Flow produced by a free-moving floating magnet driven electromagnetically

The flow generated by a free-moving magnet floating in a thin electrolyte layer is studied experimentally and numerically. The magnet is dragged by a traveling vortex dipole produced by a Lorentz force created when a uniform dc current injected in the electrolyte interacts with the magnetic field of the same magnet. The problem represents a typical case of fluid-solid interaction but with a localized electromagnetic force promoting the motion. Classical wake flow structures are observed when the applied current varies in the range of 0.2 to 10 A. Velocity fields at the surface of the electrolyte are obtained for different flow conditions through particle image velocimetry. Quasi-two-dimensional numerical simulations, based on the immersed boundary technique that incorporates the fluid-solid interaction, reproduce satisfactorily the dynamics observed in the experiments.

Figure 1

Sketch of the experimental device, not drawn to scale. Upper panel: plan view. Lower panel: lateral view. The magnetic field ${\mathbf{B}}^0$ is generated by a permanent magnet floating on the surface of the fluid layer. The electrical current ${\mathbf{j}}^0$ is injected through two cooper electrodes. The main direction of the Lorentz force is denoted by ${\mathbf{F}}^0$.

Figure 2

Experimental visualization of the flow patterns observed for different applied currents. (a) $I=400$ mA. (b) $I=2$ A. (c) and (d) $I=10$ A. (c) and (d) correspond to the close and far wake regions, respectively. The black disk in (a), (b), and (c) indicates the size of the magnet. The solid line in (d) indicates the diameter of the magnet.

Figure 3

Velocity fields for three different applied currents. (a) $I=400$ mA. (b) $I=2$ A. (c) $I=10$ A. For the velocity scale see Fig. 5. Experimental measurements.

Figure 4

Position of the moving magnet as a function of time. Upper panel: Horizontal position. Lower panel: Vertical position. $I=10$ A. Experimental measurements.

Figure 5

Time dependence of the axial, $u$, and transversal, $v$, velocity components of the moving magnet. $I=10$ A. Experimental measurements.

Figure 6

Flow structure for different applied currents. (a) $I=400$ mA. (b) $I=2$ A. (c) $I=10$ A. Numerical particle tracking visualization.

Figure 7

Position of the moving magnet as a function of time. Upper panel: horizontal position. Lower panel: vertical position. $I=10$ A. Numerical calculations.

Figure 8

Time dependence of the horizontal $u$ (continuous line) and vertical $v$ (dashed line) velocity components of the moving magnet. $I=10$ A. Numerical calculations.

Figure 9

Frequency (blue curve) and dimensionless amplitude (black curve) of the oscillation of the magnet as function of the Reynolds number, based on the magnet's average velocity $u_{\mathrm{av}}$. Numerical calculations.

Figure 10

Map of physical behavior in terms of the Reynolds number and the applied current. The continuous black line and dashed blue line denote the experimental and numerical observations, respectively.

Figure 11

Vorticity distribution in the wake of an electromagnetically driven free moving obstacle (upper panel) and a fixed solid obstacle (lower panel). $\text{Re}=104$. Numerical calculations.