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

Spreading law of non-Newtonian power-law liquids on a spherical substrate by energy balance approach