Effect of the thermal noise on torque-driven steering of magnetic nanohelices

Torque-driven actuation of nanohelices by a rotating magnetic field is one of the most promising techniques of controlled propulsion at the microscale and it has been the focus of modern biomedical applications. In these applications, the required size of the propeller ranges between tens to hundreds of nanometers. At this scale, the nanobots are subjected to strong thermal fluctuations that become comparable to the driving torque. We theoretically investigate the effect of the thermal noise on torque-driven rotation and propulsion of the nanomotors in a viscous fluid using Langevin and Fokker-Planck formulations. We show that the noise hinders the nanobot's propulsion by (i) reducing its forced rotation and by (ii) increasing the precession (wobbling) angle between the nanohelix long axis and the axis of the field rotation. We further demonstrate that already for fairly low thermal noise (Péclet number, Pe ≈ 0.1), the velocity of the forced rotation drops 2-3 times, and the precession angle increases 2-3 times as compared to the zero-Pe limit. Both these effects result in an approximately 2.5-fold reduction of the propulsion velocity. Furthermore, when the noise is comparable to driving (Pe ≈ 1), we find an order-of-magnitude reduction in the propulsion velocity.