Magnetic steering of chiral nanobots subject to thermal noise

Torque-driven steering of magnetic micro/nanobots in fluids is one of the most promising platforms of controlled propulsion at the small scales, and it has been the focus of modern biomedical applications. The propulsion is a result of rotation–translation coupling and it requires non-trivial (e.g. chiral) geometry of the nanobot and the weak (millitesla) rotating magnetic field. At submicron scale, nanobots are subjected to intrinsic thermal fluctuations that may become comparable to the magnetic driving. We investigate the effect of Brownian fluctuations on the actuation and steering of magnetized nanohelices in a viscous fluid numerically, using Langevin simulations. First, we assume force-free propulsion and study the effect of thermal fluctuations on driven rotation and steering of the nanohelix. We demonstrate that the random Brownian torque dramatically impedes the nanobot’s propulsion via (i) hindering the rate of the forced rotation; (ii) altering its orientation, i.e. increasing the precession angle of the forced rotations. We further demonstrate that even for fairly low thermal noise (rotational Péclet number, $ \textit{Pe} \approx 10$ ), the angular velocity of the forced rotation drops by $2$ – $3$ times, while the precession angle increases two fold as compared with the non-Brownian limit. Both these factors contribute to an approximately $2.5$ -fold reduction of the propulsion velocity. Furthermore, when the magnitude of thermal fluctuations is comparable to magnetic driving ( $ \textit{Pe} \approx 1$ ), we find an order-of-magnitude reduction of the propulsion speed. Although inclusion of a stochastic thermal force does not alter the propulsion velocity on average, it considerably increases its variance and further impedes the propeller’s steerability.