  In this work, we analyze the motion of an active particle, modeled as a
spherical squirmer, in linearly varying viscosity fields. In general, the
presence of a particle will disturb a background viscosity field and the
disturbance generated depends on the boundary conditions imposed by the
particle on the viscosity field. We find that, irrespective of the details of
the disturbance, active squirmer-type particle tend to align down viscosity
gradients (negative viscotaxis). However, the rate of rotation and the swimming
speed along the gradient do depend on the details of the interaction of the
particle and the background viscosity field. In addition, we explore the
relative importance on the dynamics of the local viscosity changes on the
surface of active particles versus the (nonlocal) changes in the flow field due
to spatially varying viscosity (from that of a homogeneous fluid). We show that
the relative importance of local versus nonlocal effects depends crucially on
the boundary conditions imposed by the particle on the field. This work
demonstrates the dangers in neglecting the disturbance of the background
viscosity caused by the particle as well as in using the local effects alone to
capture the particle motion.
