  In this note, we study the effect of viscosity gradients on the energy
dissipated by the motion of microswimmers and the associated efficiency of that
motion. Using spheroidal squirmer model swimmers in weak linearly varying
viscosity fields, we find that efficiency depends on whether they generate
propulsion from the back (pushers) or the front (pullers). Pushers are faster
and more efficient when moving down gradients but slower and less efficient
moving up viscosity gradients, and the opposite is true for pullers. However,
both pushers and pullers display negative viscotaxis, therefore pushers
dynamically tend to the most efficient orientation while pullers the least. We
also evaluate the effect of shape on power expenditure and efficiency when
swimming in viscosity gradients and find that in general the change in both due
to gradients monotonically decreases with increasing slenderness. This work
shows how shape and gait play an important role in determining dynamics and
efficiency in inhomogeneous environments, and demonstrating that both
efficiency minimizing and maximizing stable dynamical states are possible.
