Fig. 3: Effect of static magnetic field on propulsion.

Velocity vs. static magnetic field for 10 μm diameter microparticles for: a static field swept at 1 mT increments between the range of −5 to 5 mT, with the microparticles rotated at 15 Hz. Four microparticles were examined and each had at least three trials in each fluid. b Static magnetic field swept at 0.2 and 1 mT increments for the same microparticle in 4% mucin. c, d Static magnetic field swept at 0.2 mT increments for 4 different particles for 4% mucin and 0.25% polyacrylamide, respectively. e, f Propulsion hysteresis in response to static magnetic field sweep at 0.2 mT increments for a single microparticle in 4% mucin and 0.25% polyacrylamide, respectively. The frequency for (f) was 40 Hz with the rotating magnetic field amplitude set to \(\left| {B_{\mathrm{r}}} \right| = 0.1750f\), where f is the frequency in Hz. In all scenarios, velocities of microparticles remained relatively constant at larger positive and negative fields, but the field at which velocity switched direction depended on static magnetic field history, increment size, and specific particle characteristics. Dashed lines in graphs represent zero propulsion velocity while lines between points in (a–f) were added to act as a guide to the eyes. Statistics: (a) Four particles were examined in 4% mucin and six particles in 0.25% polyacrylamide; each microparticle had at least three independent trials. (b) Five trials were conducted at 1 mT and four trials at 0.2 mT. (c) Six, four, five, and four trials were conducted for particles 1–4, respectively. (d) Four trials were conducted for each particle examined. (e) Ten independent trials were conducted for a single microparticle. (f) Four independent trials were conducted for a single particle. Data are presented as mean±standard error. Source data are provided as a source data file.