Janus particles propel themselves by generating concentration gradients along their active surface. This induces a flow near the surface, known as the diffusio-osmotic slip, which propels the particle even in the absence of externally applied concentration gradients. In this work, we study the influence of viscoelasticity and shear-thinning (described by the second-order fluid and Carreau model, respectively) on the diffusio-osmotic slip on an active surface. Using matched asymptotic expansions, we provide an analytical expression for the modification of slip induced by the non-Newtonian behaviour. The results reveal that the modification in slip velocity, arising from polymer elasticity, is proportional to the second tangential derivative of the concentration field. Using the reciprocal theorem, we estimate the influence of this modification on the swimming velocity of a Janus sphere: (i)for second-order fluid, the contribution is non-negligible and its sign is dependent on the surface coverage of activity and (ii) for Carreau fluid, the contribution is more pronounced and always enhances the swimming velocity. The current study also has implications on the understanding of the transport of complex fluids in diffusio-osmotic pumps.
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