Fig. 5.

Vortex emergence and rotation reversal by magnetic field inversion. a Magnetic field amplitude $B$ as a function of time. b Response in the rotational velocity of the droplet core ${\mathrm{\Omega }}^{\mathrm{d}}$ under the applied magnetic field. The error bars are the standard errors. c, d, e The stages corresponding to the particular self-assemblies representations on the sketches on the right of the figure. The coral region corresponds to the central core rotation while the blue zones represent the recirculating bacteria. The bacterial suspension is dense ($n~10^{17}$ bact m${}^{-3}$). For each time step $t$, ${\mathrm{\Omega }}^{\mathrm{d}}\left(t\right)$ is computed from instantaneous PIV maps as in Fig. 3a. From the moment when the magnetic field is set on, ${\mathrm{\Omega }}^{\mathrm{d}}$ reaches a stationary value within a few seconds ($~$4 s). When reversing quickly the magnetic field direction while the suspension rotates CW, the suspension continues rotating CW at the short times after reversal before reversing completely its rotational direction to CCW. Then, ${\mathrm{\Omega }}^{\mathrm{d}}$ reaches a stable negative value $~$10 s after the magnetic field switch