Capture of small paramagnetic particles by magnetic forces from low speed fluid flows

Abstract

SCOPEDiflerences in magnetic properties long have been considered as a possible means for separating mixtures. Magnetite is separated from silaceous rock by large magnetic drum separators. Many processes are protected from damage due to broken gears and other such pieces of magnetic metal by magnetic separators. In these cases, the particles are ferromagnetic, and the separation is relatively easy. However, the separation of very weakly magnetic or paramagnetic particles requires a more sophisticated separator design. One means for carrying out a magnetic separation is to place small diameter (100 p) ferromagnetic filaments in a solenoid magnetic through which a fluid containing paramagnetic particles is passing. Field gradients are formed in the region surrounding the filameints so that the paramagnetic particles are attracted to andl held on the filament. In a practical separator, 2 to 15 vol. yo of the magnetic field is filled with filamentary ferromagnetic material. A fluid containing the paramagnetic particles is passed through the matrix formed by the filaments. The paramagnetic material is retained in the matrix while the nonmagnetic particles and fluid pass through. The performance of these separators depends on how efficiently they capture small paramagnetic particles and how much of this material can be retained in the matrix. In this paper we present a theoretical study of the capture efficiency of a single filament of ferromagnetic material. The goal is to develop an understanding of the capture mechanisms involved. The model assumes a single bare filament, a low concentration of particles, and a fluid moving at low speeds. The equations for the magnetic, drag, and gravitational forces acting on a particle are derived and solved for a number of different conditions. The efficiency of the collector is analyzed in terms of its capture cross section. CONCLUSIONS AN D SIGN I F ICANCEThis paper presents a detailed analysis of the equations which describe the inertial, magnetic, fluid, and gravitational forces that govern the motion of a small paramagnetic particle near a bare cylindrical, ferromagnetic filament. These equations may be solved numerically to show that particle capture occurs primarily on the front of the cylinder when the flow field is parallel to the magnetic field and perpendicular to the filament. However, in several cases the particles are captured on the downstream side of the collector. A set of seven dimensionless groups can be used to describe the system. The group N M = pf H o 2 / p f v m 2 is defined to express the magnetic field strength.The magnetic force is long range and is the dominant factor in particle capture. The magnetic force acting on a paramagnetic particle in the vicinity of a ferromagnetic collector can be 100 times greater than gravity. The capture cross section of a bare collector in a magnetic field can be 100 times larger than that due to inertial impaction alone. Many materials which are not commonly thought of as being magnetic (copper oxide, aluminum) can be c...

New correlation for the capture cross section in high‐gradient magnetic separation

“…The terms Urn/Uo and Ngr on the other hand, represent ratios of the long-range magnetic and gravitational forces, respectively, to the fluid drag force. The effect of gravity, although small and normally ignored Avens et al, 1992;Cummings et al, 1976;Friedlaender et al, 1981a,b;Gerber et al, 1996;Gerber, 1994Gerber, , 1980Gerber and Lawson, 1989;Gerber and Birss, 1983;Kramer et al, 1990;Lawson and Gerber, 1990;Drummond, 1976, 1975;Prenger et al, 1993;Schake et al, 1994;Watson, 1973Watson, , 1978Worl et al, 1997), is examined here to make the correlation more complete. Similar to Watson (1973) and others (Cowen et al, 1976), the trajectory model, depicted in Eqs.…”

“…Several forces are relevant in the retention of a particle by a wire, among which the most important are the inertial, magnetic, viscous, gravitational, and Brownian forces. However, in liquid phase systems, where viscous effects are significant, inertial forces are normally assumed unimportant (Watson, 1973;Cummings et al, 1976;Friedlaender et al, 1981a;Gerher, 1994Gerher, , 1980Gerber and Birss, 1983;Kramer et al, 1990). Also, the particles are assumed large enough to neglect the disruptive effects of Brownian forces.…”

“…Note that the preceding equations are slightly different from those in the work of Cummings (1976), where the chosen characteristic length was the radius of the particle R,; here it is the radius of the wire R,. In terms of these variables, a dimensionless capture cross section is defined as Y c…”

“…The trajectory model (Watson, 1973;Cummings et al, 1976;Friedlaender et al, 1981a;Gerber, 1994Gerber, , 1980Gerber and Birss, 1983;Kramer et al, 1990) used here assumes that a particle is moving in potential flow toward a single and clean wire of cylindrical shape, with its axis placed perpendicular to the direction of flow and with the magnetic field directed toward the two given directions, as shown in Figure 1. Several forces are relevant in the retention of a particle by a wire, among which the most important are the inertial, magnetic, viscous, gravitational, and Brownian forces.…”

“…Gerber and coworkers (Gerber, 1984;Gerber et al, 1983;Takayasu et al, 1976) have shown, for example, that depending on the magnetic susceptibility, the particle radii for which Brownian motion becomes important vary from 100 (Mn2P20,) to 700 nm (A120,) if stainless-steel wires of 100 p m diameter and fields of 8 X los A m-l (that is, B, = 1 T) are used. With these studies in mind, the following dimensionless differential force balance on a single particle in cylindrical coordinates is obtained (Cummings et al, 1976): …”