  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: 1) pure swimming, and 2)
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. Two new
analytical relations are presented: 1) for predicting the swimming speed of an
unconfined particle as a function of its angular speed and geometrical
properties, and 2) 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.
