment and drainage. At the same time, fine hydrophilic gangue may be carried upward with water and recovered by entrainment. Froth behavior therefore modifies both grade and recovery and may determine whether effective bubble-particle collection in the pulp becomes useful metallurgical performance. A froth is a structured three-phase system. Thin liquid films, or lamellae, separate neighboring bubbles. Three films meet to form liquid-filled plateau borders, which connect at vertices and create a drainage network. Hydrophobic particles may remain attached to films and move with the bulk froth. Unattached particles move within the plateau borders, where they are transported by draining liquid, settle relative to that liquid and disperse through the irregular channel network. Neethling and Cilliers (2003) developed a fundamentally based model that coupled the behavior of gas, liquid and solids. The gas motion could be represented by incompressible potential flow, with a velocity potential obtained by solving Laplace’s equation. Coalescence was included because the rupture of films changes bubble size, froth structure and the state of attached particles. Liquid drainage was described through a force balance incorporating gravity, viscosity and surface-tension effects associated with plateau-border curvature (Leonard and Lemlich, 1965). The solids model distinguished attached particles from unattached particles and included liquid transport, settling and dispersion. These model components are combined into a complete froth model with a physical basis, which allows operational changes and new designs to be evaluated before they are implemented. Two boundary conditions are especially important. The first is flotation-cell geometry: the dimensions of the tank, the location and length of the overflow lip, and the arrangement of launders, crowders and other internals. These features govern froth transport distance and residence time. They can create rapid-flow regions near a lip, and slow or stagnant zones elsewhere. As drainage, coalescence and particle detachment continue while the froth travels, geometry directly affects water recovery, entrainment and valuable-mineral loss. The second boundary condition is air recovery, defined as the fraction of air entering the cell that leaves by overflowing the concentrate lip as unburst bubbles. The remainder leaves by bursting at the exposed froth surface. In simplified form:α = Qair,overflow / Qair,input Air recovery is consequently a measure of both froth stability and froth mobility: bubbles must remain intact, but they must also reach the launder before they burst. Industrial studies of air recovery produced an important operational result. Air recovery increases with air rate only up to a point and then passes through a maximum, the peak air recovery (PAR) condition. At low air rates, bubbles may be strongly loaded and the froth relatively stable, but the froth moves slowly. The extended residence time increases the chance that bubbles will coalesce and burst before overflowing. Increasing air initially improves froth mobility and raises air recovery. Figure 2: The effect of operating a bank of flotation cells at the peak air recovery on the grade-recovery curve. At high air rates, the froth moves more rapidly, but the bubbles may be less fully covered by particles and the froth can become less stable. More bubbles then burst before they reach the lip, and air recovery falls. PAR represents a balance between mobility and stability. In trials on a South African copper sulfide flotation bank, the air rate producing PAR also corresponded to the highest overall mineral recovery (Hadler and Cilliers, 2009). The grade-recovery relationship was shifted toward higher recovery at a comparable grade (Fig. 2), demonstrating that a variable grounded in froth physics could identify an economically valuable operating condition. The operating implications are useful but require care. Below PAR, an increase in air rate will commonly increase recovery, although grade may decline as water recovery and entrainment rise. Above PAR, reducing the air rate may improve froth stability and valuable-mineral recovery. The exact response also depends on froth depth, particle loading, reagents and cell position within a bank. PAR should therefore be treated as a physically meaningful operating target, not as a universal set point independent of the rest of the circuit. Continuous control at PAR is difficult. The volume of overflowing air must be estimated reliably, conditions vary and cells interact. Industrial plants often use easier proxies such as concentrate mass flow or mass pull. These are convenient for control but provide a less direct description of froth behavior. The continuing challenge is to combine measurable variables with models that retain a clear physical meaning. An example is the work of Neethling and Brito-Parada (2018) that develops further the link between froth stability and gas flux. Particle motion, PEPT and flotation-cell design The froth models predict how liquid and particles move, but their value depends on experimental validation. Bulk assays provide grade and recovery, yet they do not show the trajectory of an individual particle or identify when it attaches to a bubble, enters the froth, detaches, drains or overflows. This gap motivated the application of PEPT. PEPT follows a single tracer particle through an opaque system (Parker et al., 1993). A representative particle is labeled with a short-lived positron-emitting radionuclide. When a positron annihilates with an electron, two gamma rays are emitted in nearly opposite directions. Coincident detection around the experimental vessel defines a line on which the event occurred; repeated detections allow the particle position to be reconstructed in three dimensions and followed through time. The method is particularly well suited to flotation. It does not require optical access, can be used in concentrated suspensions and can operate through steel vessels. Tracers can be prepared over a wide size range and modified to reproduce selected density and surface properties. Early flotation studies demonstrated the ability of PEPT to map particle motion in both pulp and froth (Waters et al., 2008). Later work developed directly activated mineral tracers and surface coatings that allowed hydrophobic and hydrophilic particle classes to be compared while retaining representative properties (Boucher et al., 2017; Cole et al., 2022). Gigure 3: The PEPT trajectory of a hydrophobic tracer, and the estimated velocity distribution and flow lines. A single particle trajectory may show circulation in the pulp, attachment to a bubble, rapid ascent, entry into the froth, detachment during coalescence, drainage, and eventual overflow or return to the pulp. With sufficient data, individual tracks can be converted into occupancy maps, average velocity fields and residence-time distributions. Comparing hydrophobic and hydrophilic tracers provides an experimental basis for estimating how valuable and gangue particles populate different regions of a cell. This information is valuable for launder and crowder design. A model may predict that forcing froth inward toward an annular launder produces a different surface-grade distribution from forcing it outward toward a peripheral lip. PEPT and related measurements help determine whether the predicted residence times and transport patterns are physically correct. They also support the redesign and retrofit of launders and crowders to shorten transport distances and reduce stagnant regions. PEPT has become a mature and powerful research method: tracers can be custom designed and data processing is increasingly standardized. However, only a handful of facilities exist worldwide. They require specialist isotope production, detectors, experimental infrastructure and sustained expertise. These facilities should be used and supported while they remain available. A practical PEPT experiment requires more than a radioactive label. The tracer must remain representative of the particle class being studied, the vessel must operate at stable conditions for long enough to obtain meaningful trajectories, and the location algorithm must separate true coincidence events from background detections. The continuously overflowing system developed at PEPT Cape Town allows several hours of acquisition at steady air recovery, while modern processing can generate high-frequency location data and compare different tracer classes on a common spatial grid (Cole et al., 2022). PEPT does not replace bulk metallurgical measurements; rather, it explains the motion that produces them. Hydrocyclone design: convex bodies and surface roughness Hydrocyclones are mature devices, but their classification performance remains sensitive to internal geometry. In closed grinding circuits, fines bypass to the underflow returns already fine material to the mill, encouraging overgrinding, consuming energy and occupying capacity that could be used for coarser particles. The question was whether the conventional straight conical body could be modified to reduce bypass while retaining a useful cut size. Convex-conic designs were developed through a rapid cycle of CFD simulation, three-dimensional printing, laboratory testing and refinement. This approach allowed numerical concepts to be converted quickly into working prototypes and tested before the next design iteration. Across the conditions examined, convex-conic hydrocyclones produced a coarser cut size with lower fines bypass than standard conical designs (Pukkella et al., 2025a). Empirical models and Monte Carlo simulations indicated that the convex geometry offered a wider cut-size operating range while maintaining relatively low bypass. The design is therefore attractive for closed grinding circuits, where reduced bypass may lower overgrinding and increase effective throughput. A second result emerged unexpectedly. Nominally identical cyclones manufactured on different three-dimensional printers did not perform identically because their internal surfaces had different roughness. Purpose-made smooth, medium and rough surfaces were then tested systematically. Increasing roughness reduced the underflow spray angle and, above a threshold roughness, increased water and solids recovery to the underflow (Pukkella et al., 2025b). Rough surfaces are therefore potentially useful in dewatering or high-solids-recovery duties, while smooth surfaces may remain preferable where sharp classification is the priority. The broader contribution is methodological. CFD, additive manufacture and experiment can now be combined in design-test cycles completed in days rather than months. Equally important, the work shows the value of taking anomalous results seriously. Surface texture had usually been treated as a manufacturing detail; it became a controllable design variable because an unexpected observation was investigated rather than discarded. Scale-up remains essential. The convex body was investigated from small printed units through larger geometries, and industrial application requires attention to wear, manufacturing tolerances and the persistence of the predicted flow structures at scale. Roughness will also evolve during service as liners wear or particles abrade the surface. This creates both a challenge and an opportunity: a texture selected for a particular duty must be maintainable, but measured changes in performance may also provide information about the condition of the internal surface. Electrostatic traveling waves The final topic is earlier in its development but responds to an important need. Mineral processing will increasingly be required to operate with less water, particularly in arid regions and where water supply, tailings management or environmental constraints limit conventional wet processing. New methods are needed for handling and separating fine dry particles. An electrostatic traveling wave (ETW) system comprises an insulating surface with an array of embedded parallel electrodes. Time-varying voltages applied to the electrodes generate an electric field above the surface. With a single phase, or certain two-phase arrangements, the field varies with time but remains spatially fixed, producing a standing-wave pattern. With three or more suitably phase-shifted signals, the field pattern travels along the electrode array.Particles placed in the field experience electrical forces together with gravity, inertia, adhesion and contact forces. They may carry an initial charge or acquire charge by contact with the dielectric surface. Motion depends on particle size, charge and other physical properties, as well as voltage, frequency, electrode spacing and waveform. A particle may travel with the wave, move against it, oscillate or become temporarily suspended. The same device can therefore provide nonmechanical transport and, where particle responses differ, separation (Yu et al., 2022, 2023). Experiments with fine silica particles showed that transport direction is strongly frequency dependent. At lower frequencies, most particles moved with the traveling wave; as frequency increased, a greater proportion moved in the opposite direction. Yu et al. (2024) defined the crossover frequency as the frequency at which a particle is equally likely to move forward or backward. The crossover frequency decreases with increasing particle size. Selecting a frequency between the crossover frequencies of two size classes can cause them to move in different directions. Particles in the ranges of 30 to 50 μm and 75 to 110 μm were successfully separated, with the desired product exceeding 90 percent concentration and recovery exceeding 79 percent under the reported conditions. These results establish a genuine separation mechanism rather than conveyance alone. The distance from a laboratory experiment to an industrial mineral separator remains substantial. Real ores contain broad distributions of size, shape, conductivity, mineralogy, surface condition and charge. Humidity, contamination, adhesion, particle-particle interaction, throughput, power consumption and electrode durability must all be addressed. Nevertheless, the ETW demonstrates that fine dry particles can be transported and separated without mechanical moving parts or a fluid carrier. That is a promising foundation for further development. Summary and conclusions The research considered here covers different unit operations and stages of technological maturity, but it is unified by a consistent approach. Flotation froth models begin with the structures and forces that govern gas, liquid and solids. Air recovery links those mechanisms to an operating variable and to plant performance. PEPT tests model predictions by revealing particle trajectories that bulk sampling cannot resolve. Hydrocyclone research combines CFD with rapid manufacture and experiment, while the ETW extends particle manipulation into an emerging dry-processing technology. Several lessons follow. First, models are most useful when their variables and assumptions remain connected to physical mechanisms. Second, measurements create particular value when they expose behavior hidden within opaque multiphase equipment. Third, rapid prototyping can transform the speed at which equipment concepts are tested. Fourth, apparently mature technologies still contain opportunities for improvement. Finally, serendipity has value only when unexpected observations are examined systematically. These advances are built on the foundations laid by earlier scientists and engineers. They represent the efforts of students, researchers, colleagues and industrial partners. Bubbles and particles are simple objects, but their collective behavior is not. Understanding that behavior remains intellectually rewarding and industrially valuable. When it leads to higher recovery, better grade, increased capacity, lower energy consumption or a new process, it can indeed be both fun and profitable. Acknowledgments The research summarized here represents the work of many students, researchers, colleagues and industrial partners. Particular acknowledgment is due to Stephen Neethling, Pablo Brito-Parada, Kathryn Hadler, Esther Ventura-Medina, Katie Cole, Dennis Vega-Garcia, Arjun Pukkella and the many other excellent researchers who contributed to the projects described. I am also grateful for the influence and encouragement of Professors Peter King, Len Austin and Ted Woodburn. References Boucher, D., Jordens, A., Sovechles, J.M., Langlois, R., Leadbeater, T.W., Rowson, N.A., Cilliers, J.J. and Waters, K.E. (2017). Direct mineral tracer activation in positron emission particle tracking of a flotation cell. Minerals Engineering, 100, 155–165. https://doi.org/10.1016/j.mineng.2016.10.022.Cole, K., Barker, D.J., Brito-Parada, P.R., Buffler, A., Hadler, K., Mackay, I., Mesa, D., Morrison, A.J., Neethling, S.J., Norori-McCormac, A., Shean, B. and Cilliers, J.J. (2022). Standard method for performing positron emission particle tracking (PEPT) measurements of froth flotation at PEPT Cape Town. MethodsX, 9, 101680. https://doi.org/10.1016/j.mex.2022.101680.Hadler, K. and Cilliers, J.J. (2009). The relationship between the peak in air recovery and flotation bank performance. Minerals Engineering, 22(5), 451–455. https://doi.org/10.1016/j.mineng.2008.12.004.Leonard R and Lemlich R (1965) A study of interstitial liquid flow in foam A. I. Chem. Eng. J. 11 18-25Neethling, S.J. and Brito-Parada, P.R. (2018) Predicting flotation behaviour – The interaction between froth stability and performance, Minerals Engineering, 120, 60-65, https://doi.org/10.1016/j.mineng.2018.02.002.Neethling, S.J. and Cilliers, J.J. (2003). Modeling flotation froths. International Journal of Mineral Processing, 72(1–4), 267–287. https://doi.org/10.1016/S0301-7516(03)00104-2.Parker D.J., Broadbent C.J., Fowles P., Hawkesworth M.R., McNeil, P. (1993) Positron emission particle tracking - a technique for studying flow within engineering equipment, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 326 (3), 592-607, https://doi.org/10.1016/0168-9002(93)90864-E.Pukkella, A.K., Vega-Garcia, D., Hadler, K. and Cilliers, J. (2025a). Influence of conic shape on bypass and cut-size in hydrocyclones. Separation and Purification Technology, 361, 131224. https://doi.org/10.1016/j.seppur.2024.131224.Pukkella, A.K., Vega-Garcia, D., Hadler, K. and Cilliers, J. (2025b). The influence of surface-wall roughness on hydrocyclone performance. Separation and Purification Technology, 360, 131109. https://doi.org/10.1016/j.seppur.2024.131109.Waters, K.E., Rowson, N.A., Fan, X., Parker, D.J. and Cilliers, J.J. (2008). Positron emission particle tracking as a method to map the movement of particles in the pulp and froth phases. Minerals Engineering, 21(12–14), 877–882. https://doi.org/10.1016/j.mineng.2008.02.007.Yu, Y., Cilliers, J., Hadler, K., Starr, S. and Wang, Y. (2022). A review of particle transport and separation by electrostatic traveling wave methods. Journal of Electrostatics, 119, 103735. https://doi.org/10.1016/j.elstat.2022.103735.Yu, Y., Cilliers, J., Hadler, K., Starr, S. and Wang, Y. (2023). The motion of small particles in electrostatic travelling waves for transport and separation. Powder Technology, 425, 118587. https://doi.org/10.1016/j.powtec.2023.118587.Yu, Y., Cilliers, J., Hadler, K., Starr, S. and Wang, Y. (2024). Dry particle size separation using electrostatic traveling wave methods. Separation and Purification Technology, 336, 126275. https://doi.org/10.1016/j.seppur.2024.126275.

Bubbles and particles for fun and profit

Authored by: Jan Cilliers

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