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

Masao Iwamatsu
Phys. Rev. E 96, 012803 – Published 24 July 2017

Abstract

The spreading of a cap-shaped spherical droplet of non-Newtonian power-law liquids, both shear-thickening 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 that governs the evolution of the contact line. The time evolution of the dynamic contact angle θ of a droplet obeys a power law θtα with the spreading exponent α, 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.

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  • Received 24 May 2017
  • Corrected 6 October 2017

DOI:https://doi.org/10.1103/PhysRevE.96.012803

©2017 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Polymers & Soft Matter

Corrections

6 October 2017

Erratum

Authors & Affiliations

Masao Iwamatsu*

  • Department of Physics, Faculty of Liberal Arts and Sciences, Tokyo City University, Setagaya-ku, Tokyo 158-8557, Japan

  • *iwamatsu@ph.ns.tcu.ac.jp

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Issue

Vol. 96, Iss. 1 — July 2017

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