Fig. 2.

Influence of the cell density $n$ and the magnetic field $B$ on the emergence of collective vortical motion. a–c $\times 40$ phase-contrast images of droplets superimposed with time average PIV velocity fields (green arrows). We show the influence of the cell density $n$ on the phenomenology, the magnetic field is fixed $B=$ 4 mT. (a) $n~10^{14}$ bact m${}^{-3}$, $R=$ 43 µm: Bacteria accumulate at the poles of the droplet. (b) $n~10^{15}$ bact m${}^{-3}$, $R=$ 89 µm: unstable recirculation flows appear at the poles of the droplet. (c) $n~10^{17}$ bact m${}^{-3}$, $R=$ 55 µm: the bacteria self-organize to form a stable vortex flow at the center of the droplet. d–f Colored maps of the orthoradial projection of the instantaneous PIV velocity fields $V_{\theta }^{\mathrm{d}}$ (red-blue colormap, enhancing positive and negative values) superimposed with the instantaneous PIV velocity field (green arrows). The radius of the droplet is constant $R=$ 83 µm. We show the influence of the magnetic field magnitude on the phenomenology, the cell density is fixed $n=10^{17}$ bact m${}^{-3}$. d $B=$ 0.2 mT: no large scale collective motion is observed. e $B=$ 2 mT: vortex flow centered at the droplet center. f $B=$ 4 mT: the vortex flow is stronger than at $B=$ 2 mT. e, f Recirculation flows (negative values of $V_{\theta }^{\mathrm{d}}$) close to the poles are identified in blue