  The spreading of a cap-shaped spherical droplet of non-Newtonian power-law
liquids, both shear-thinning and shear-thinning liquids, that completely wet a
spherical substrate is theoretically investigated in the capillary-controlled
spreading regime. The crater-shaped droplet model with the wedge-shaped
meniscus near the three-phase contact line is used to calculate the viscous
dissipation near the contact line. Then the energy balance approach is adopted
to derive the equation which governs the evolution of the contact line. The
time evolution of the dynamic contact angle $\theta$ of a droplet obeys a power
law $\theta \sim t^{-\alpha}$ with the spreading exponent $\alpha$, which is
different from Tanner's law for Newtonian liquids and those for non-Newtonian
liquids on a flat substrate. Furthermore, the line-tension dominated spreading,
which could be realized on a spherical substrate for late-stage of spreading
when the contact angle becomes low and the curvature of the contact line
becomes large, is also investigated.

Soft Condensed Matter