مرکز منطقه ای اطلاع رساني علوم و فناوري - Effective capture radius estimated from single wire buildup process in high gradient magnetic separation

Abstract :

The effective capture radius $\\zeta _{eff}$ is shown to be estimated from the single wire buildup study through the next equation. $\\zeta _{eff} = (K\\rho_{p}/2av_{o}C_{\\in})(dS/dt)$ , where $K\\rho_{p}$ is the effective density of as-captured particles, dS/dt is the rate of increase of the particle retention cross section, Cinand voare the concentration and the velocity of the feed slurry, respectively, and a is the wire radius. Using α-Fe2O3particles, it is found that $S/S_{o} \\simeq (t/\\tau )^{1/2}$ , where S is the buildup cross section, $S_{o}=\\pi a^{2}$ , and τ is the characteristic time depending on voand the applied field Ho. From these two equations, it is found that $\\zeta _{eff} \\simeq a(\\tau t)^{-1/2} = (A/\\tau ) (S_{o}/S)$ , where $A=(\\pi aK\\rho _{p}/4v_{o}C_{in})$ . This relation can adequately be explained by the existing theory. Another finding is $\\tau \\propto v_{o}/H_{o}$ or $\\zeta _{eff} (t:const.) \\propto H\\min{o}\\max {1/2}v\\min{o}\\max {-3/2}$ . The dependence of τ or $\\zeta _{eff}$ on Hocan be explained by considering the weak ferromagnetic nature of α-Fe2O3. However, to explain the dependence of τ or $\\zeta _{eff}$ on vo, the introduction of the sticking factor, namely the probability that a particle arrived at the wire surface is actually captured, seems to be required.