Magnetic velocity

In general, the approaches of the trajectory analysis and the build-up models are based on the force-balance equation. Among the forces (external and interparticle) involved in the system, magnetic and hydrodynamic forces, the most significant ones, also compete with one another. The performance of magnetic separation is, therefore, examined in terms of magnetic velocity (Vjj ) and superficial velocity ( Vq) (Watson, 1973),... 

The instantaneous velocity information is obtained from a (coil and magnet) velocity transducer the resulting voltage is used to code the velocity information into the amplitude of the y-ray counts, which are then stored by pulse height analyzer. The disadvantage of this method is that any nonlinearity in velocity appears as modulation of the no-absorption spectrum. 

When inserting Eq. (6) into Eq. (5), it can be seen that, for a given magnetic field and a given viscosity, the magnetic velocity, t/mag, is dependent on the size and the magnetic characteristics of the particle. It is proportional to the square of the particle radius and to the magnetic susceptibility of the particle ... 

This magnetic migration velocity (Watson, 1973), also called the magnetic velocity, may be expressed in terms of a magnetophoretic mobility mo and the magnetic field force strength S ag (Moore et al, 2004) by... 

The source is brought to a. positive poteptial (I/) of several kilovolts and the ions are extracted by a plate at ground potential. They acquire kinetic energy and thus velocity according to their mass and charge. They enter a magnetic field whose direction is perpendicular to their trajectory. Under the effect of the field, Bg, the trajectory is curved by Lorentz forces that produce a centripetal acceleration perpendicular to both the field and the velocity. 

Magnetic sector instruments typically operate with ion sources held at a potential of between 6 and 10 kV. This results in ions with keV translational kinetic energies. The ion kinetic energy can be written as zt V = Ifur and thus the ion velocity is given by the relationship... 

Flow which fluctuates with time, such as pulsating flow in arteries, is more difficult to experimentally quantify than steady-state motion because phase encoding of spatial coordinate(s) and/or velocity requires the acquisition of a series of transients. Then a different velocity is detected in each transient. Hence the phase-twist caused by the motion in the presence of magnetic field gradients varies from transient to transient. However if the motion is periodic, e.g., v(r,t)=VQsin (n t +( )q] with a spatially varying amplitude Vq=Vq(/-), a pulsation frequency co =co (r) and an arbitrary phase ( )q, the phase modulation of the acquired data set is described as follows ... 

In a sector instrument, which acts as a combined mass/velocity filter, this difference in forward velocity is used to effect a separation of normal and metastable mj" ions (see Chapter 24, Ion Optics of Magnetic/Electric-Sector Mass Spectrometers ). However, as discussed above, the velocity difference is of no consequence to the quadmpole instrument, which acts only as a mass filter, so the normal and metastable mj ions formed in the first field-free region (Figure 33.1) are not differentiated. 

Thus, it can be said that conventional magnetic sectors separate ions into individual m/z values by dispersion in space (spatially) and not according to their flight times. Contrarily, TOP analyzers separate ions of different m/z values according to their velocities (temporally) but not spatially. 

Double-focusing analyzer. A magnetic analyzer and an electrostatic analyzer combined in either sequence to effect direction and velocity focusing. 

Electrostatic analyzer. A velocity-focusing device for producing an electrostatic field perpendicular to the direction of ion travel (usually used in combination with a magnetic analyzer for mass analysis). The effect is to bring to a common focus all ions of a given kinetic energy. 

Wien analyzer. A velocity filter with crossed homogeneous electric and magnetic fields for transmitting only ions of a fixed velocity. 

Most of the above apphcations are in clarification duties. The use of HGMS to dewater relatively concentrated, paramagnetic mineral slurries has been demonstrated on 2 to 12 wt % feed concentration of synthetic malachite (7) concentrated to 40%. The magnetic collection was optimized at flow velocities of 1 mm/s, and product concentrations greater than 40% were not possible unless the collected material could be removed from the matrix with less than the equivalent of one canister of washwater. 

Sectors. In a sector mass spectrometer, ions are formed in an ion source that is at a potential V, usually 8 to 10 kV. Upon leaving the ion source they undergo acceleration to a velocity v, where eU = y rriv, and then enter a magnetic sector which separates the beam of ions according to their corresponding momenta. The transmission of ions through such a device is described by... 

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