Spreading law on a completely wettable spherical substrate: The energy balance approach

Abstract

The spreading of a cap-shaped spherical droplet on a completely wettable spherical substrate is studied. The non-equilibrium thermodynamic formulation is used to derive the thermodynamic driving force of spreading including the line-tension effect. Then the energy balance approach is adopted to derive the evolution equation of the spreading droplet. The time evolution of the contact angle $\theta$ of a droplet obeys a power law $\theta \sim t^{-\alpha }$ with the exponent $\alpha$, which is different from that derived from Tanner's law on a flat substrate. Furthermore, the line tension must be positive to promote complete wetting on a spherical substrate, while it must be negative on a flat substrate.

7 pages, 2 figures, to be published in Physical Review E

References in corpus (3)

• Conceptual aspects of line tensions
• Line tension and morphology of a sessile droplet on a spherical substrate
• Size-dependent contact angle, and wetting and drying transition of a droplet adsorbed on to a spherical substrate: Line tension effect

Cited by in corpus (5)

• Investigations into the complete spreading dynamics of a viscoelastic drop on a spherical substrate
• Spreading law of non-Newtonian power-law liquids on a spherical substrate by energy balance approach
• 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
• A generalized Young's equation to bridge a gap between the experimentally measured and the theoretically calculated line tensions