Sedimentation of a suspension of paramagnetic particles in an external magnetic field

We investigate the sedimentation of initially packed paramagnetic particles in the presence of a homogeneous external magnetic field, in a Hele-Shaw cell filled with water. Although the magnetic susceptibility of the particles is small and the particle-particle-induced magnetic interactions are significantly smaller compared to the gravitational acceleration, we do observe a measurable reduction of the decompaction rate as the amplitude of the applied magnetic field is increased. While induced magnetic dipole-dipole interactions between particles can be either attractive or repulsive depending on the particles relative alignment, our observations reveal an effective overall enhancement of the cohesion of the initial pack of particles due to the induced interactions, very likely promoting internal chain forces in the initial pack of particles. The influence of the magnetic field on the particles once they disperse after being decompacted is, however, found to remain marginal.

Figure 1

Temporal series of images showing sedimentation subjected to gravity and a horizontal magnetic field in a steady flow with $250\mu \mathrm{m}$ diameter paramagnetic particles in a closed Hele-Shaw cell. The cell is 200 mm high, 50 mm wide, and 1 mm depth. The cell is illuminated with a backlight, such that particles appear as dark spots on the original images.

Figure 2

(a) Front and (b) side views of the Hele-Shaw cell and (c) automated experimental setup with magnetic coils (1), Hele-Shaw cell (2), backlight LED panel (3), high-speed camera (4), stepper motor (5), shaker (6), and Raspberry-Pi controller (7).

Figure 3

Successive steps of image processing to determine the solid phase [upper green area in (d)] and liquid phase [middle yellow area in (d)] of particles starting from the raw image (a).

Figure 4

(a) Averaged time evolution of the solid area without any applied magnetic field (solid black line) and with an applied field with amplitude $B_0=800$ G (dashed red line, corresponding to a magnetogravitational number $\mathrm{\Psi }\simeq 0.26$). To illustrate the averaging procedure, the light gray lines represent the individual time evolution of the solid area for 50 independent realizations for the case without any applied magnetic filed. The solid black line correspond to the average of the light gray lines. The bars at 0.5 s, 1 s, and 3 s indicate the standard deviation among the 50 realizations at each of these instants. (b) Time evolution of the liquefaction velocity for $B_0=$ 0 G (solid black line); $B_0=$ 800 G (dashed red line).

Figure 5

(a) Terminal liquefaction rate of the solid phase and (b) terminal growth rate of the liquid phase as a function of the magnetogravitational number $\mathrm{\Psi }$. (c) Relative liquefaction for the solid phase and (d) growth rate for the liquid phase, as a function $\mathrm{\Psi }$. Solid and dashed lines correspond to the power-law fit Eq. (10).

Figure 6

Evolution with time of the solid to liquid rate ratio. In the terminal steady state, the solid-to-liquid rate ratio reaches an asymptotic value of the order of 0.25, independent of the magnetic field amplitude, indicating that the liquid phase is about four times more dilute than the solid phase.