  Recent findings of possible applications of bio-friendly synthetic
self-phoretic swimmers, have motivated the researchers in investigating the
various motion-generating mechanisms to optimize the operating characteristics
of the same. In this paper we model the auto-electrophoretic motion of a
bimetallic (Au-Pt) spherical swimmer in a non-Newtonian medium. In view of the
fact that many bio-fluids closely follow the generalized Newtonian rheology,
the rheology of the surrounding swimming medium is considered to follow the
Carreau-Yasuda viscosity model. Further to capture the experimentally observed
effects of peroxide concentration and feedback of generated proton
concentration on the surface cation flux, we incorporate a Michaelis-Menten
like surface reaction kinetics. The electrocatalytic efficiency defined as a
ratio between the cost of swimming of an equivalent passively dragged particle
and the input chemical energy via surface reaction, is utilized to assess the
influence of the rheological parameters on the swimmer performance. The results
indicate that the shear thinning and shear thickening nature of the surrounding
fluid causes an enhancement and reduction in swimmer velocity, respectively.
However, an increase in the shear thinning effect does not always guarantee an
efficient operation of the microswimmer. A competition between the particle
velocity and reduction in the drag force on the particle, decides whether the
propulsion efficiency will have a relative augmentation or attenuation with
varying power law index. We further report the existence of maximum efficiency
points for some specific range of Weissenberg number and optimum power law
indices. Moreover the behaviour of such optimum operating conditions strongly
depends on the non-trivial and highly coupled interplay among the rheology and
electrocatalytic parameters.
