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The spreading of a cap-shaped spherical droplet of non-Newtonian power-law liquids on a flat and a spherical rough and textured substrate is theoretically studied in the capillary-controlled spreading regime. A droplet whose scale is much larger than that of the roughness of substrate is considered. The equilibrium contact angle on a rough substrate is modeled by the Wenzel and the Cassie-Baxter model. Only the viscous energy dissipation within the droplet volume is considered, and that within the texture of substrate by imbibition is neglected. Then, the energy balance approach is adopted to derive the evolution equation of the contact angle. When the equilibrium contact angle vanishes, the relaxation of dynamic contact angle θ of a droplet obeys a power law decay θ ∼ t −α except for the Newtonian and the non-Newtonian shear-thinning liquid of the Wenzel model on a spherical substrate. The spreading exponent α of the non-Newtonian shear-thickening liquid of the Wenzel model on a spherical substrate is larger than others. The relaxation of the Newtonian liquid of the Wenzel model on a spherical substrate is even faster showing the exponential relaxation. The relaxation of the non-Newtonian shear-thinning liquid of Wenzel model on a spherical substrate is fastest and finishes within a finite time. Thus, the topography (roughness) and the topology (flat to spherical) of substrate accelerate the spreading of droplet.

This study discusses the spreading of a non-Newtonian, power-law, film formed after a drop impinges on a flat surface (i.e., a pharmaceutical tablet). Non-Newtonian drop spreading is described by a model based on the one of Roisman et al. [2002]. The effects of variations in non-Newtonian liquid rheological parameters m (the consistency index) and n (the fluid behavior index) are shown to be significant. In either case, changes leading to a reduction in viscous forces result in enhanced spreading of the film, followed by more rapid recession. Both are expected. Of interest is the observation that an increase in consistency index can be compensated for by a reduction in flow behavior index since the sensitivity of film recession to a change in n is larger than that to variations in m.