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

Abstract

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.

7 pages, 3 figures, Physical Review E to be published. arXiv admin note: text overlap with arXiv:1704.08399

References in corpus (4)

• Conceptual aspects of line tensions
• Precursor films in wetting phenomena
• Size-dependent contact angle, and wetting and drying transition of a droplet adsorbed on to a spherical substrate: Line tension effect
• Line-tension effects on heterogeneous nucleation on a spherical substrate and in a spherical cavity

Cited by in corpus (4)

• Investigations into the complete spreading dynamics of a viscoelastic drop on a spherical substrate
• Spreading of a viscoelastic drop on a solid substrate
• Four stages of droplet spreading on a spherical substrate and in a spherical cavity -Surface tension vs line tension and viscous dissipation vs frictional dissipation-
• Topography- and topology-driven spreading of non-Newtonian power-law liquids on a flat and a spherical substrate