Non-Stokesian dynamics of magnetic helical nanoswimmers under confinement

Electromagnetically propelled helical nanoswimmers offer great potential for nanorobotic applications. Here, the effect of confinement on their propulsion is characterized using lattice-Boltzmann simulations. Two principal mechanisms give rise to their forward motion under confinement: (i) pure swimming and (ii) the thrust created by the differential pressure due to confinement. Under strong confinement, they face greater rotational drag but display a faster propulsion for fixed driving frequency in agreement with experimental findings. This is due to the increased differential pressure created by the boundary walls when they are sufficiently close to each other and the particle. We have proposed two analytical relations (i) for predicting the swimming speed of an unconfined particle as a function of its angular speed and geometrical properties, and (ii) an empirical expression to accurately predict the propulsion speed of a confined swimmer as a function of the degree of confinement and its unconfined swimming speed. At low driving frequencies and degrees of confinement, the systems retain the expected linear behavior consistent with the predictions of the Stokes equation. However, as the driving frequency and/or the degree of confinement increase, their impact on propulsion leads to increasing deviations from the Stokesian regime and emergence of nonlinear behavior.