  Shear-thinning viscosity is a non-Newtonian behaviour that active particles
often encounter in biological fluids such as blood and mucus. The fundamental
question of how this ubiquitous non-Newtonian rheology affects the propulsion
of active particles has attracted substantial interest. In particular,
spherical Janus particles driven by self-diffusiophresis, a major
physico-chemical propulsion mechanism of synthetic active particles, were shown
to always swim slower in a shear-thinning fluid than in a Newtonian fluid. In
this work, we move beyond the spherical limit to examine the effect of particle
eccentricity on self-diffusiophoretic propulsion in a shear-thinning fluid. We
use a combination of asymptotic analysis and numerical simulations to show that
shear-thinning rheology can enhance self-diffusiophoretic propulsion of a
spheroidal particle, in stark contrast to previous findings for the spherical
case. A systematic characterization of the dependence of the propulsion speed
on the particle's active surface coverage has also uncovered an intriguing
feature associated with the propulsion speeds of a pair of complementarily
coated particles not previously reported. Symmetry arguments are presented to
elucidate how this new feature emerges as a combined effect of anisotropy of
the spheroidal geometry and nonlinearity in fluid rheology.
