Apparatus and method for separating different chemical species

Abstract

An apparatus 10a comprises a vessel 2 for containing liquid metal which is continuously axially symmetric about a longitudinal axis Z. At least a part of the vessel 2 tapers to an apex and the vessel

Description

Field of the Invention The present invention concerns an apparatus and method for separating different chemical species from each other when the species are suspended or entrained in a fluid as solid particles. Background of the Invention Different chemical species may be separated from each other when they are suspended or entrained in a fluid as solid particles, by using the fluid as a transport medium for the particles and introducing the fluid with the particles suspended or entrained therein into a cyclonic separator. The transporting fluid may be a gas, such as air, or a liquid, such as water, in which case the cyclonic separator is generally known as a hydrocyclone. In a cyclonic separator, solid particles suspended or entrained in the fluid are made to rotate in a vortex. This vortex is structured and comprises a forced vortex surrounded by a free vortex, which have different flow patterns from each other and which may be modelled together as a Rankine vortex. During operation of a cyclonic separator, solid particles are thrown radially outwards by a centrifugal force which is proportional to the mass of each particle and to the square of their tangential velocity. This means that for any given particle velocity, larger and / or denser particles experience a greater centrifugal force than smaller and / or less dense particles. Thus if the solid particles comprise different chemical species of respectively different densities, the different chemical species can be separated from each other (or "classified") according to their different densities, even if the range of particle sizes for each of the different chemical species are similar to each other or overlap. For example, less dense microplastic particles may be separated from similarly sized but denser particles of sand in this way. A cyclonic separator generally comprises a vortex chamber which is continuously axially symmetric about a longitudinal axis and at least part of which tapers towards an apex. The vortex chamber has an inlet or feed, an underflow outlet for more massive particles and an overflow outlet for less massive particles. The underflow outlet is connected to the periphery of the vortex, where there is the highest proportion of more massive particles, and is often located at or near to the apex of the vortex chamber. The vortex chamber may also contain, coaxial therewith, a continuously axially symmetric vortex finder for connecting the eye of the vortex, where there is the highest proportion of less massive particles, to the overflow outlet. During operation of a cyclonic separator, the fluid used as a transport medium has an axial velocity component near the periphery of the vortex which is towards the apex of the vortex chamber. This therefore tends to carry the more massive particles towards the underflow outlet. In contrast, the fluid has an axial velocity component near the eye of the vortex which is away from the apex of the vortex chamber. This therefore tends to carry the less massive particles towards the overflow outlet. The vortex may be generated, for example, by propelling or impelling the transporting fluid into the inlet or feed at sufficient velocity to allow classification of a particular range of particle masses transported by the fluid, as well as to suit the properties of the fluid itself (such as its viscosity), which also exerts a drag force on the particles suspended or entrained therein. The design parameters of any individual cyclonic separator, such as the shape or profile of the vortex chamber and the shapes, relative sizes and / or locations of the inlet and underflow and overflow outlets, as well as of any possible vortex finder, may therefore all be adjusted to suit a particular combination of particle and fluid properties. Many different geometries of cyclonic separators are also known, including ones arranged in series and / or in parallel to achieve a higher degree of separation and / or greater operating efficiency overall. By way of further background, a magnetic field may be applied to a liquid metal through which an electrical current flows, in order to generate a Lorentz force. The Lorentz force causes the liquid metal to move in a direction which is determined by the direction of the electrical current and of the applied magnetic field according to Fleming's right-hand rule. The magnitude of the Lorentz force per unit volume of the liquid metal is given by the cross product of the electrical current density with the magnetic flux density. This is the operating principle of magnetohydrodynamic (MHD) pumps. MHD pumps are used, for example, in the nuclear power industry to pump liquid metals, such as liquid sodium and liquid sodium-potassium alloy (NaK), around heat transfer circuits as heat transfer fluids, without any need for moving parts to be immersed in the liquid metal. In contrast, without an electrical current passing through them, static bodies of liquid metal in thermal equilibrium are only negligibly affected by applying a stationary magnetic field to them, and conversely, have little effect on the applied magnetic field. This is because liquid metals are generally either diamagnetic or only weakly paramagnetic and therefore have only low magnetic susceptibility. Moreover, the respective Curie temperatures of the ferromagnetic metals iron, cobalt and nickel, at which they cease to be ferromagnetic and become paramagnetic, all lie well below their respective melting points. For many decades, however, magnetic fields have also been used to control liquid metals without passing an electrical current through them as well, when a liquid metal is already in motion or is not in thermal equilibrium, such as when casting liquid metals, in order to stir them and therefore to help homogenise them as they solidify, or to reduce turbulent flows when they are poured. For example, an a.c. electromagnetic field may be applied to a body of liquid metal to induce eddy currents in the liquid metal. These eddy currents then interact with such a non-stationary magnetic field to generate corresponding Lorentz forces within the liquid metal. In another example, a stationary magnetic field may be applied to a liquid metal which is already subject to convective flows as it cools and solidifies, thereby generating Lorentz forces which oppose the local fluid velocity. Finally by way of background, some liquid metals, such as some alkali liquid metals, may be used as chemical reducing agents. If so, this may result in large quantities of insoluble reaction products, such as another reduced metal and / or metal oxides, being suspended or entrained in the liquid metal as solid particles. The present invention addresses the problem of howto separate such different species of insoluble reaction products from each other. Object of the Invention It is therefore an object of the invention to provide an apparatus and method for separating different chemical species from each other when they are suspended or entrained in liquid metal as solid particles. Description of the Invention Accordingly, in one aspect, the present invention provides an apparatus comprising a vessel for containing liquid metal which is continuously axially symmetric about a longitudinal axis, wherein at least part of the vessel tapers to an apex and the vessel comprises an inlet for the liquid metal having suspended or entrained therein, particles of a plurality of different chemical species of respectively different densities each in solid phase, an underflow outlet for the liquid metal with a majority of particles of a first, denser one of the plurality of different chemical species suspended or entrained therein, and an overflow outlet for the liquid metal with a majority of particles of a second, less dense one of the plurality of different chemical species suspended or entrained therein. The underflow outlet is nearer to the apex than the overflow outlet. The apparatus also comprises a first electrode coaxial with the longitudinal axis of the vessel, one or more second electrodes spaced apart from the first electrode, and a source of a magnetic field. The first and one or more second electrodes each have a magnetic susceptibility with an absolute value of less than 10-2 and are arranged within the vessel to be immersed in the liquid metal when the vessel contains the same, thereby allowing an electrical current to flow through the liquid metal between the first and one or more second electrodes. The magnetic field has a major component which is substantially perpendicular to the flow of electrical current through the liquid metal between the first and one or more second electrodes, thereby generating a Lorentz force acting on the liquid metal which causes it to rotate around the longitudinal axis of the vessel. During operation of such an apparatus, a Lorentz force is generated in the liquid metal by the interaction between the electrical current flowing between the first and one or more second electrodes and the component of the magnetic field which is perpendicular to the electrical current. Since the first and one or more second electrodes have a magnetic susceptibility with an absolute value of less than 10-2, they do not affect this magnetic field to any appreciable extent in comparison to the same magnetic field in free space. A magnetic susceptibility with an absolute value of less than 10-2 means that the first and one or more second electrodes each consist of paramagnetic and / or diamagnetic material(s). If such a material is paramagnetic, its magnetic susceptibility will have a small positive value less than 10-2, whereas if the material is diamagnetic, its magnetic susceptibility will have a small negative value less than 10-2. If one of the electrodes instead comprised a ferromagnetic material for example, at least some of the magnetic field would be diverted into that electrode and away from the liquid metal between the first and one or more second electrodes, as in a transformer core. Both the first and the one or more second electrodes are preferably made of materials which are chemically compatible with being immersed in the liquid metal and with the chemical species suspended or entrained therein, as described further below. The source of the magnetic field may comprise a permanent magnet and / or an electromagnet. The magnetic field itself may comprise magnetic poles of either polarity ( / .e., north or south). The source of the magnetic field may be located on the same side and / or on an opposite side of a plane which is perpendicular to the longitudinal axis of the vessel and which divides the first and one or more second electrodes as the apex of the vessel. In some embodiments, the apparatus may comprise a plurality of magnetic field sources, each of which may be located on the same or opposite side of this plane as the apexof the vessel. Any such magnetic field source may also be located inside or outside the vessel. For example, if it is located inside the vessel, it may either be immersed in the liquid metal or located in a headspace of the vessel above the liquid metal, depending, for example, on the chemical compatibility of the magnetic field source with the liquid metal. As used herein, the term "liquid metal" includes liquid metal alloys. If the source of the magnetic field is located outside the vessel, at least a part of the vessel should be constructed of a material which allows the magnetic field to penetrate inside the vessel and reach the space between the first and one or more second electrodes. In other words, at least this part of the vessel should be constructed of a material which has a magnetic susceptibility with an absolute value of less than 10-2. For example, it may be made of an austenitic stainless steel, titanium or a titanium alloy, such as one having a composition by weight of 98.8% Ti, 0.8% Ni and 0.4% Mo, all of which are only weakly paramagnetic. The vessel may be sealed in a gas-tight manner from the external environment and when it contains a liquid metal, if there is any headspace above the liquid metal inside the vessel, the headspace may be occupied by an inert atmosphere to prevent a chemical reaction between the liquid metal and atmospheric air. This inert atmosphere may consist of at least one of nitrogen and argon, which may be produced on site by pressure swing adsorption (PSA) of atmospheric air. Because of the symmetries which exist between electrical and magnetic effects, there are two alternative geometries for the electrical current and magnetic field in an apparatus according to the invention: a radial electrical current interacting with an axial magnetic field to generate the Lorentz force, and an axial electrical current interacting with a radial magnetic field to generate the Lorentz force instead. The former of these two alternative possible geometries will be described first, after which the latter will then be described. In embodiments with the first geometry, the one or more second electrodes are spaced apart from the first electrode in a radial direction, whereby the electrical current can flow radially through the liquid metal between the first and one or more second electrodes, and the magnetic field has a major axial component between the first and one or more second electrodes which is substantially parallel to the longitudinal axis of the vessel. Since the electrical current is radial in a plane perpendicular to the longitudinal axis of the vessel, and the major axial component of the magnetic field transects that plane, the Lorentz force generated by their interaction acts in the plane in a direction which encircles the first electrode. This causes the liquid metal to circulate in a forced vortex between the first and one or more second electrodes. Outside the space between the first and one or more second electrodes, where there is no flow of electrical current and therefore no such Lorentz force acting on the liquid metal, the liquid metal can form a free vortex instead. The free vortex may be located radially outside and / or axially offset from the forced vortex. A plurality of different chemical species of respectively different densities suspended or entrained in the liquid metal can therefore be classified by the vortex into more massive and less massive particles, which are respectively directed by the vortex to the underflow and overflow outlets of the vessel, in a manner similar to that in a known cyclonic separator. However, the apparatus of the invention, regardless of whether it has the first or second geometry, differs significantly from known cyclonic separators in several respects, including the features of the first and second electrodes and of the magnetic field. These features can generate a Lorentz force in the liquid metal which is sufficient to create a structured vortex that can be modelled as a Rankine vortex, rather than creating such a vortex by propelling or impelling the liquid metal into the vessel at sufficient velocity via the inlet thereof. These significant differences have several advantages, as follows. Firstly, the shape of the magnetic field may be designed to give particular Lorentz forces of different magnitudes acting at different locations in the liquid metal, whereby the shape and behaviour of the vortex may be controlled in a manner which could not be achieved in a known cyclonic separator (controlling the vortex in the spatial domain). Secondly, the rotation speed of the vortex may not only be precisely and easily controlled, but also rapidly changed, by altering at least one of the electrical current and the strength of the magnetic field, in a manner which could not be achieved if the liquid metal were just being impelled or propelled into the inlet of the vessel instead (controlling the vortex in the time domain). For example, in such an apparatus, the vortex may be brought to a rapid halt or even reversed in direction by rapidly altering at least one of the electrical current and the strength of the magnetic field. Thirdly, liquid metal entering the inlet of the vessel does not need to be impelled or propelled into the vessel at sufficient velocity to create a vortex inside the vessel. This might otherwise be difficult to achieve if the liquid metal has a high density of solid particles suspended or entrained therein, and particularly if at least some of these solid particles also have a high magnetic susceptibility. A further significant advantage of the apparatus, however, is that if one or more of the different chemical species suspended or entrained in the liquid metal as solid particles does have high magnetic susceptibility, for example if that species is ferromagnetic, then the magnetic field may be used not only to help generate the Lorentz force acting on the liquid metal, but also to interact directly with the solid particles themselves. This can be used to enhance the degree of separation of the different chemical species which can be achieved using such an apparatus, in a manner to be described below. For reasons of economy of construction and efficiency of operation, in embodiments with the first geometry, the one or more second electrodes are preferably arranged axially symmetrically around the first electrode. They do not have to form a continuous circuit about the first electrode and may be interrupted at one or more locations, for example by the inlet to the vessel. The one or more second electrodes may be integrated with or separated from the inner circumferential surface of the vessel. If they are integrated with the inner circumferential surface of the vessel, they may, for example, comprise a continuous circuit which is coaxial with the first electrode. If the vessel also comprises a vortex finder, the first electrode may be integrated with or separated from an outer surface of the vortex finder. In some embodiments with the first geometry, the first and one or more second electrodes may extend the same distance as each other in a longitudinal direction and be coaxial with each other. If so, the electrical current flowing radially through the liquid metal is not confined just to a plane which is perpendicular to the longitudinal axis of the vessel and is instead evenly distributed through a bulk volume of the liquid metal. This has the advantage of considerably reducing the electrical resistance between the first and one or more second electrodes. Furthermore, the Lorentz force acting on the liquid metal is then not confined to this plane either, but instead extends in three dimensions through the liquid metal and with axial symmetry about the first electrode, unlike the torque generating a vortex in a conventional cyclonic separator. In such embodiments with the first geometry, if the vessel also comprises a vortex finder coaxial with the longitudinal axis of the vessel and leading to the overflow outlet, the first electrode may have a tubular topology also oriented coaxially with the longitudinal axis of the vessel. For example, the first electrode may surround the vortex finder and / or be axially offset from it. The tubular topology of the first electrode has the advantage that no electrical current flows through and therefore no Lorentz force acts on liquid metal inside the tube of the first electrode. This allows the liquid metal with a majority of particles of the second one of the plurality of different chemical species suspended or entrained therein to flow axially through the first electrode, into the vortex finder and to the overflow outlet. If the vortex rotates at sufficient speed, it also allows the liquid metal to form a surface (in other words, for the vortex to form an eye) inside the first electrode or the vortex finder, without the first electrode losing electrical contact with the liquid metal outside the first electrode. The development of such an eye in a vortex is generally indicative of the stability of that vortex. In some embodiments with the first geometry, at least one of the first and one or more second electrodes may comprise a surface of revolution about the longitudinal axis of the vessel. This has the advantages of reducing the fluid resistance which the first and one or more second electrodes present to the circulation of the vortex, as well as reducing wear on the electrodes by particles suspended or entrained in the liquid metal. For example, the surface of revolution may comprise any one or more of a cylinder, a frustoconical shape or an open horn shape, which may be chosen best to suit the overall design of the shape of the vessel. The shapes of the first and one or more second electrodes do not have to be the same as each other. For example, the shape of the first electrode may be an (open or closed) cylinder, whereas the one or more second electrodes may have an open frustoconical shape or an open horn shape. In embodiments with the second geometry, the one or more second electrodes are spaced apart from the first electrode in an axial direction, whereby the electrical current can flow axially through the liquid metal between the first and one or more second electrodes, and the magnetic field has a major radial component between the first and one or more second electrodes which is substantially perpendicular to the longitudinal axis of the vessel. Since the major component of the magnetic field is radial in a plane perpendicular to the longitudinal axis of the vessel, and the axial flow of electrical current transects that plane, the Lorentz force generated by their interaction acts in the plane in a direction which encircles the longitudinal axis of the vessel. This causes the liquid metal to circulate in a forced vortex between the first and one or more second electrodes. Outside the space between the first and one or more second electrodes, where there is no flow of electrical current and therefore no such Lorentz force acting on the liquid metal, the liquid metal can form a free vortex instead. The free vortex may be located radially outside and / or axially offset from the forced vortex. A plurality of different chemical species of respectively different densities suspended or entrained in the liquid metal can therefore be classified by the vortex into more massive and less massive particles, which are respectively directed by the vortex to the underflow and overflow outlets of the vessel, as in embodiments with the first geometry. Embodiments with the second geometry have all the same advantages in comparison to known cyclonic separators as embodiments with the first geometry already described above. In some embodiments with the second geometry, the first and one or more second electrodes may extend the same distance as each other in a radial direction and be parallel to each other. If so, the electrical current flowing axially through the liquid metal is not confined just to a narrow path which is parallel to the longitudinal axis of the vessel and is instead evenly distributed through a bulk volume of the liquid metal. This has the advantage of considerably reducing the electrical resistance between the first and one or more second electrodes. Furthermore, the Lorentz force acting on the liquid metal is then not confined just to a small part of the liquid metal where the current flows either, but instead extends in three dimensions through the liquid metal between the first and one or more second electrodes, unlike the torque generating a vortex in a conventional cyclonic separator. In such embodiments with the second geometry, if the vessel also comprises a vortex finder coaxial with the longitudinal axis of the vessel and leading to the overflow outlet, at least one of the first and one or more second electrodes may comprise an annulus also centred on the longitudinal axis of the vessel. For example, first and / or one or more second electrodes comprising such an annulus may surround the vortex finder and / or be axially offset from it. This has the advantage that no electrical current flows and therefore no Lorentz force acts on the liquid metal inside the hole in the annulus of the first and / or one or more second electrodes. This allows the liquid metal with a majority of particles of the second one of the plurality of different chemical species suspended or entrained therein to flow axially through the hole in the annulus of the first and / or one or more second electrodes, into the vortex finder and to the overflow outlet. If the vortex rotates at sufficient speed, it is also able to form an eye which passes through the hole in the annulus of the first and / or one or more second electrodes. Magnetic fields of course comprise one or more dipole pairs of magnetic poles of opposite polarity to each other: one north, one south. In free space, the magnetic field around one of these poles is generally more divergent on an opposite side of that pole from the other pole of the same dipole pair than it is in a region between the two poles of the same dipole. In some embodiments with the first geometry, therefore, the magnetic field may comprise a pair of poles of opposite polarity to each other, not necessarily both belonging to the same dipole pair, with one of those poles located on the same side of a plane perpendicular to the longitudinal axis of the vessel and dividing the first and one or more second electrodes as the apex of the vessel and the other pole located on an opposite side of that plane from the apex of the vessel. The magnetic field between the two poles of opposite polarity to each other transecting the plane is then less radial and more axial than if both of these poles were instead located on the same side of the plane as each other. This has the advantage that it makes the magnetic field more perpendicular to the radial electrical current between the first and one or more second electrodes over a wider area of the plane. In contrast, in some embodiments with the second geometry, the magnetic field may instead comprise at least two dipole pairs of poles of opposite polarity to each other, arranged such that a pair of poles of the same polarity as each other, each of which therefore belongs to a different one of the dipole pairs, are located on opposite sides of the plane perpendicular to the longitudinal axis of the vessel and dividing the first and one or more second electrodes, with one of the poles of the same polarity located on the same side of the plane as the apex of the vessel and the other pole of the same polarity located on the opposite side of the plane from the apex of the vessel. The magnetic field between the two poles of the same polarity as each other transecting the plane is then less axial and more radial than if just one dipole pair of poles of opposite polarity to each other were instead located on only one side of the plane. Put simply, the magnetic field lines emanating from each of the pair of poles of the same polarity as each other squash each other flat ( / .e., are more radial) in the plane. This has the advantage that it makes the magnetic field more perpendicular to the axial electrical current between the first and one or more second electrodes over a wider area of the plane. In embodiments with either the first or the second geometry, a pair of magnetic poles each located on opposite sides of the plane dividing the first and one or more second electrodes could just be provided by a pole of one permanent magnet facing a pole of another permanent magnet on the opposite side of the plane, with the poles of opposite polarity to each other in embodiments with the first geometry and of the same polarity as each other in embodiments with the second geometry. In both cases, however, the source of the magnetic field is preferably an electromagnet. This has the advantage that the Lorentz force may then be precisely and rapidly controlled by altering an electrical current flowing through the electromagnet. In a simplest case with the first geometry, the electromagnet may comprise a single conductive coil (with multiple turns) located in the plane dividing the first and one or more second electrodes. If so, the magnetic field of an electrical current flowing in the coil perpendicularly transects the plane in the same direction everywhere inside the coil, but also has a significant radial field component outside that plane. It is therefore preferable in embodiments with the first geometry for the electromagnet to comprise at least one pair of coaxial coils each oriented parallel to the plane dividing the first and one or more second electrodes and / or a solenoid oriented with its longitudinal axis parallel to the longitudinal axis of the vessel. If the electromagnet comprises such a pair of coils, one of the pair of coils is located on the same side of the plane as the apex of the vessel, and the other of the pair of coils is located on the opposite side of the plane from the apex of the vessel, whereas if the electromagnet comprises such a solenoid, one end of the solenoid is located on the same side of a plane as the apex of the vessel and the other end of the solenoid is located on the opposite side of the plane from the apex of the vessel. In comparison to only a single coil, the magnetic fields from at least one pair of coaxial coils or from a solenoid, each oriented and positioned as just described, both have the advantage that they remain perpendicular to the plane dividing the first and one or more second electrodes further away from that plane in an axial direction, according to the distance between the pair of coaxial coils or the length of the solenoid, respectively. In embodiments with the second geometry comprising an electromagnet, the electromagnet may comprise at least one pair of coaxial coils each oriented parallel to the plane dividing the first and one or more second electrodes and / or at least one pair of solenoids each oriented with their longitudinal axes aligned with each other and parallel to the longitudinal axis of the vessel. If the electromagnet comprises such a pair of coils, one of the pair of coils is located on the same side of the plane as the apex of the vessel, and the other is located on the opposite side of the plane from the apex of the vessel, whereas if the electromagnet comprises such a pair of solenoids, one of the pair of solenoids is located on the same side of the plane as the apex of the vessel and the other is located on the opposite side of the plane from the apex of the vessel, so that an end of one solenoid opposes an end of the other solenoid across the plane. In embodiments with the first geometry comprising an electromagnet, the inner diameter of the coil(s) and / or of the solenoid is also preferably greater than an inner diameter of the one or more second electrodes, so that a Lorentz force can be generated throughout the space between the first and one or more second electrodes occupied by the liquid metal. Even if the inner diameter of the coil(s) and / or of the solenoid is greater than an outer diameter of the one or more second electrodes, no such Lorentz force is generated radially outside the one or more second electrodes because no electrical current flows through the liquid metal there. For simplicity of construction, therefore, if the vessel is made of a material which allows the magnetic field emanating from the coils and / or from the solenoid to penetrate inside the vessel, the coils and / or solenoid may simply be located outside and encircling the vessel. In embodiments with the second geometry comprising an electromagnet, the separation of the pair of coaxial coils or of the pair of opposing solenoids is also preferably greater than the separation of the first and one or more second electrodes, so that a Lorentz force can be generated throughout the space between the first and one or more second electrodes occupied by the liquid metal. Even if the separation of the pair of coaxial coils or of the pair of opposing solenoids is greater than the separation between the first and one or more second electrodes, no such Lorentz force is generated axially outside the space between the first and one or more second electrodes because no electrical current flows through the liquid metal there. Embodiments with the first geometry comprising an electromagnet and embodiments with the second geometry comprising an electromagnet are distinguished from each other in that in embodiments with the first geometry, the current(s) circulating in the coil(s) and / or solenoid all flow in the same direction as each other, whereas in embodiments with the second geometry, the current circulating in the coil and / or solenoid on one side of the plane dividing the first and one or more second electrodes flows in an opposite direction to the current circulating in the coil and / or solenoid on the opposite side of that plane. For example, in embodiments with the first geometry, a pair of Helmholtz coils can be used to provide an axial magnetic field perpendicularly transecting the plane between the first and one or more second electrodes. In embodiments with the second geometry, a pair of anti-Helmholtz coils or a pair of opposing solenoids with currents circulating in them in opposite directions to each other can instead be used to provide a radial magnetic field in the plane dividing the first and one or more second electrodes. All such arrangements of coaxial coils and / or solenoids have the advantage of generating a Lorentz force acting on the liquid metal in an annular direction when an electrical current flows therethrough between the first and one or more second electrodes. In embodiments with the first geometry, a trio of Maxwell coils may be used to provide a more highly uniform magnetic field perpendicularly transecting the plane between the first and one or more second electrodes than a pair of Helmholtz coils, by locating the outermost pair of the Maxwell coils on opposite sides of this plane similarly to the Helmholtz coils, and by locating the third Maxwell coil in the plane intersecting the first and one or more second electrodes, but located radially outside the one or more second electrodes, encircling the vessel. The uniformity of the magnetic field perpendicularly transecting the plane between the first and one or more second electrodes may be increased still further by using more elaborate arrangements of coils, such as Braunbek coils, Barker coils, and so on. In embodiments with the first geometry in which the source of the magnetic field comprises a solenoid, a similar result is achieved if the solenoid perpendicularly transects the plane between the first and one or more second electrodes because the magnetic field across an inner diameter of the solenoid is substantially uniform. However, for a real solenoid of finite length, a magnetic field gradient also exists along the length of the solenoid, between the middle of the solenoid, where the magnetic flux density is at a maximum, and each end of the solenoid, where there is a lower magnetic flux density. If one or more of the different chemical species suspended or entrained in the liquid metal as solid particles has high magnetic susceptibility, for example if that species is ferromagnetic, this magnetic field gradient may therefore be exploited to give enhanced separation of the different chemical species. Accordingly, in some embodiments comprising a solenoid, a midplane of the solenoid perpendicular to the longitudinal axis and bisecting the length of the solenoid, where the magnetic flux density is at its greatest, may be axially offset in the longitudinal direction from the plane dividing the first and one or more second electrodes, so that the magnetic field gradient inside the solenoid attracts non-diamagnetic species towards and repels diamagnetic species away from either the underflow or overflow outlet according to whether the direction of this axial offset is towards or away from the underflow outlet. Alternatively or additionally, an axial magnetic field gradient may be created by varying a number of turns per unit length and / or a diameter of the solenoid along the length of the solenoid, i.e., by using a varied pitch solenoid instead of a solenoid with windings of uniform pitch and / or a frustoconical solenoid instead of a cylindrical one. Thus, for example, if the number of turns of the solenoid increases in a direction towards the underflow outlet, ferromagnetic particles, like elemental iron or Fe3O4, and strongly paramagnetic particles, like manganese (11,111) oxide or manganese (III) oxide, as well as ferrimagnetic particles, like FejOa, any of which are suspended or entrained in the liquid metal, will be attracted to the underflow outlet by the axial magnetic field gradient inside the solenoid, whereas diamagnetic species, like NajO, SiOz or AI2O3, will be repelled from the underflow outlet by the same axial magnetic field gradient, in addition to these different chemical species being separated according to their respectively different densities, which are generally greater for the non-diamagnetic species just mentioned than they are for the diamagnetic species just mentioned, as described further below. It is also possible to create an axial magnetic field gradient if the source of the magnetic field comprises a pair of coaxial coils as described above, instead of a solenoid. This may be done if the source of the magnetic field further comprises an auxiliary pair of magnetic poles of the same polarity as each other (for example, two north poles or two south poles), in addition to the principal pair of coils used to create the Lorentz force in the liquid metal. Like these, one of the auxiliary magnetic poles is located on the same side of the plane between the first and one or more second electrodes as the apex of the vessel and the other one of the auxiliary magnetic poles is located on an opposite side of this plane from the apex of the vessel, such that the auxiliary pair of magnetic poles are coaxial with the principal pair of coils, and the one of the auxiliary magnetic poles and the one of the principal pair of coils on the same side of the plane as the apex of the vessel are reflection symmetric with the other one of the auxiliary magnetic poles and the other one of the principal pair of coils on the opposite side of the plane from the apex of the vessel, although they do not all have to be reflection symmetric about the plane between the first and one or more second electrodes, depending on their positions in the axial direction relative to that plane. With such an arrangement, if the magnetic field produced by the auxiliary pair of magnetic poles is made weaker than the magnetic field produced by the principal pair of coils, the total magnetic flux density at any location, which is given by the sum of the magnetic field strength from the auxiliary pair of magnetic poles at that location with the magnetic field strength from the principal pair of coils at the same location, has an axial field component which is greater on the side of the plane where one of the auxiliary magnetic poles has the same polarity as the magnetic field produced by the principal pair of coils and is less on the side of the plane where the other of the auxiliary magnetic poles has the opposite polarity to the magnetic field produced by the principal pair of coils, thereby generating an axial magnetic field gradient across the plane. However, the magnetic flux density of the field produced by the auxiliary magnetic poles approaches zero in a region between these poles because they have the same polarity as each other. Thus the field produced by the auxiliary magnetic poles has a negligible effect on the Lorentz force produced by the interaction between the magnetic field from the principal pair of coils and the electrical current flowing between the first and one or more second electrodes. As well as it being possible to produce an axial magnetic field gradient in this manner, such an auxiliary pair of magnetic poles has the further advantage that it can be used to produce a radial magnetic field gradient, as follows. Whereas the magneticfluxdensity of the field produced by the auxiliary magnetic poles approaches zero in a region between these poles, it increases radially outwards from there to a maximum value before it starts to decrease again as the radial distance increases to infinity. This magnetic field therefore has a substantial radial component which reaches a maximum in an annulus surrounding the region between the auxiliary magnetic poles, whilst the axial field component in this annulus approaches zero. In contrast, the magnetic field produced by the principal pair of coils is almost entirely axial in a region between the principal pair of coils and therefore has a radial field component in this region which is almost zero, whilst radially outside the region between the principal pair of coils, the magnetic field they produce is relatively weak and continues to decrease in strength as the radial distance goes to infinity. Thus the total magnetic field, equal to the sum of the magnetic field from the principal pair of coils with the magnetic field from the auxiliary pair of magnetic poles, is dominated by the magnetic field from the principal pair of coils in the region between them, where the total field is therefore also almost entirely axial, whereas in an annulus radially outside the auxiliary pair of magnetic poles, the total magnetic field is instead dominated by the magnetic field from this auxiliary pair of poles, where the total field is therefore predominantly radial and also has a radial magnetic field gradient, such that the magnetic flux density firstly increases in a radial direction to a local maximum before then decreasing again as the radial distance goes to infinity. In some embodiments, therefore, the radial distance of this locally maximum flux density (in other words, the radius of a midline of the annulus) may be chosen to be similar to or slightly greater than one-half of an inner diameter of the vessel where the plane of the annulus transects the vessel, whereby the radial component of the magnetic field increases in strength towards an inner circumferential surface of the vessel. Accordingly, if one or more of the different chemical species suspended or entrained in the liquid metal as solid particles has a highly positive magnetic susceptibility, for example if that species is ferromagnetic, this radial magnetic field gradient may be used to enhance the separation of the different chemical species, by attracting that species towards the inner circumferential surface of the vessel whilst repelling diamagnetic species therefrom, in addition to them being separated according to their respectively different densities as a result of the different centrifugal forces acting on them. On the other hand, the position of the annulus relative to the position of the one or more second electrodes is of less importance, because the magnetic field in the annulus is predominantly radial, and is therefore either parallel or antiparallel to the electrical current flowing through the liquid metal between the first and one or more second electrodes. The cross product of the electrical current density with the magnetic flux density in the annulus therefore approaches zero, generating no Lorentz force in the liquid metal. Moreover, whereas the polarity of the magnetic field produced by the auxiliary pair of magnetic poles is reflection symmetric, since the polarity of the magnetic field produced by the principal pair of coils is not, the total magnetic field given by their sum is not reflection symmetric either. As a result, the location of the annulus of maximum flux density does not coincide with the plane of reflection symmetry between the principal pair of coils, but is offset from it in an axial direction. This axial offset may therefore also be exploited by placing it nearer to the underflow or overflow outlet of the vessel, as desired. In principle, the auxiliary pair of magnetic poles can be provided by a pole from one permanent magnet facing a pole of the same polarity from another permanent magnet on the opposite side of the plane dividing the first and one or more second electrodes. Preferably, however, they are instead provided by an electromagnet comprising an auxiliary pair of coils each oriented parallel to this plane. Unlike the principal pair of coils, which are adapted and arranged to have electrical currents flowing in them in the same direction as each other so that they produce a single dipole pair of magnetic poles of opposite polarity from each other, the auxiliary pair of coils are instead adapted and arranged to have electrical currents flowing in them in opposite directions from each other, for example as in a pair of anti-Helmholtz coils, so that they produce two magnetic dipoles with a pole of one of the dipoles facing a pole of the same polarity from the other dipole. However, like the principal pair of coils, more elaborate arrangements of coils, such as Braunbek coils, Barker coils, and so on, can be used to provide the auxiliary pair of magnetic poles, and therefore shape the total magnetic field as desired. In comparison to using a pair of permanent magnets, an advantage of using an electromagnet comprising an auxiliary pair of coils to provide the auxiliary pair of magnetic poles is that simply by reversing the direction of the electrical currents flowing in these coils, the polarity of the auxiliary pair of magnetic poles can also be reversed, thereby quickly and easily reversing the direction of the axial magnetic field gradient they produce. Thus, if one or more of the different chemical species suspended or entrained in the liquid metal as solid particles has high magnetic susceptibility, for example if that species is ferromagnetic, the direction of the axial magnetic field gradient may be chosen to direct those particles preferentially towards either the underflow or the overflow outlet of the vessel, according to whether they are respectively more or less massive than any diamagnetic particles it is desired to separate them from. Reversing the polarity of the auxiliary pair of magnetic poles in this way also reverses the direction of the axial offset in the annulus of maximum flux density of the radial field, thereby giving the same benefit. This may all be achieved without having to reverse the direction of circulation of the vortex ( / .e., whether it circulates clockwise or anticlockwise), which would be the result of reversing the direction of the electrical currents flowing in the principal pair of coils instead. Doing the latter might be undesirable if, for example, the shapes and / or locations of any of the inlet and underflow and overflow outlets of the vessel were designed for the vortex to circulate in a particular direction. In some embodiments, the apparatus may comprise an electromagnet comprising both at least one auxiliary pair of coils as described above and a solenoid. In such embodiments, the design parameters of the solenoid may be chosen to create an axial magnetic field gradient which is substantially equal in magnitude but opposite in direction to the axial magnetic field gradient created by the auxiliary pair of coils, thereby cancelling it out to leave only the annulus of maximum flux density of the radial field created by the auxiliary pair of coils, in addition to the magnetic field created by the principal pair of coils. Conversely, if it is desired to use just the axial magnetic field gradient produced by at least one auxiliary pair of coils but not the radial magnetic field gradient they also produce, then in alternative embodiments comprising at least one auxiliary pair of coils but no solenoid, the radial distance of the locally maximum flux density from the longitudinal axis of the vessel may be chosen to be significantly greater than one-half of an inner diameter of the vessel where the plane of the annulus transects the vessel, so that the annulus lies well outside the vessel, leaving only the axial magnetic field gradient created by the auxiliary pair of coils inside the vessel, in addition to the magnetic field created by the principal pair of coils. In embodiments with either the first or the second geometry, at least one of the first and one or more second electrodes may be divided into one or more sectors about the longitudinal axis of the vessel. For example, in embodiments with the first geometry, if they are separated from the inner circumferential surface of the vessel, the one or more second electrodes may be divided into one or more sectors about the longitudinal axis of the vessel. This therefore allows the liquid metal and the solid particles suspended or entrained therein to move in a radial direction at azimuthal angles where the one or more second electrodes are absent. In embodiments with the second geometry, dividing at least one of the first and one or more second electrodes into one or more sectors about the longitudinal axis of the vessel allows the liquid metal and the solid particles suspended or entrained therein to move in an axial direction at azimuthal angles where the first and / or one or more second electrodes are absent. In embodiments having either the first or second geometry, at least one of the first and one or more second electrodes may be mounted on a strut having a magnetic susceptibility with an absolute value of less than 10-2 and an elongate shape which extends in the longitudinal direction. For example, such a strut allows the one or more second electrodes to be mounted in a location which is separated from the inner circumferential surface of the vessel, or for the first electrode to be mounted in a location separated from a vortex finder. The elongate shape and orientation of the strut mean that it presents less fluid resistance to the rotation of the liquid metal in the vortex and that the strut also experiences less buffeting by particles suspended or entrained therein than if the strut instead had an elongate shape extending in a radial direction. For increased strength and rigidity, any one electrode may be mounted on a plurality of such struts. Since like the electrodes, the strut has a magnetic susceptibility with an absolute value of less than 10-2, the effect of the strut on the magnetic field is also negligible. In some embodiments, the strut may be electrically insulated from the liquid metal and contain an electrically conductive current carrier having a magnetic susceptibility with an absolute value of less than 10-2, for carrying the electrical current to the electrode mounted on the strut. Thus if any one of the electrodes is mounted on such a strut, electrical current can only flow through the liquid metal between that electrode and its counterelectrode and not between the counterelectrode and the strut. This maintains the flow of electrical current through the liquid metal in its intended direction. Nonetheless, the electrode mounted on the strut can still be supplied with electrical current by the current carrier contained within the strut, which is therefore also electrically insulated from the liquid metal. However, since this current carrier has a magnetic susceptibility with an absolute value of less than 10-2 (for example, it may be made of copper), the current carrier does not affect the magnetic field to any appreciable extent either. The strut may be electrically insulated from the liquid metal, for example, by an electrically non-conductive surface layer made of a non-conductive diamagnetic material, such as a titania- or zirconia-based ceramic. In embodiments with either the first or second geometry, at least one of the first and one or more second electrodes may have a composite structure, which includes a surface layer comprising at least one of tungsten, rhodium and molybdenum. Tungsten, rhodium and molybdenum all have the advantage of the following desirable combination of physical characteristics. As well as being only weakly paramagnetic, they are also much harder than copper, for example, and therefore highly resistant to abrasion by particles suspended or entrained in the liquid metal. Furthermore, they still have a relatively high electrical conductivity, which is much higher than that of, say, titanium or of an austenitic stainless steel. On the other hand, the composite structure of such an electrode allows a portion of the electrode beneath the surface layer to be made of at least one other material which is less brittle than tungsten or rhodium, for example, but which may have a different electrical conductivity, be chemically incompatible with the liquid metal and / or be less resistant to abrasion by particles suspended or entrained therein. Since the electrical current can still be transmitted through the highly conductive surface layer, this gives the electrode greater material strength, without affecting the electrode's overall electrical conductivity. For example, the surface layer may consist of a molybdenum-tungsten alloy prepared with a d.c. bias voltage to avoid formation of a metastable P-W phase, as described in Seung-Ik Jun et al.: "Electrical and Microstructural Characterization of Molybdenum Tungsten Electrodes using a Combinatorial Thin Film Sputtering Technique", Journal of Applied Physics, Vol. 97, No. 5 (April 2005), pp. 054906-1 - 054906-6. Other design parameters of the apparatus, such as the shape or profile of the vessel for containing the liquid metal and the shapes, relative sizes and / or locations of the inlet and underflow and overflow outlets, as well as of any possible vortex finder, may all be adjusted to suit a particular combination of properties of the solid particles and liquid metal, in a manner similar to that used to design known cyclonic separators. Similarly, a plurality of apparatuses of the invention may also be arranged in series and / or in parallel to achieve a higher degree of separation and / or greater operating efficiency overall. In a second aspect, the present invention also provides a method comprising the following. Introducing into a vessel for containing liquid metal which is continuously axially symmetric about a longitudinal axis and wherein at least part of the vessel tapers to an apex, a liquid metal having suspended or entrained therein, particles of a plurality of different chemical species of respectively different densities each in solid phase. Immersing in the liquid metal within the vessel a first electrode coaxial with the longitudinal axis of the vessel and one or more second electrodes spaced apart from the first electrode, wherein the first and one or more second electrodes have a magnetic susceptibility with an absolute value of less than 10-2. Maintaining the vessel and the one or more second electrodes at the same electrical potential as each other whilst establishing a potential difference between the first and one or more second electrodes to cause an electrical current to flow through the liquid metal between the first and one or more second electrodes. Applying to the liquid metal a magnetic field having a major component which is substantially perpendicular to the flow of electrical current through the liquid metal between the first and one or more second electrodes, thereby generating a Lorentz force acting on the liquid metal which causes it to rotate around the longitudinal axis of the vessel. Varying a rotation speed of the liquid metal by adjusting at least one of the electrical current and the strength of the magnetic field to separate particles of the different chemical species suspended or entrained in the liquid metal from each other according to their densities, then abstracting the liquid metal with a majority of particles of a first, denser one of the plurality of different chemical species suspended or entrained therein from an underflow outlet of the vessel, and abstracting the liquid metal with a majority of particles of a second, less dense one of the plurality of different chemical species suspended or entrained therein from an overflow outlet of the vessel which is further away from the apex of the vessel than the underflow outlet. Maintaining the vessel and the one or more second electrodes at the same electrical potential as each other prevents an electrical current from flowing between them, as well as between the first and one or more second electrodes. For example, the vessel and the one or more second electrodes may both be maintained at ground potential, whereas the potential difference between the first and one or more second electrodes need only be of the order of about one to a very few volts, depending on the electrical resistance to the flow of current therebetween. On the other hand, a current of the order of about 60, 80, 100 or 120 A, or even more, may be applied to induce a vortex sufficient to separate particles of the different chemical species suspended or entrained in the liquid metal from each other, depending on the strength of the magnetic field applied to the liquid metal, and on the sizes and separation between the first and one or more second electrodes, which also affect the current density. The temporal order in which (i) the electrical current is caused to flow through the liquid metal, and (ii) the magnetic field is applied to the liquid metal is arbitrary. In other words, either of these two events may precede the other, or they may be simultaneous. If the magnetic field is applied to the liquid metal before the electrical current is caused to flow, it may already be present inside the vessel before the liquid metal is introduced thereto (for example, if the source of the magnetic field comprises a permanent magnet), or it may be applied thereafter but before the electrodes are immersed in the liquid metal, or after their immersion. The method of the invention has at least the following advantages. As already described above, the Lorentz force acting on the liquid metal, which causes it to rotate in a vortex, can be quickly and easily controlled, both in the spatial domain and in the time domain, by altering either or both of the magnetic field and the electrical current. However, apart from the interaction between the magnetic field and the electrical current which generates the Lorentz force, the magnetic field also acts directly on the particles suspended or entrained in the liquid metal. If any of these particles are ferromagnetic, ferrimagnetic or strongly paramagnetic, the particles are each magnetized with orientations depending on the direction of the applied magnetic field, and the degree of their magnetization is sufficiently great that they are mutually repelled from each other. This helps to prevent their agglomeration, including with particles of other chemical species, thereby aiding their separation. This is in addition to the shear forces generated in the vortex, which help to separate agglomerated particles from each other, as in a conventional cyclonic separator. In some embodiments, introducing into the vessel a liquid metal having suspended or entrained therein, particles of a plurality of different chemical species each in solid phase may comprise introducing into the vessel a liquid metal having suspended or entrained therein particles of a diamagnetic chemical species and particles of a non-diamagnetic chemical species with different densities from each other, and applying a magnetic field to the liquid metal may comprise applying a magnetic field which has a gradient in at least one of an axial direction and a radial direction, which enhances separation of the particles according to their different densities. This has the advantage that the magnetic field gradient helps to separate particles of different chemical species according to their different magnetic properties, in addition to their cyclonic separation according to their different densities, with the non-diamagnetic particles being attracted to regions of stronger magnetic field and the diamagnetic particles being repelled from them. Thus if the non-diamagnetic particles are denser than the diamagnetic particles, an axial magnetic field gradient directed such that the magnetic field increases in strength towards the apex of the vessel, and / or a radial magnetic field gradient, such that the magnetic field increases in strength radially outwards towards an inner circumferential surface of the vessel, will each help to direct non-diamagnetic particles towards the underflow outlet and diamagnetic particles towards the overflow outlet, in addition to their cyclonic separation according to their different densities. If, on the other hand, the diamagnetic particles are denser than the non- diamagnetic particles, an axial magnetic field gradient directed such that the magnetic field increases in strength away from the apex of the vessel, and / or a radial magnetic field gradient, such that the magnetic field increases in strength radially inwards towards the longitudinal axis of the vessel, will each help to direct diamagnetic particles towards the underflow outlet and non-diamagnetic particles towards the overflow outlet, in addition to their cyclonic separation according to their different densities. In particular, in some embodiments, the liquid metal may comprise liquid sodium (in which case, the cyclonic separator may be called a "natrocyclone"), the non-diamagnetic chemical species may comprise at least one of iron, an iron oxide, manganese and a manganese oxide as the first one of the plurality of different chemical species, the diamagnetic chemical species may comprise sodium oxide as the second one of the plurality of different chemical species, and a direction of the magnetic field gradient may be such that the strength of the magnetic field increases towards at least one of the apex of the vessel and an inner circumferential surface of the vessel. Such combinations of diamagnetic and non-diamagnetic chemical species suspended or entrained in liquid sodium may, for example, be the insoluble reaction products, along with various other gangue mineral species like silica and / or alumina, from a redox reaction between the liquid sodium and an ore of iron and / or of manganese, in which the liquid sodium acts as a chemical reducing agent on iron oxides and / or manganese oxides present in the ore and unreacted liquid sodium in excess of the stoichiometric amount thereof acts as a transport medium for the insoluble reaction products. As Table 1 below shows, all of these non-diamagnetic chemical species are denser than the diamagnetic chemical species, with the elemental metals themselves being very significantly denser than sodium oxide: Non-diamagnetic species Density / gem'3 Iron (Fe) 7.87 Manganese (Mn) 7.20 Iron (II) oxide (FeO) 5.75 Iron (III) oxide (FejOa) 5.25 Iron (11,111) oxide (Fe3O4) 5.0 Manganese (II) oxide (MnO) 5.46 Manganese (IV) oxide (MnO?) 5.03 Manganese (11,111) oxide (MnsO4) 4.86 Manganese (III) oxide (MnjOs) 4.50 Diamagnetic species Density / gem'3 Alumina (AI2O3) 3.99 Silica (SiOz) 2.65 Sodium oxide (NajO) 1.T1 Table 1 Thus a magnetic field gradient of one of the types specified above enhances the cyclonic separation of these non-diamagnetic species from these diamagnetic species according to their different densities. In some embodiments in which the magnetic field has a gradient both in an axial direction, such that the strength of the magnetic field increases towards the apex of the vessel, and in a radial direction, the strength of the magnetic field may increase with radial distance from the longitudinal axis of the vessel to a local maximum before decreasing thereafter as the radial distance continues to increase, and applying a magnetic field to the liquid metal may comprise positioning the magnetic field such that a plane containing the local maximum is axially offset towards the apex of the vessel from a plane perpendicular to the longitudinal axis of the vessel and dividing the first and one or more second electrodes. Arranging and positioning the magnetic field in this manner has the advantage that the axial field gradient and the radial field gradient then work together to direct non-diamagnetic particles towards the underflow outlet and diamagnetic particles towards the overflow outlet, in addition to their cyclonic separation according to their different densities. Brief Description of the Drawings Further features and advantages of the present invention will become apparent from the following detailed description, which is given by way of example and in association with the accompanying drawings, in which: Figs. 1A and IB are longitudinal cross-sections through respective examples of cyclonic separators; Fig. 2A is an isometric view of a first arrangement of electrodes and magnetic field coils; Fig. 2B is a transverse cross-section through the arrangement of Fig. 2A, in the plane labelled P in Fig. 2A and looking in the direction of the arrow labelled A in Fig. 2A; Fig. 2C is a longitudinal cross-section through the arrangement of Fig. 2A in the plane of the paper of Fig. 2A; Fig. 3A is an isometric view of a second arrangement of electrodes and magnetic field coils; Fig. 3B is a transverse cross-section through the arrangement of Fig. 3A, in the plane labelled P in Fig. 3A and looking in the direction of the arrow labelled A in Fig. 3A; Fig. 3C is a longitudinal cross-section through the arrangement of Fig. 3A in the plane of the paper of Fig. 3A; Fig. 4A is a longitudinal cross-section through a magnetic field coil sub-assembly; Fig. 4B is a transverse cross-section through the sub-assembly of Fig. 4A, in the plane labelled P in Fig. 4A and looking in the direction of the arrow labelled A in Fig. 4A; Fig. 5 is a longitudinal cross-section through a first embodiment of a cyclonic separator; Fig. 6A is a longitudinal cross-section through a second embodiment of a cyclonic separator; Fig. 6B is a close-up of a portion of Fig. 6A labelled C in Fig. 6A; Fig. 7A is a longitudinal cross-section through a third embodiment of a cyclonic separator according to the invention; Fig. 7B is a transverse cross-section through the embodiment of Fig. 7A, in the plane labelled P in Fig. 7A and looking in the direction of the arrow labelled A in Fig. 7A; Fig. 8 is a longitudinal cross-section through a fourth embodiment of a cyclonic separator; Fig. 9A is a longitudinal cross-section through a fifth embodiment of a cyclonic separator; Fig. 9B is a close-up of a portion of Fig. 9A labelled E in Fig. 9A; Fig. 10 is a longitudinal cross-section through a sixth embodiment of a cyclonic separator; Fig. 11A is a longitudinal cross-section through a seventh embodiment of a cyclonic separator; Fig. 11B is a transverse cross-section through the embodiment of Fig. 11A, in the plane labelled P in Fig. 11A and looking in the direction of the arrow labelled A in Fig. 11A; Fig. 12 is a longitudinal cross-section through an eighth embodiment of a cyclonic separator; Fig. 13 is a longitudinal cross-section through a ninth embodiment of a cyclonic separator; Fig. 14 is a longitudinal cross-section through a tenth embodiment of a cyclonic separator; Fig. 15 is a flow diagram of a first embodiment of a method of separating different chemical species from each other; Fig. 16 is a flow diagram of a second embodiment of a method of separating different chemical species from each other; Fig. 17 is a flow diagram of a third embodiment of a method of separating different chemical species from each other; and Fig. 18 is a flow diagram of a fourth embodiment of a method of separating different chemical species from each other. Nothing may be inferred from the relative dimensions of any apparatus or its elements shown in the accompanying drawings, which are schematic only. Detailed Description Figs. 1A and IB schematically show respective examples of cyclonic separators la, lb. Each comprises a vessel 2, which is continuously axially symmetric about a longitudinal axis Z and at least part 3 of which tapers towards an apex. In both cases, the vessel 2 does not actually include the apex because the part 3 is truncated before it reaches the apex. These examples of cyclonic separators la, lb are only representative of a variety of different possible shapes and configurations for cyclonic separators. For example, the length-to-width ratio of vessel 2 may be varied, as may the relative length and angle of taper of its part 3. Moreover, whereas in both the cyclonic separators la, lb, this part 3 has a frustoconical shape, in other examples, the part 3 may be a different tapering surface of revolution, such as a flared horn shape. In each of the cyclonic separators la, lb, the vessel 2 comprises an inlet 4 for a fluid acting as a transport medium for solid particles suspended or entrained therein, an underflow outlet 5 and an overflow outlet 6, wherein the underflow outlet 5 is nearer to the apex than the overflow outlet 6. In both cases, the inlet 4 is perpendicular to the longitudinal axis Z, even though the inlet 4 of the cyclonic separator la lies in the plane of the longitudinal section of Fig. 1A, whereas the inlet 4 of the cyclonic separator lb is perpendicular thereto, as represented in Fig. IB by the arrow cross in inlet 4. However, the cyclonic separator la of Fig. 1A differs from the cyclonic separator lb of Fig. IB in that it also comprises a vortex finder 7 for connecting an eye of vortex 8 to the overflow outlet 6, which the cyclonic separator lb of Fig. IB does not. Furthermore, the overflow outlet 6 of the cyclonic separator la is coaxial with the longitudinal axis Z, whereas the overflow outlet 6 of the cyclonic separator lb is perpendicular to the longitudinal axis Z. Whereas the underflow outlet 5 of both cyclonic separators la, lb is coaxial with the longitudinal axis Z, in other possible examples, it could be perpendicular to the longitudinal axis Z instead. Figs. 2A to 2C schematically show a first arrangement of first and second electrodes 12, 14 and principal magnetic field coils 16a, 16b. This first arrangement may be used to generate the first geometry of electrical current and magnetic field described above. The first electrode 12 is in the shape of a right circular cylinder open at both ends, which gives the first electrode 12 a tubular topology. The second electrode 14, which is also in the shape of a right circular cylinder open at both ends, surrounds and is spaced apart from the first electrode 12 in a radial direction, so that if the first and second electrodes 12,14 are placed at different electrical potentials from each other, an electrical current lr may flow radially through liquid metal between the first and second electrodes 12, 14, in the manner shown in Fig. 2B, wherein the density of the arrows represents the electrical current density. The first and second electrodes 12, 14 extend the same distance as each other in a longitudinal direction and are coaxial with each other, so that the electrical current lr flows not only in the plane P, but also in parallel planes to either side of P in the longitudinal direction. The principal magnetic field coils 16a, 16b are a pair of Helmholtz coils, in each of which a coil current lH circulates in the same direction. These principal magnetic field coils 16a, 16b are separated from each other by a distance which is equal to their radius, so that the magnetic field generated by the coil currents lH has a major axial component Ba which is substantially parallel in the longitudinal direction, as shown in Fig. 2C. A stronger but less axially uniform magnetic field may be generated by instead using a solenoid oriented with its longitudinal axis parallel to the longitudinal axis Z. With the Helmholtz coils, however, the major axial component Ba of the magnetic field uniformly fills the space between the first and second electrodes 12, 14, as shown in Fig. 2A. It therefore interacts with the electrical current lr flowing between the first and second electrodes 12, 14 to generate a Lorentz force, which acts on the liquid metal, causing it to rotate around the first electrode 12. In Figs. 2A to 2C, the directions both of the electrical current lr and of the axial component Ba of the magnetic field have been chosen arbitrarily, so that the direction of either of them could be reversed by reversing the polarity of the electrodes or the direction of the coil currents lH, respectively. However, if they are as represented by the directions of the respective arrows in these figures, then the liquid metal would rotate in the same direction as the coil current lH circulating in the magnetic field coils 16a, 16b. Figs. 3A to 3C schematically show a second arrangement of first and second electrodes 12, 14 and principal magnetic field coils 16a, 16b. This second arrangement may be used to generate the second geometry of electrical current and magnetic field described above. In this case, the first and second electrodes 12, 14, which are both in the shape of circular discs, are spaced apart from each other in an axial direction. Thus if the first and second electrodes 12, 14 are placed at different electrical potentials from each other, an electrical current la may flow axially through liquid metal between them, in the manner shown in Fig. 3A. The first and second electrodes 12,14 are parallel to each other and extend the same distance as each other in a radial direction. In other words, the radii of the first and second electrodes 12, 14 are the same as each other, so that the electrical current la uniformly fills the space between the first and second electrodes 12, 14, as shown in Fig. 3A. The principal magnetic field coils 16a, 16b are a pair of anti-Helmholtz coils, in each of which a coil current ±IH circulates in opposite directions. These principal magnetic field coils 16a, 16b are separated from each other by a distance which is equal to their radius, so that the magnetic field generated by the countercirculating coil currents ±IH has a major radial component Br between the coils 16a, 16b which is substantially perpendicular to the longitudinal direction, as shown in Fig. 3C. A stronger but more axially extensive magnetic field may be generated by instead using a pair of opposing solenoids each oriented with their longitudinal axes parallel to the longitudinal axis Z and aligned with each other, in which the solenoid currents circulate in opposite directions from each other. The radial component Br of the magnetic field between the anti-Helmholtz coils 16a, 16b (or between opposing solenoids of the same radius) is zero on the longitudinal axis Z, but increases in strength with increasing radial distance from the longitudinal axis Z until it reaches a local maximum at the radius of the magnetic field coils 16a, 16b, before then decreasing in strength as the radial distance continues to increase beyond the radius of the magnetic field coils 16a, 16b. This is represented in Fig. 3B, wherein the length of each arrow represents the strength of the radial component Br of the magnetic field at the location of the arrow and the direction of each arrow represents the direction of the radial magnetic field component Br. Since the radius of the first and second electrodes 12, 14 is less than the radius of the magnetic field coils 16a, 16b, the radial component Br of the magnetic field therefore has a gradient which is directed radially outwards everywhere in the space between the first and second electrodes 12,14. The radial magnetic field component Br interacts with the electrical current la flowing between the first and second electrodes 12, 14 to generate a Lorentz force, which acts on the liquid metal therebetween, causing it to rotate around the longitudinal axis Z not only in the plane P, but also in parallel planes to either side of P in the longitudinal direction. Near the longitudinal axis Z, where the radial component Br of the magnetic field approaches zero and the major component of the magnetic field is instead axial, the electrical current la is either parallel or antiparallel to this axial field component, so their cross product also tends to zero, and as a result, the Lorentz force acting on the liquid metal tends to zero as well. However, the Lorentz force increases in strength with increasing radial distance from the longitudinal axis Z in line with the radial magnetic field gradient. In addition, this magnetic field gradient directs particles with positive magnetic susceptibility (for example, ferromagnetic or paramagnetic particles) radially outwards and particles with negative magnetic susceptibility ( / .e., diamagnetic particles) radially inwards. Thus if the particles with positive magnetic susceptibility are more massive than those with negative magnetic susceptibility, this enhances their separation from each other according to their different masses. In Figs. 3A to 3C, the directions both of the electrical current la and of the radial component Br of the magnetic field have been chosen arbitrarily, so that the direction of either of them could be reversed by reversing the polarity of the electrodes or the directions of the coil currents ±IH, respectively. However, if they are as represented by the directions of the respective arrows in these figures, then the liquid metal would rotate in the same direction as the coil current -lH circulating in the magnetic field coil 16b. Figs. 4A and 4B schematically show a magnetic field coil sub-assembly, which may be used to generate a radial magnetic field with a different type of magnetic field gradient from that produced by the magnetic field coils 16a, 16b of the second arrangement shown in Figs. 3A to 3C. The magnetic field coil sub-assembly of Figs. 4A and 4B comprises a magnetic field coil 19 having multiple turns wound onto a core 20 with a shape as shown in Fig. 4A and which, like a transformer core, is made of a high magnetic susceptibility material. When a coil current circulates in the coil 19, the coil 19 and core 20 combine to produce a radial magnetic field Br between the poles of the core 20 of the type shown in Figs. 4A and 4B. (In Figs. 4A and 4B, the polarity of the poles of the core 20, and therefore the directions of the arrows representing the radial magnetic field Br, have been chosen arbitrarily and could both be reversed by reversing the direction of the coil current.) The magnetic field coil subassembly of Figs. 4A and 4B may therefore be used together with axially spaced first and second electrodes, similar to the first and second electrodes 12, 14 of the second arrangement, but each perforated with a central hole to accommodate the central pole of core 20, in order to generate the second geometry of electrical current and magnetic field described previously. However, whereas the radial magnetic field Br in the second arrangement of Figs. 3A to 3C increases in strength with increasing radial distance from the longitudinal axis Z as described above in relation to Fig. 3B, the radial magnetic field Br produced by the sub-assembly of Figs. 4A and 4B decreases in strength with increasing radial distance from the longitudinal axis Z instead. The sub-assembly of Figs. 4A and 4B therefore produces a radial magnetic field Br which has a field gradient opposite to that in Figs. 3A to 3C, even though both are radial magnetic fields. The magnetic field gradient produced by the subassembly of Figs. 4A and 4B therefore directs particles with positive magnetic susceptibility (for example, ferromagnetic or paramagnetic particles) radially inwards and particles with negative magnetic susceptibility ( / .e., diamagnetic particles) radially outwards. Thus if the particles with positive magnetic susceptibility are less massive than those with negative magnetic susceptibility, this enhances their separation from each other according to their different masses. Unlike the arrows in Fig. 3B, the different lengths of which represent the radially increasing field gradient, the arrows in Fig. 4B just represent lines of magnetic flux in the same manner as the magnetic field lines in Figs. 2A, 2C, 3C and 4A, and it is the density of the arrows in Fig. 4B which represents the magnetic field strength at any location instead, from which it can be seen that the strength of the magnetic field decreases with increasing radial distance from the longitudinal axis Z. Fig. 5 schematically shows a first embodiment of a cyclonic separator 10a. By way of example, the cyclonic separator 10a combines features from the cyclonic separator la of Fig. 1A with features of the first arrangement of first and second electrodes 12, 14 and principal magnetic field coils 16a, 16b of Figs. 2A to 2C, with the following additional features and modifications. The first and second electrodes 12, 14 are aligned axially with the inlet 4 to the vessel 2, so that the second electrode 14 does not form a continuous circuit about the first electrode 12 and is instead interrupted by the inlet 4. The magnetic field coils 16a, 16b encircle the vessel 2 on either side of the inlet 4. The vessel 2 is made of a material having a magnetic susceptibility with an absolute value of less than 10-2, such as an austenitic stainless steel, titanium or a titanium alloy, whereby the magnetic field generated by the coils 16a, 16b can penetrate the vessel 2. The first electrode 12 forms an integral part of the vortex finder 7, whereas the second electrode 14 forms a lining on the inner circumferential surface 2a of the vessel 2. Each electrode 12, 14 is electrically connected to a current carrying conductor outside the vessel 2. To prevent an electrical current from flowing axially through liquid metal between the first electrode 12 and either other portions of the vortex finder 7 or an end face of the vessel 2, both of which are in close proximity to the first electrode 12, these other portions of the vortex finder 7 and the end face of the vessel 2 each have an electrically non-conductive surface layer 21 as shown in Fig. 5. The electrically non-conductive surface layer 21 is made of a non-conductive diamagnetic material, such as a titania- or zirconia-based ceramic. Consequently, the electrical current flowing radially through the liquid metal between the first and second electrodes 12, 14 has substantially the same form as the electrical current lrshown in Fig. 2Band interacts with the axial magneticfield Bagenerated by the Helmholtz coils 16a, 16b to generate a Lorentz force encircling the first electrode 12, which produces vortex 8. Figs. 6A and 6B schematically show a second embodiment of a cyclonic separator 10b. The cyclonic separator 10b differs from the cyclonic separator 10a of Fig. 5 in the following respects. The first and second electrodes 12,14 are axially offset from the inlet 4 to the vessel 2, so that the second electrode 14 now forms a continuous circuit about the first electrode 12. The magnetic field coils 16a, 16b in the cyclonic separator 10a of Fig. 5 are replaced in the cyclonic separator 10b by a solenoid 17 encircling the vessel 2. The first electrode 12 is mounted on one end of the vortex finder 7, a portion of which in close proximity to the first electrode 12 has an electrically non-conductive surface layer 21 as shown in Fig. 6a to prevent electrical current from flowing axially through liquid metal between the first electrode 12 and this portion of the vortex finder 7. The first electrode 12 is supplied with electrical current by an electrically insulated current carrying conductor buried within the wall of the vortex finder 7. The second electrode 14 is integrated into the inner circumferential surface 2a of the vessel 2 in a manner which may be better understood by reference to the close-up C of Fig. 6B. Whereas a majority of the vessel 2 is made of a material such as an austenitic stainless steel, titanium or a titanium alloy, the second electrode 14 is made of a more highly conductive material, like copper, and has a composite structure including a surface layer 13 comprising at least one of tungsten, rhodium and molybdenum. This surface layer 13 protects the softer copper from the liquid metal, whilst also having a higher electrical conductivity than steel or titanium, for example. The second electrode 14 is electrically connected to earth potential as shown, so that an electrical current flowing through the liquid metal between the first and second electrodes 12, 14 flows through the surface layer 13 in preference to flowing through the higher resistance material from which the majority of vessel 2 is constructed. The electrical current flowing through the liquid metal between the first and second electrodes 12, 14 therefore has substantially the same form as the electrical current lr shown in Fig. 2B and interacts with the axial magnetic field Ba of the solenoid 17 to generate a Lorentz force encircling the first electrode 12, which produces vortex 8. Figs. 7A and 7B schematically show a third embodiment of a cyclonic separator 10c. The cyclonic separator 10c differs from the cyclonic separator 10a of Fig. 5 in that the first and second electrodes 12, 14 and the principal magnetic field coils 16a, 16b now have the second geometry of Figs. 3A to 3C instead of the first geometry of Figs. 2A to 2C. Thus the magnetic field coils 16a, 16b in the cyclonic separator 10c are now a pair of anti-Helmholtz coils, in which the coil currents circulate in opposite directions from each other. The first electrode 12 has an annular shape and is mounted on an end face of the vessel 2. However, the first electrode 12 is also electrically insulated from this end face and from other portions of the vessel 2 and the vortex finder 7 in close proximity to the first electrode 12 by an electrically non-conductive surface layer 21 as shown in Fig. 7A, whereas the second electrode 14 is not electrically insulated in this manner. The first electrode 12 is supplied with electrical current from a current carrying conductor outside the vessel 2. An electrical current flowing through the liquid metal between the first and second electrodes 12, 14 therefore has substantially the same form as the electrical current la shown in Fig. 3A and interacts with the radial magnetic field Br of the anti-Helmholtz coils 16a, 16b to generate a Lorentz force encircling the vortex finder 7, which produces vortex 8. To reduce its electrical resistance, the second electrode 14 may have a composite structure similar to that described above in relation to Fig. 6B and be electrically connected to earth potential by an electrically insulated current carrying conductor buried within the wall of the vortex finder 7. Alternatively, for greater ease of construction, the second electrode 14 may just be made of the same material as and integrated with the vortex finder 7. In either case, the second electrode 14 is separated by a gap from the inner circumferential surface 2a of the vessel 2, so that liquid metal and more massive particles thrown against the inner circumferential surface 2a by the vortex 8 can move axially towards the underflow outlet 5. In addition, the second electrode 14 is divided into a plurality of sectors 14a, 14b, 14c, 14d about the longitudinal axis Z of the vessel 2, as shown in the cross-section of Fig. 7B, so that the liquid metal and less massive particles suspended or entrained therein can also move axially at azimuthal angles where these sectors 14a, 14b, 14c, 14d are absent. Fig. 8 schematically shows a fourth embodiment of a cyclonic separator lOd. The cyclonic separator lOd comprises all the same features as the cyclonic separator 10c of Figs. 7A and 7B, except that in the present case, the pair of anti-Helmholtz coils 16a, 16b have been replaced by a pair of opposing solenoids 17a, 17b, in which the solenoid currents circulate in opposite directions from each other. In comparison to the anti-Helmholtz coils 16a, 16b of the cyclonic separator 10c, the pair of opposing solenoids 17a, 17b generate a stronger radial magnetic field Br between the first and second electrodes 12, 14. The strength of the magnetic field generated by each respective one of the solenoids 17a, 17b is the same as that generated by the other solenoid 17b, 17a of the pair, in order to ensure that the radial magnetic field Br between the first and second electrodes 12, 14 remains planar and thus perpendicular to the current flowing through the liquid metal between the first and second electrodes 12, 14. As is known, the respective strengths of the magnetic fields generated by the opposing solenoids 17a, 17b can be made the same as each other by ensuring that the respective products of their number of turns per unit length with the solenoid currents respectively circulating through them are the same as each other. However, provided that this condition is met, the two solenoids 17a, 17b may have different lengths from each other, as Fig. 8 shows. In a possible variant of this embodiment, the solenoid 17b may continue with a frustoconical shape around the tapering part 3 of the vessel 2, parallel to and coaxial with the tapering part 3. As a result of the frustoconical shape of this tapering part of the solenoid 17b, its magnetic field would have a gradient inside the tapering part 3 in the axial direction, such that the magnetic field increases in strength towards the underflow outlet 5. Such an axial magnetic field gradient inside the tapering part 3 may also be generated by surrounding it with another solenoid (not shown), in which the solenoid current circulates in the same direction as in the solenoid 17b, but which has an increasing number of turns per unit length towards the underflow outlet 5 as well or instead. Figs. 9A and 9B schematically show a fifth embodiment of a cyclonic separator lOe. The cyclonic separator lOe differs from the cyclonic separator 10c of Figs. 7A and 7B in the following respects. The first and second electrodes 12, 14 and the principal magnetic field coils 16a, 16b are all axially offset from the inlet 4 to the vessel 2. Unlike the first electrode 12 in the cyclonic separator 10c of Figs. 7A and 7B, which has an annular shape, the first electrode 12 in the cyclonic separator lOe is now divided into a plurality of sectors about the longitudinal axis Z of the vessel 2 in the same manner as the second electrode 14 described above and for the same reasons. Each sector of the first electrode 12 is also separated by a gap from the inner circumferential surface 2a of the vessel 2 for the same reasons as also described above. The sectors of the first electrode 12 are axially aligned with the sectors of the second electrode 14 to maintain the flow of electrical current through the liquid metal between them in an axial direction. Each sector 14a, 14b, 14c, 14d of the second electrode 14 is mounted on a strut 15 having a magnetic susceptibility with an absolute value of less than 10-2 and an elongate shape extending in the longitudinal direction. Each of these elongate struts 15 is in turn itself mounted on the vortex finder 7. Thus, whereas the vortex finder 7 has an annular cross-section, each strut 15, on which a respective one of the sectors 14a, 14b, 14c, 14d is mounted, is separated from the other struts 15, so that liquid metal may move freely between them. The structure of each of these struts 15 may be better understood by reference to the close-up E of Fig. 9B. As may be seen therein, each strut 15 is electrically insulated from the liquid metal by an electrically non-conductive surface layer 21 to prevent electrical current from flowing through liquid metal between the first electrode 12 and the strut 15, instead of between the first electrode 12 and the second electrode 14. Each strut 15 also contains an electrically conductive current carrier 11 having a magnetic susceptibility with an absolute value of less than 10-2, for carrying electrical current to the respective one of the sectors 14a, 14b, 14c, 14d mounted on that strut 15. For example, the current carriers 11 may be made of a material such as copper. The respective current carriers 11 therefore electrically connect the respective sectors 14a, 14b, 14c, 14d with minimal electrical resistance to the vortex finder 7, which is at earth potential. The sectors of the first electrode 12 are similarly supplied with electrical current by an electrically insulated current carrying conductor buried within the wall of the vortex finder 7. An electrical current flowing through the liquid metal between the first and second electrodes 12, 14 therefore has substantially the same form as the electrical current la shown in Fig. 3A and interacts with the radial magnetic field Br of the anti-Helmholtz coils 16a, 16b to generate a Lorentz force encircling the vortex finder 7, which produces vortex 8. Fig. 10 schematically shows a sixth embodiment of a cyclonic separator lOf. By way of example, the cyclonic separator lOf combines features from the cyclonic separator lb of Fig. IB with features of the second arrangement of first and second electrodes 12, 14 and principal magnetic field coils 16a, 16b of Figs. 3A to 3C, with the following additional features and modifications. The first and second electrodes 12, 14 are positioned on either side of the inlet 4 to the vessel 2 in an axial direction, as are the magnetic field coils 16a, 16b. The first and second electrodes 12, 14 are both disc-shaped, with the first electrode 12 mounted to the vessel 2 but insulated therefrom by an electrically non-conductive surface layer 21, which also continues around portions of the inner circumferential surface 2a of the vessel 2 which are in close proximity to the first electrode 12. The second electrode 14 is mounted on a single, centrally located strut 15, depending from the first electrode 12. This strut 15 has an elongate shape extending in the longitudinal direction and a structure similar to that described above in relation to Fig. 9B, including having an electrically non-conductive surface layer 21 to prevent electrical current from flowing through liquid metal between the first electrode 12 and the strut 15, instead of between the first electrode 12 and the second electrode 14. The strut 15 also contains an electrically conductive current carrier 11 having a magnetic susceptibility with an absolute value of less than 10-2, for connecting the second electrode 14 to earth potential. The first electrode 12 is supplied with electrical current from a current carrying conductor outside the vessel 2. Like the first and second electrodes 12,14 in Fig. 3A, the first and second electrodes 12,14 in the cyclonic separator lOf are both disc-shaped and have equal radii to each other, so that the electrical current flowing through liquid metal between them remains axial. Thus an electrical current flowing through the liquid metal between the first and second electrodes 12, 14 has substantially the same form as the electrical current la shown in Fig. 3A and interacts with the radial magnetic field Br of the antiHelmholtz coils 16a, 16b to generate a Lorentz force encircling the vortex finder 7, which produces vortex 8. The outer circumference of each of the first and second electrodes 12,14 is separated by a respective gap from the inner circumferential surface 2a of the vessel 2, so that liquid metal and more massive particles thrown against the inner circumferential surface 2a by vortex 8 can move axially through the gap between surface 2a and the second electrode 14, towards the underflow outlet 5. However, due to the tapering of vessel 2, a size of the gap between its inner circumferential surface 2a and the first electrode 12 is significantly greater than that between the surface 2a and the second electrode 14, so that liquid metal and less massive particles can also move unimpeded in an axial direction towards the overflow outlet 6. Figs. 11A and 11B schematically show a seventh embodiment of a cyclonic separator 10g. By way of example, the cyclonic separator 10g combines features from the cyclonic separator lb of Fig. IB with features of the first arrangement of first and second electrodes 12, 14 and principal magnetic field coils 16a, 16b of Figs. 2A to 2C, with the following additional features and modifications. Since the cyclonic separator 10g does not have a vortex finder, the first electrode 12 in the present case has the form of a solid right circular cylinder without a tubular topology. The first electrode 12 is electrically insulated from portions of the vessel 2 in close proximity thereto by an electrically non-conductive surface layer 21 as shown in Fig. 11A and is supplied with electrical current from a current carrying conductor outside the vessel 2. The second electrode 14 is mounted to and at the same earth potential as the vessel 2, so that an electrical current flowing through the liquid metal between the first and second electrodes 12, 14 has substantially the same radial form as the electrical current lr shown in Fig. 2B and interacts with the axial magnetic field Ba generated by the Helmholtz coils 16a, 16b to generate a Lorentz force encircling the first electrode 12 to produce vortex 8. Although the second electrode 14 surrounds the first electrode 12, it is divided into a plurality of sectors about the longitudinal axis Z of the vessel 2, like those labelled 14a, 14b in the cross-section of Fig. 11B. This allows liquid metal and any particles suspended or entrained therein to move radially at azimuthal angles where these sectors of the second electrode 14 are absent. Thus the forced vortex produced radially within the second electrode 14 is connected to and maintained in fluid communication with a free vortex which can form radially outside the second electrode 14. Fig. 12 schematically shows an eighth embodiment of a cyclonic separator lOh. The cyclonic separator lOh differs from the cyclonic separator 10g of Figs. 11A and 11B in the following respects. Firstly, in the present case, the source of the axial magnetic field is a solenoid 17 encircling the vessel 2, instead of the principal magnetic field coils 16a, 16b in the cyclonic separator 10g. The solenoid 17 is positioned such that one end of the solenoid 17 is located on the same side of a plane P perpendicular to the longitudinal axis Z and dividing the first and one or more second electrodes 12, 14 as the apex of the vessel 2 and the other end of the solenoid 17 is located on the opposite side of the plane P from the apex of the vessel 2. Secondly, the inlet 4 to the vessel 2 is axially offset from the locations of the first and second electrodes 12, 14 and of the solenoid 17 towards the overflow outlet 6, so that the inlet 4 does not interrupt the continuous windings of the solenoid 17. The first and second electrodes 12, 14, including the division of the second electrode 14 into sectors, are, however, the same as in the cyclonic separator 10g of Figs. 11A and 11B. Fig. 13 schematically shows a ninth embodiment of a cyclonic separator lOj. The cyclonic separator lOj differs from the cyclonic separator lOh of Fig. 12 in the following respects. Firstly, the first electrode 12 has a solid frustoconical shape which continues that of the tapering part of the vessel 2. Secondly, the second electrode 14 is integrated into the inner circumferential surface 2a of the vessel 2 in a similar manner to the second electrode 14 of the cyclonic separator 10b described above in relation to Figs. 6A and 6B. The second electrode 14 in the present case therefore has a frustoconical shape with a tubular topology, which forms a continuous circuit about the first electrode 12, like the second electrode 14 does in the embodiment of Figs. 6A and 6B. In the present case, however, the second electrode 14 is slightly offset from the first electrode 12 in an axial direction towards the underflow outlet 5. Thus the direction of the electrical current I flowing through the liquid metal between the first and second electrodes 12, 14 remains substantially perpendicular to the surfaces of these two electrodes facing each other, even though the electrical current I is no longer exactly radial, as shown in Fig. 13. The solenoid 17 also has a frustoconical shape, parallel to and coaxial with the tapering part of the vessel 2. As a result of its frustoconical shape, the solenoid 17 generates a magnetic field with a gradient in the axial direction, such that the magnetic field increases in strength from the wider end of the solenoid 17 towards the narrower end thereof, which is also towards the underflow outlet 5. In a possible variant of this embodiment, an axial magnetic field gradient may be generated by varying a number of turns per unit length along the length of the solenoid 17 as well or instead. In any such case, this axial magnetic field gradient therefore directs particles with positive magnetic susceptibility (for example, ferromagnetic or paramagnetic particles) towards the underflow outlet 5 and particles with negative magnetic susceptibility ( / .e., diamagnetic particles) towards the overflow outlet 6. Thus if the particles with positive magnetic susceptibility are more massive than those with negative magnetic susceptibility, the axial magnetic field gradient enhances their cyclonic separation from each other according to their different masses. Moreover, despite the axial asymmetry of the magnetic field created by the frustoconical shape of solenoid 17, because the first and second electrodes 12, 14 also have a frustoconical shape and are axially offset from each other, the magnetic field within the solenoid 17 remains substantially perpendicular to the flow of electrical current I through the liquid metal between the first and second electrodes 12, 14, so that the Lorentz force generated by their interaction which acts on the liquid metal still causes it to rotate around the longitudinal axis Z of the vessel 2. Furthermore, a midplane S of the solenoid 17, which is perpendicular to the longitudinal axis Z of the vessel 2 and which bisects the length of the solenoid 17, is located nearer to the underflow outlet 5 in a longitudinal direction than the plane P dividing the first and second electrodes 12, 14. Thus the magnetic field within the solenoid 17, and therefore the axial magnetic field gradient as well, continue to act on particles suspended or entrained in the liquid metal nearer to the underflow outlet 5, where no such Lorentz force is generated, as well as in the forced vortex created by the Lorentz force acting on the liquid metal between the first and second electrodes 12, 14. Fig. 14 schematically shows a tenth embodiment of a cyclonic separator 10k. The cyclonic separator 10k comprises all the same features as the cyclonic separator 10a of Fig. 5. In the present embodiment, however, the cyclonic separator 10k also comprises an auxiliary pair of coils 18a, 18b, which are coaxial with each other and with the principal pair of coils 16a, 16b. As may be seen in Fig. 14, the auxiliary pair of coils 18a, 18b are each oriented parallel to the plane P dividing the first and one or more second electrodes 12, 14. One 18b of the auxiliary pair of coils is located on the same side of the plane P as the apex of the vessel 2, and the other 18a of the auxiliary pair of coils is located on the opposite side of the plane P from the apex of the vessel 2. Unlike the principal pair of coils 16a, 16b, which are a pair of Helmholtz coils, the auxiliary pair of coils 18a, 18b are instead a pair of antiHelmholtz coils, in each of which a coil current circulates in opposite directions. This auxiliary pair of coils 18a, 18b are separated from each other by a distance equal to V3 times their radius, which is the same as the radius of the principal pair of coils 16a, 16b. Thus the ones 16b, 18b of the principal and auxiliary pairs of coils which are on the same side of the plane P as the apex of the vessel 2 are reflection symmetric with the others 16a, 18a of the principal and auxiliary pairs of coils on the opposite side of the plane P from the apex of the vessel 2. During operation of the cyclonic separator 10k, the auxiliary pair of coils 18a, 18b generate a magnetic field having the form shown in Fig. 3C, whereas the principal pair of coils 16a, 16b generate a magnetic field having the form shown in Fig. 2C. These two fields add together to produce a total magnetic field. However, the magnetic field generated by the auxiliary pair of coils 18a, 18b is weaker than the magnetic field generated by the principal pair of coils 16a, 16b. The axial components of the magnetic fields generated by the auxiliary pair of coils 18a, 18b and the principal pair of coils 16a, 16b point in the same direction as each other on the side of the plane P nearer to the apex of the vessel 2, thereby reinforcing each other to produce the axial component of the total magnetic field, whereas they are antiparallel to each other on the side of the plane P further from the apex of the vessel 2, tending to cancel each other out and reduce the axial component of the total magnetic field. This results in a gradient in the total magnetic field in the axial direction, with increasing field strength towards the underflow outlet 5. Accordingly, this axial gradient in the total magnetic field directs particles with positive magnetic susceptibility towards the underflow outlet 5 and particles with negative magnetic susceptibility towards the overflow outlet 6, which enhances their cyclonic separation from each other according to their different masses if the particles with positive magnetic susceptibility are more massive than those with negative magnetic susceptibility. On the other hand, between the first and second electrodes 12, 14, the radial component of the magnetic field generated by the principal pair of coils 16a, 16b approaches zero, whereas the radial component of the magnetic field generated by the auxiliary pair of coils 18a, 18b is significant. The radial component of the total magnetic field is therefore dominated by the radial component of the magnetic field generated by the auxiliary pair of coils 18a, 18b. This results in a gradient in the total magnetic field in the radial direction, such that the radial component of the total magnetic field is zero on the longitudinal axis Z, but increases in strength with increasing radial distance from the longitudinal axis Z, until it reaches a local maximum at the radius of both the principal and auxiliary pairs of coils, before then decreasing in strength as the radial distance increases further. Accordingly, this radial gradient in the total magnetic field directs particles with positive magnetic susceptibility outwards towards the inner circumferential surface 2a of the vessel 2 and particles with negative magnetic susceptibility inwards towards the longitudinal axis Z, which also enhances their cyclonic separation from each other according to their different masses if the particles with positive magnetic susceptibility are more massive than those with negative magnetic susceptibility. However, due to the axial asymmetry ( / .e., the axial gradient) in the total magnetic field, a plane M which contains the local maximum in the radial component of the total magnetic field is axially offset from the plane P in a direction towards the underflow outlet 5, as shown in Fig. 14. This has the additional advantage that the plane M thereby avoids the inlet 4. Fig. 15 shows a first embodiment of a method 100a of separating different chemical species from each other. The method 100a firstly comprises introducing 101 into a vessel for containing liquid metal which is continuously axially symmetric about a longitudinal axis and wherein at least part of the vessel tapers to an apex, a liquid metal having suspended or entrained therein, particles of a plurality of different chemical species of respectively different densities each in solid phase. For example, the vessel may be any of the vessels 2 shown in the first to tenth embodiments of a cyclonic separator lOa-lOk described above in relation to Figs. 5 to 14, and may be selected and designed to suit the properties of the liquid metal and of the particles suspended or entrained therein. The method 100a then comprises immersing 102 in the liquid metal within the vessel a first electrode coaxial with the longitudinal axis of the vessel and one or more second electrodes spaced apart from the first electrode, wherein the first and one or more second electrodes have a magnetic susceptibility with an absolute value of less than 10-2. For example, the first and second electrodes may be any of those shown in respective ones of the first to tenth embodiments of a cyclonic separator lOa-lOk described above in relation to Figs. 5 to 14. The method 100a also comprises maintaining the vessel and the one or more second electrodes at the same electrical potential as each other whilst establishing a potential difference between the first and one or more second electrodes to cause 103 an electrical current to flow through the liquid metal between the first and one or more second electrodes. In addition, the method 100a comprises applying 104 to the liquid metal a magnetic field having a major component which is substantially perpendicular to the flow of electrical current through the liquid metal between the first and one or more second electrodes, thereby generating a Lorentz force acting on the liquid metal, which causes it to rotate around the longitudinal axis of the vessel. For example, a source of the magnetic field may be any of those shown in respective ones of the first to tenth embodiments of a cyclonic separator lOa-lOk described above in relation to Figs. 5 to 14. The method 100a then comprises varying 105 a rotation speed of the liquid metal by adjusting at least one of the electrical current and the strength of the magnetic field to separate particles of the different chemical species suspended or entrained in the liquid metal from each other. In other words, the rotation speed is varied until it is sufficient to achieve at least partial cyclonic separation of the different chemical species from each other. The method 100a then comprises abstracting 106 the liquid metal with a majority of particles of a first, denser one of the plurality of different chemical species suspended or entrained therein from an underflow outlet of the vessel, and abstracting 107 the liquid metal with a majority of particles of a second, less dense one of the plurality of different chemical species suspended or entrained therein from an overflow outlet of the vessel which is further from the apex of the vessel than the underflow outlet. For example, the underflow and overflow outlets may be arranged like any of those shown in respective ones of the first to tenth embodiments of a cyclonic separator lOa-lOk described above in relation to Figs. 5 to 14. Fig. 16 shows a second embodiment of a method 100b of separating different chemical species from each other. The method 100b comprises all the same processes as the first method 100a described above in relation to Fig. 15, except that in the method 100b, introducing 101 into the vessel a liquid metal having suspended or entrained therein, particles of a plurality of different chemical species each in solid phase comprises introducing 101a into the vessel a liquid metal having suspended or entrained therein particles of a diamagnetic chemical species and particles of a non-diamagnetic chemical species with different densities from each other. Furthermore, applying 104 a magnetic field to the liquid metal in the method 100b comprises applying 104a a magnetic field which has a gradient in at least one of an axial direction and a radial direction, where the sense of the magnetic field gradient (i.e., either parallel or antiparallel to the longitudinal axis of the vessel, and either radially inwards towards or radially outwards away from the longitudinal axis) is chosen to enhance cyclonic separation 105 of the particles according to their different densities. This magnetic field gradient may be created by a permanent magnet, a non-uniform solenoid as described above in relation to Fig. 13, and / or an auxiliary pair of magnetic field coils as described above in relation to Fig. 14, for example. When the magnetic field gradient is applied 104a to the liquid metal, the method 100b continues by separating 105 and abstracting 106, 107 the different chemical species from the respective outlets of the vessel, as in the method 100a. Apart from the interaction between the magnetic field and the electrical current which generates the Lorentz force acting on the liquid metal, the magnetic field gradient acts directly on the diamagnetic and non-diamagnetic particles suspended or entrained therein, attracting the non-diamagnetic particles towards and repelling the diamagnetic particles away from where the magnetic field is stronger. If the non-diamagnetic particles are denser, the magnetic field gradient is chosen such that the magnetic field increases in strength towards the apex of the vessel and / or radially outwards, thereby directing them towards the underflow outlet, whereas if the diamagnetic particles are denser, the magnetic field gradient is chosen such that the magnetic field increases in strength away from the apex of the vessel and / or radially inwards, thereby directing the diamagnetic particles towards the overflow outlet. Fig. 17 shows a third embodiment of a method 100c of separating different chemical species from each other. The method 100c is a special case of the method 100b, wherein the liquid metal introduced 101a into the vessel comprises liquid sodium (for example, it may be just liquid sodium or a liquid sodium-potassium alloy (NaK)), the non-diamagnetic chemical species comprise iron, which is ferromagnetic, and the diamagnetic chemical species comprise sodium oxide. Such a combination 101b of species may be the products of a redox reaction between one or more iron oxides and an amount of liquid sodium in excess of a stoichiometric amount thereof required for the reaction, in which the liquid sodium reduces the iron oxide(s) into elemental iron, the stoichiometric amount of liquid sodium is oxidized to produce the sodium oxide, and the remaining excess liquid sodium acts as a transport medium for the reaction products, which are insoluble in the liquid sodium. In the method 100c, the first and one or more second electrodes are immersed 102a in the liquid sodium and an electrical current is caused 103a to flow through the liquid sodium between them. Because the ferromagnetic iron is more than three times denser than the diamagnetic sodium oxide, when the magnetic field is applied 104a, the direction of the magnetic field gradient is chosen 104b such that the strength of the magnetic field increases towards at least one of the apex of the vessel and radially outwards, towards an inner circumferential surface of the vessel. This magnetic field gradient therefore enhances the cyclonic separation of the insoluble particles according to their different densities. On the other hand, the magnetic field gradient has a negligible effect on the liquid sodium, which is only very weakly paramagnetic, because the Lorentz forces acting on the liquid sodium, and the fluid dynamic forces in the vortex created by them, are much greater than any force on the liquid sodium from the magnetic field gradient. The method 100c then proceeds in the same manner as the method 100b. Fig. 18 shows a fourth embodiment of a method lOOd of separating different chemical species from each other. The method lOOd comprises all the same processes as the second method 100b described above in relation to Fig. 16, where in this case, the magnetic field is chosen 104a to have a gradient both in an axial direction, such that the strength of the magnetic field increases towards the apex of the vessel, and in a radial direction, such that the strength of the magnetic field increases with radial distance from the longitudinal axis of the vessel and towards an inner circumferential surface of the vessel. The method lOOd is therefore suited to separating non-diamagnetic from diamagnetic particles when the non-diamagnetic particles are denser than the diamagnetic particles, as for example, is the case in the method 100c described above in relation to Fig. 17. Furthermore, in the present embodiment, the strength of the magnetic field increases with radial distance from the longitudinal axis to a local maximum before decreasing thereafter as the radial distance continues to increase. This may be achieved, for example, by means of a pair of anti-Helmholtz coils or a pair of opposing solenoids, as described above in relation to Figs. 3B and 3C. The method lOOd comprises axially offsetting 104c a plane containing this local maximum towards the apex of the vessel from a plane which is perpendicular to the longitudinal axis of the vessel and which divides the first and one or more second electrodes. This may be achieved, for example, by using a pair of anti-Helmholtz coils as an auxiliary pair of coils, as described above in relation to Fig. 14. The radial and axial magnetic field gradients therefore act together to direct the denser non-diamagnetic particles towards the underflow outlet of the vessel and the diamagnetic particles towards the overflow outlet, in addition to the fluid dynamic forces acting on the particles as a result of the vortex. Whereas the present invention has been described above by reference to particular examples and embodiments, the scope of the invention should not be taken to be limited thereby and is instead defined by the appended claims.

Claims

1. An apparatus (10a - 10k) comprising:a vessel (2) for containing liquid metal which is continuously axially symmetric about a longitudinal axis (Z), wherein at least a part (3) of the vessel (2) tapers to an apex and the vessel (2) comprises:an inlet (4) for the liquid metal having suspended or entrained therein, particles of a plurality of different chemical species of respectively different densities each in solid phase;an underflow outlet (5) for the liquid metal with a majority of particles of a first, denser one of the plurality of different chemical species suspended or entrained therein; andan overflow outlet (6) for the liquid metal with a majority of particles of a second, less dense one of the plurality of different chemical species suspended or entrained therein;wherein the underflow outlet (5) is nearer to the apex than the overflow outlet (6), the apparatus (1) further comprising:a first electrode (12) coaxial with the longitudinal axis (Z) of the vessel;one or more second electrodes (14) spaced apart from the first electrode (12); anda source (16a, 16b, 17,19, 20) of a magnetic field;wherein:the first and one or more second electrodes (12, 14) have a magnetic susceptibility with an absolute value of less than 10-2 and are arranged within the vessel (2) to be immersed in the liquid metal when the vessel (2) contains the same, thereby allowing an electrical current (lr, la) to flow through the liquid metal between the first and one or more second electrodes (12,14); andthe magnetic field has a major component (Ba, Br) which is substantially perpendicular to the flow of electrical current (lr, la) through the liquid metal between the first and one or more second electrodes (12, 14), thereby generating a Lorentz force acting on the liquid metal which causes it to rotate around the longitudinal axis (Z) of the vessel (2).

2. An apparatus (10a, 10b, 10g, lOh, lOj, 10k) according to claim 1, wherein:the one or more second electrodes (14) are spaced apart from the first electrode (12) in a radial direction, whereby the electrical current (lr) can flow radially through the liquid metal between the first and one or more second electrodes (12,14); andthe magnetic field has a major axial component (Ba) between the first and one or more second electrodes (12, 14) which is substantially parallel to the longitudinal axis (Z) of the vessel (2).

3. An apparatus (10a, 10b, 10g, lOh, lOj, 10k) according to claim 2, wherein the first and one or more second electrodes (12, 14) extend the same distance as each other in a longitudinal direction and are coaxial with each other.

4. An apparatus (10a, 10b, 10k) according to claim 3, wherein:the vessel (2) comprises a vortex finder (7) coaxial with the longitudinal axis (Z) of the vessel (2) and leading to the overflow outlet (6); andthe first electrode (12) has a tubular topology oriented coaxially with the longitudinal axis (Z) of the vessel (2).

5. An apparatus (10a, 10b, 10g, lOh, lOj, 10k) according to claim 3 or claim 4, wherein at least one of the first and one or more second electrodes (12, 14) comprises a surface of revolution about the longitudinal axis of the vessel (Z).

6. An apparatus (10b, lOh, lOj) according to any one of claims 2 to 5, wherein the source of the magnetic field comprises an electromagnet including a solenoid (17) oriented with its longitudinal axis parallel to the longitudinal axis (Z) of the vessel (2), wherein one end of the solenoid (17) is located on the same side of a plane (P) perpendicular to the longitudinal axis (Z) and dividing the first and one or more second electrodes (12, 14) as the apex of the vessel (2), and the other end of the solenoid (17) is located on the opposite side of the plane (P) from the apex of the vessel (2).

7. An apparatus (lOj) according to claim 6, wherein at least one of a number of turns per unit length and a diameter of the solenoid (17) vary along the length of the solenoid (17).

8. An apparatus (lOj) according to claim 6 or claim 7, wherein a midplane (S) of the solenoid (17) perpendicular to the longitudinal axis (Z) and bisecting the length of the solenoid (17), is axially offset in the longitudinal direction from the plane (P) dividing the first and one or more second electrodes (12, 14).

9. An apparatus (10c - lOf) according to claim 1, wherein:the one or more second electrodes (14) are spaced apart from the first electrode (12) in an axial direction, whereby the electrical current (la) can flow axially through the liquid metal between the first and one or more second electrodes (12,14); andthe magnetic field has a major radial component (Br) between the first and one or more second electrodes (12,14) which is substantially perpendicular to the longitudinal axis (Z) of the vessel (2).

10. An apparatus (10c - lOf) according to claim 9, wherein the first and one or more second electrodes (12, 14) extend the same distance as each other in a radial direction and are parallel to each other.

11. An apparatus (10c) according to claim 10, wherein:the vessel (2) comprises a vortex finder (7) coaxial with the longitudinal axis (Z) of the vessel (2) and leading to the overflow outlet (6); andat least one of the first and one or more second electrodes (12, 14) comprises an annulus centred on the longitudinal axis (Z) of the vessel (2).

12. An apparatus (lOd) according to anyone of claims 9 to 11, wherein the source of the magnetic field comprises an electromagnet including a pair of opposing solenoids (17a, 17b) oriented with their longitudinal axes parallel to the longitudinal axis (Z) of the vessel (2) and aligned with each other, wherein one (17b) of the pair of opposing solenoids is located on the same side of a plane (P) perpendicular to the longitudinal axis (Z) and dividing the first and one or more second electrodes (12, 14) as the apex of the vessel (2), and the other (17a) of the pair of opposing solenoids is located on the opposite side of the plane (P) from the apex of the vessel (2).

13. An apparatus (lOd) according to claim 12, wherein at least one of a number of turns per unit length and a diameter of at least one of the solenoids (17a, 17b) vary along the length of the respective one of the solenoids (17a, 17b).

14. An apparatus (10a, 10c, lOe, lOf, 10g 10k) according to any one of the preceding claims, wherein the source of the magnetic field comprises an electromagnet having at least a principal pair of coaxial coils (16a, 16b) each oriented parallel to a plane (P) perpendicular to the longitudinal axis (Z) of the vessel (2) and dividing the first and one or more second electrodes (12, 14), wherein one of the principal pair of coils (16a, 16b) is located on the same side of the plane (P) as the apex of the vessel (2), and the other of the principal pair of coils (16a, 16b) is located on the opposite side of the plane (P) from the apex of the vessel (2).

15. An apparatus (10k) according to claim 14, wherein the electromagnet further comprises an auxiliary pair of coils (18a, 18b), which are coaxial with each other and with the principal pair of coils (16a, 16b), wherein the auxiliary pair of coils (18a, 18b) are each oriented parallel to the plane (P) dividing the first and one or more second electrodes (12, 14), one of the auxiliary pair of coils (18a, 18b) is located on the same side of the plane (P) as the apex of the vessel (2), and the other of the auxiliary pair of coils (18a, 18b) is located on the opposite side of the plane (P) from the apex of the vessel (2), such that the ones of the principal and auxiliary pairs of coils (16a, 16b; 18a, 18b) on the same side of the plane (P) as the apex of the vessel (2) are reflection symmetric with the others of the principal and auxiliary pairs of coils (16b, 16a; 18b, 18a) on the opposite side of the plane (P) from the apex of the vessel (2).

16. An apparatus (10c - lOh) according to any one of the preceding claims, wherein at least one of the first and one or more second electrodes (12, 14) is divided into one or more sectors (14a, 14b, 14c, 14d) about the longitudinal axis (Z) of the vessel (2).

17. An apparatus (lOe, lOf) according to any one of the preceding claims, wherein at least one of the first and one or more second electrodes (12, 14) is mounted on a strut (15) having a magnetic susceptibility with an absolute value of less than 10-2 and an elongate shape extending in the longitudinal direction.

18. An apparatus (lOe, lOf) according to claim 17, wherein the strut (15) is electrically insulated from the liquid metal and contains an electrically conductive current carrier (11) having a magnetic susceptibility with an absolute value of less than 10-2, for carrying the electrical current to the electrode (14) mounted on the strut (15).

19. An apparatus (10a - 10k) according to any one of the preceding claims, wherein at least one of the first and one or more second electrodes (12, 14) has a composite structure including a surface layer (13) comprising at least one of tungsten, rhodium and molybdenum.

20. A method (100a - lOOe) comprising:introducing (101) into a vessel (2) for containing liquid metal which is continuously axially symmetric about a longitudinal axis (Z) and wherein at least part (3) of the vessel (2) tapers to an apex, a liquid metal having suspended or entrained therein, particles of a plurality of different chemical species of respectively different densities each in solid phase;immersing (102) in the liquid metal within the vessel (2) a first electrode (12) coaxial with the longitudinal axis (Z) of the vessel (2) and one or more second electrodes (14) spaced apart from the first electrode (12), the first and one or more second electrodes (12, 14) having a magnetic susceptibility with an absolute value of less than 10-2;maintaining (103) the vessel (2) and the one or more second electrodes (12, 14) at the same electrical potential as each other whilst establishing a potential difference between the first and one or more second electrodes (12, 14) to cause an electrical current to flow through the liquid metal between the first and one or more second electrodes (12, 14);applying (104) to the liquid metal a magnetic field having a major component (Ba, Br) which is substantially perpendicular to the flow of electrical current (lr, la) through the liquid metal between the first and one or more second electrodes (12,14), thereby generating a Lorentz force acting on the liquid metal which causes it to rotate around the longitudinal axis (Z) of the vessel (2);varying (105) a rotation speed of the liquid metal by adjusting at least one of the electrical current (lr, la) and the strength of the magnetic field to separate particles of the different chemical species suspended or entrained in the liquid metal from each other according to their densities;abstracting (106) the liquid metal with a majority of particles of a first, denser one of the plurality of different chemical species suspended or entrained therein from an underflow outlet (5) of the vessel (2); andabstracting (107) the liquid metal with a majority of particles of a second, less dense one of the plurality of different chemical species suspended or entrained therein from an overflow outlet (6) of the vessel (2) which is further from the apex of the vessel (2) than the underflow outlet (5).

21. A method (100b) according to claim 20, wherein:introducing (101) into the vessel (2) a liquid metal having suspended or entrained therein, particles of a plurality of different chemical species each in solid phase comprises introducing (101a) into the vessel (2) a liquid metal having suspended or entrained therein particles of a diamagnetic chemical species and particles of a non-diamagnetic chemical species with different densities from each other; andthe magnetic field has (104a) a gradient in at least one of an axial direction and a radial direction which enhances separation (105) of the particles according to their different densities.

22. A method (100c) according to claim 21, wherein:the liquid metal comprises liquid sodium;the non-diamagnetic chemical species comprise at least one of iron, an iron oxide, manganeseand a manganese oxide as the first one of the plurality of different chemical species;5 the diamagnetic chemical species comprise sodium oxide as the second one of the plurality ofdifferent chemical species; anda direction of the magnetic field gradient is chosen (104b) such that the strength of the magnetic field increases towards at least one of the apex of the vessel (2) and an inner circumferential surface (2a) of the vessel (2).1023. A method (lOOd) according to claim 21 or claim 22, wherein:the magnetic field has a gradient both in an axial direction, such that the strength of the magnetic field increases towards the apex of the vessel (2), and in a radial direction, such that the strength of the magnetic field increases with radial distance from the longitudinal axis (Z) of the vessel 15 (2) to a local maximum before decreasing thereafter as the radial distance continues to increase; anda plane (M) containing the local maximum is axially offset (104c) towards the apex of the vessel (2) from a plane (P) perpendicular to the longitudinal axis (Z) of the vessel (2) and dividing the first and one or more second electrodes (12, 14).T +44(0)30 0300 2000A

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