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A 10 mm hydrocyclone was operated using a barite suspension with a maximum particle size of dmax = 7 μm. The test rig was equipped with a piston diaphragm pump for pressures up to 60 bar. At 40 bar and 20 °C, cut sizes d50 were obtained down to 0.7 μm; increasing the temperature to 50 °C resulted in d50 values down to 0.5 μm for a throughput of 0.6 m3/h. Another experiment was conducted at 40 bar using a batch hydrocyclone technology. Only the overflow was recirculated to the feed box, whereas the underflow was discharged via a collection box. Increasing the number of recirculations increased the separation of fines in the submicron range. The results showed that after 20 min particles with dmax = 1 μm were obtained in the hydrocyclone overflow. After 120 min, the particles size distribution had a dmax = 0.5 μm and a mean size of d50 = 0.2 μm. This procedure requires high energy consumption and is thus suitable only for fractionating small quantities of particles in the submicron range.

In many cases, the hydrocyclone partition curve exhibits a non-monotonic course in the fine particle range. The so-called fish-hook effect indicates an increased separation of the fine fraction, which is of practical interest and has a positive effect on solid/liquid separation. However, for classification purposes, the separation is less distinct. In this contribution an equation of a partition curve containing a fish-hook is derived considering the laws of disturbed settling in dense, polydisperse suspensions. The following effects are considered: the entrainment of fine particles in the boundary layer of the coarse settling particles, the hindered settling due to the increased effective density and viscosity of the fluid, and the counter flow of the displaced fluid caused by the settling particles. The calculations indicate that the fish-hook effect is primarily caused by fine particle entrainment, which is influenced by the feed solid content and the feed particle size distribution. An approximated analytical solution for the partition curve is presented for aRosin–Rammler–Sperling–Bennet (RRSB)-distributed feed. Experiments using 25-mm hydrocyclone confirm the calculations.

A simple interpolation formula for the sedimentation velocity of a particle, including the limiting cases of small and large Reynolds numbers is proposed. A comparison with other known similar formulas is given. It is shown that the adjustment of sedimentation law is important to describe the hydrocyclones separation curve for large particles. A way of representing the separation curve, which allows justify the assumptions underlying the model of Schubert–Neesse is shown. It is shown that the correction of formula for the sedimentation velocity significantly affects the estimate of the effective coefficient of turbulent diffusion in the apparatus.

In nanotechnology, classification in the micron and submicron range is of growing interest. Usually, hydrocyclones do not reach these low cut sizes. This study presents a special batch processing technique using a 20 mm hydrocyclone for classification in the micron range. This hydrocyclone was equipped with a special underflow box that stored the coarse particles. The overflow was recirculated to the hydrocyclone entrance. A set of experiments was conducted using this batch hydrocyclone technology. Quartz with particle size 1 μm in the first 60 min. Later, the particles in the submicron range were increasingly discharged in the underflow. A simulation for the classification in a batch hydrocyclone with a closed circuit and underflow box is presented.

In hydrocyclones, the particle separation efficiency is limited by the suspended fine particles, which are discharged with the coarse product in the underflow. It is well known that injecting water in the conical part of the cyclone reduces the fine particle fraction in the underflow. This paper presents a mathematical model that simulates the water injection in the conical component. The model accounts for the fluid flow and the particle motion. The stationary concentration distributions result from superpositioning the turbulent particle diffusion and particle settling. Particle interaction, due to hindered settling caused by increased density and viscosity of the suspension, and fine particle entrainment by settling coarse particles are included in the model. Water injection in the conical part of the hydrocyclone is performed to reduce fine particle discharge in the underflow. This added water transports the fine particles of the sediment to the center, where they are directed to the overflow. The model demonstrates the impact of the injection rate, injection velocity, and injection location on the shape of the partition curve. Under optimal conditions, the so-called “fish hook” of the curve is reduced without changing the cut size. The simulations are compared with experimental data of a 50-mm cyclone.

The geometry and movement of the air core are sensitive indicators of the operational state of hydrocyclones. Therefore, an increased knowledge of the air core behaviour is desirable. Measurements of the air-core diameter in transparent hydrocyclones operated with a suspension of glass spheres are presented. The experiments indicate the dependencies between feed-solids content, air-core diameter, and spray angle of the underflow. Additionally, the air flow inside the air core in a transparent 50 mm water cyclone was experimentally investigated. Visualization techniques show the whirling motion of the air-core flow that is driven by the rotating liquid boundary of the air core. The radial distribution of the tangential air velocity was determined. The mean axial air velocity was shown to be dependent on the pressure drop and the hydrocyclone geometry. At the overflow discharge the air core is dispersed, and forms an aero suspension. Thus, the paper presents new aspects of the complex multi-phase flow in the hydrocyclone considering the gaseous phase.

A simulation of filter cake formation as a random process has been conducted. The random packing occurs after spherical particles are generated at a randomly selected coordinate above the cake. The force balance of the particles considers the driving force of filtration, skeleton forces due to virtually overlying particle layers, and adhesive forces. The factors for determining when a particle stops are defined as follows: a. Adhesion to the contacting particles based on the force balance. b. Finding a steady position if contacting three or more particles of the cake. The calculations deliver local porosities, mean porosities and size distributions of the pores dependent on the filtration parameters. The results confirm observations made in filtration experiments.

Air core formation has been investigated in hydrocyclones operated with clear water and a lucid suspension of glass balls. Hydrocyclones form a central air core which extends over the complete hydrocyclone length. Air is sucked in the core at the underflow discharge. The air core diameter can be determined balancing the positive pressure gradient and the centrifugal force in the rotational flow field. In dense flow separation (high feed solids content) the air core in the conical part of the hydrocyclone is suppressed. The hydrocyclone operates as it is air sealed because the solids are discharged trough the underflow as a rope. Then, air can be introduced to the hydrocyclone only on the feed side. In practice, feed suspension always contains more or less dissolved or dispersed air. Observations in a transparent hydrocyclone show that dissolved gas is released due to the pressure drop inside the hydrocyclone. The generated micro bubbles grow by coalescence and move in the centrifugal field toward the centre, where an air core is formed.

In hydrocyclone separation optimal results regarding solids recovery and solids content in the underflow can be expected at the transition point rope/spray discharge. It is calculated under which conditions this transition between the two discharge types appears. Furthermore, a control system has been developed, which enables a forced transition from rope to spray discharge even at high feed solids concentrations. Applying this control system, which is focused on the hydrocyclone operation at the transition point, remarkably good separation effects could be achieved.

In many cases, finest particles in hydrocyclones present higher separation efficiencies than can be expected when considering the theory of single particle sedimentation. The analysis of sedimentation of polydisperse particle systems shows that particle movement is influenced remarkably by solids concentration and particle size distribution. Sedimentation experiments with a special centrifuge confirm the action of combined effects, of particle entrainment, of countercurrent flow of displaced water and of elevated values of pulp density and viscosity due to the disperse solid phase. These influences can be summarized in a sedimentation model which allows better calculation of the separation result of the hydrocyclone. As a consequence, the typical course of the separation curve of the hydrocyclone indicates a more or less marked so-called fish-hook in the fine particle range.