Fig. 2: Generation and locomotion of the swarms in ionic and viscous fluids.

a Schematics and an experimental image of the medium-induced swarms. The actuation fields are indicated by the blue planes. b Schematics and an experimental image of the MF-induced swarms. Oscillating magnetic fields are used to trigger the swarm behaviour, and the fields are shown by the blue planes. When the direction of the oscillating field changes, the angle between the centre line and y-axis is labelled using \(\theta\). The red dashed ellipses indicate the central areas of the swarms. c, d The percentages of the central areas of the swarms in fluid with different ionic strengths and viscosities, respectively. The ionic strengths of the fluids are normalised using PBS solution, and the ionic strength in PBS solution is 1.0\(\times\). e, f The translational velocities of the medium-induced and MF-induced swarms in fluids with different viscosities, respectively. g The experimental results of the medium-induced swarms generated in fluids with and without mesh-like structures. The viscosities of the fluids are kept the same, i.e. 60 and 200 cp, respectively. The shear rate is 5 s\({}^{-1}\). h The comparisons between the central percentages of the medium-induced swarms generated in fluids with and without mesh-like structures. The scale bars indicate 500 μm.