Magnetic particle separation in a liquid column based on magnetophoresis
In this paper, the topic of magnetic particle separation in a liquid column based on magnetophoresis is studied in depth. Magnetic powders are important basic materials for filaments, pastes and inks that need to exhibit magnetic properties. The geometric dimensions of the particles are decisive for further processing (e.g. fused filament printing or inkjet printing) and the material properties for the specific application (e.g. inductive electronic components). Magnetic powders (see Figure 1) are often a low-cost side product in certain recycling processes and therefore usually have a wide range of particle sizes. Figure 2 shows the size distribution of the investigated magnetic powder with an average particle diameter (d50) of approx. 8µm. This wide particle size distribution leads to problems during further processing, such as the clogging of printing nozzles or, as a result, to strongly fluctuating component properties (e.g. permeability of inductors). It is therefore often necessary to design the particle sizes within a narrow range or to limit them to a maximum particle size. This is traditionally achieved by mechanical sieving, but this has a number of disadvantages, such as clogging of the sieves due to electrostatic charging. This paper presents an alternative separation respectively sorting process based on the utilization of gravity and magnetic fields. Here, particles sink downwards within a liquid column due to the gravitational force. In doing so, they are subjected to Stokes friction, which leads to vertical separation depending on the particle size. Large particles sink much faster than small particles (see Figure 3a). Here, the sinking velocity is proportional to the square of the particle radius. Subsequently, the so vertically separated particles can be deflected horizontally by an external magnetic field. Figure 4 shows an equation set of the magnetophoretic phenomenon which is modeled and simulated in detail within COMSOL utilizing AC/DC Module and Particle Tracing Module. Particular emphasis is placed on the modeling of the radius-dependent and frequency-dependent complex permeability of the magnetic particles, which is based on specific electrical measurements. In addition, it is investigated which coil geometry and arrangement shows good performance in terms of horizontal particle deflection. In the presented experimental setup, the magnetic field is coupled into a diamagnetic liquid (e.g. water) by means of multiple electromagnetic coils in order to manipulate magnetic particles. This phenomenon is also known as positive magnetophoresis. In contrast, the term negative magnetophoresis is used when diamagnetic particles are manipulated in a ferrofluid. Figure 3b illustrates the particle trajectories for different particle sizes. Consequently, it is possible to selectively manipulate the vertically separated particles of different sizes by applying a suitable time-dependent magnetic field in the horizontal direction. Furthermore, the paper presents a detailed model that simulates the ability of separating respectively sorting by particle size and elaborates the chances and limitations with respect to different material properties of diamagnetic liquid and magnetic particles.
