  Magnetic nanogels (MNG) -- soft colloids made of polymer matrix with embedded
in it magnetic nanoparticles (MNPs) -- are promising magneto-controllable drug
carriers. In order to develop this potential, one needs to clearly understand
the relationship between nanogel magnetic properties and its behaviour in a
hydrodynamic flow. Considering the size of the MNG and typical time and
velocity scales involved in their nanofluidics, experimental characterisation
of the system is challenging. In this work, we perform molecular dynamics (MD)
simulations combined with the Lattice-Boltzmann (LB) scheme aiming at
describing the impact of the shear rate on the shape, magnetic structure and
motion of an MNG. We find that in a shear flow the centre of mass of an MNG
tends to be in the centre of a channel and to move preserving the distance to
both walls. The MNG monomers along with translation are involved in two more
types of motion, they rotate around the centre of mass and oscillate with
respect to the latter. It results in synchronised tumbling and wobbling of the
whole MNG accompanied by its volume oscillates. The fact the MNG is a highly
compressible and permeable for the carrier liquid object makes its behaviour
different from that predicted by classical Taylor-type models. We show that the
frequency of volume oscillations and rotations are identical and are growing
function of the shear rate. We find that the stronger magnetic interactions in
the MNG are, the higher is the frequency of this complex oscillatory motion,
and the lower is its amplitude. Finally, we show that the oscillations of the
volume lead to the periodic changes in MNG magnetic energy.
