Tracking the rotation of light magnetic particles in turbulence

TL;DR

The study tackles the challenging problem of measuring rotational dynamics of light magnetic particles in turbulent flows. It introduces a single-camera, 2D-imaging-based 3D rotation-tracking method to resolve all three components of particle angular velocity for particles with $\eta < D_p < \lambda$, co-located with a rotating planar magnetic field. The experimental platform combines a Von Kármán turbulence generator with Helmholtz coils to provide simultaneous turbulent and magnetic forcing, and uses surface-patterned polystyrene particles with anisotropic magnetic susceptibility to enable magnetic torque-driven rotation. Experiments and complementary simulations reveal two regimes—magnetically driven and turbulence-dominated rotation—with a transition around $f_m \approx 20$–$25$ Hz, highlighting the role of magnetic anisotropy in governing rotational dynamics. The method provides a powerful tool for probing rotational intermittency and offers pathways to modulate turbulence from within, as well as to integrate Lagrangian translation tracking for a complete view of particle–turbulence interactions.

Abstract

Particle-laden turbulence involves complex interactions between the dispersed and continuous phases. Given that particles can exhibit a wide range of properties, such as varying density, size, and shape, their interplay with the flow can lead to various modifications of the turbulence. Therefore, understanding the dynamics of particles is a necessary first step toward revealing the behavior of the multiphase system. Within the context of particle dynamics, accurately resolving rotational motion presents a significantly greater challenge compared to translational motion. We propose an experimental method to track the rotational motion of spherical, light, and magnetic particles with sizes significantly smaller than the Taylor microscale, typically an order of magnitude larger than the Kolmogorov scale of the turbulence in which they are suspended. The method fully resolves all three components of the particle angular velocity using only 2D images acquired from a single camera. This technique enables a detailed investigation of the rotational dynamics of magnetic particles subjected simultaneously to small-scale turbulent structures and external magnetic forcing. Beyond advancing the study of particle dynamics in turbulence, this approach opens new possibilities for actively modulating turbulence through externally applied magnetic fields.

Figures (12)

• Figure 1: (a) The turbulence generator, commonly referred to as the French washing machine, is shown with the primary and secondary flow directions indicated by blue and yellow arrows, respectively. The radius of each of the two identical impellers is represented by $R_\text{d}$, and they are separated by a distance of $H_\text{d} = 2R_\text{d}$. The impellers rotate in opposite directions at a frequency $\Omega$. (b) Two pairs of Helmholtz coils are mounted perpendicularly, with their axes aligned along the x and y axes, respectively. The amplitudes of the alternating currents in the two coil pairs, $I_\text{X}$ and $I_\text{Y}$, are slightly adjusted to ensure that the magnetic flux densities $\bm{B_x}$ and $\bm{B_y}$ have equal magnitudes at the origin $\bm{O}$, compensating for the difference in coil radii. A 90° phase difference between $I_\text{X}$ and $I_\text{Y}$ results in a rotating planar magnetic field in the xy plane.
• Figure 2: (a) Schematic drawing of the experimental setup. The radius of each impeller is $R_\text{d} = 75$ mm, and the axial separation between the two impellers is $H_\text{d} = 150$ mm. Two torque meters are used to measure the energy input from the motors to the water to calculate the turbulence dissipation rate. The vertical coils, aligned along the x axis, have a radius of 150 mm and consist of 34 wire turns. The horizontal coils, aligned along the y axis, have a radius of 125 mm with 28 turns. Together, the two coil pairs generate a planar rotating magnetic field with a magnitude of 1.6 mT. (b) Photograph of the experimental setup. The water tank is filled from the bottom through an inlet pipe and drained from the top through an outlet pipe.
• Figure 3: (a) Schematic illustration of the fabrication process for magnetic particles. Polystyrene particles are secured on a flat plastic board using adhesive tape. Magnetic paint is manually sprayed from the top left and top right at a $45^\circ$ angle, coating the particles with a thin layer of magnetic material that can be magnetized in the presence of a magnetic field but exhibits no residual magnetism in free space. (b) Optical microscopic image for the comparison of polystyrene particles before (on the left with brighter surface) and after (on the right with darker surface) coating. The magnetic layer increases mass and rigidity of the particle, and introduces a non-uniform surface pattern, which is essential for rotation tracking.
• Figure 4: Top view of the one-camera layout for 3D rotation tracking. The optical axis of the camera is aligned with the direction of the angular velocity $\bm{\omega_B}$ of the rotating magnetic field, as indicated by the black dashed line. This alignment ensures that the magnetic field influences only the particle angular velocity along this direction, while turbulence, if present, affects all three components. The orange dashed square marks the measurement volume, which has a side length of 12 mm. Two blue LEDs illuminate the measurement volume symmetrically from both sides, each positioned at an angle of $45\degree$ relative to $\bm{\omega_B}$.
• Figure 5: (a) An original image showing particles with radii within the acceptable range, marked by red and green circles. The autofocusing algorithm identifies well-focused particles, which are highlighted in green. (b) An example of a well-focused rotating particle. This particle appears as an 80-pixel-diameter object in the images and rotates counterclockwise within the image plane. The sequence of single-particle frames progresses from left to right, top to bottom, with the yellow arrow in each frame indicating the particle orientation.