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Universality in the nonlinear leveling of capillary films

Zhong Zheng, Marco A. Fontelos, Sangwoo Shin, and Howard A. Stone
Phys. Rev. Fluids 3, 032001(R) – Published 26 March 2018
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Abstract

Many material science, coating, and manufacturing problems involve liquid films where defects that span the film thickness must be removed. Here, we study the surface-tension-driven leveling dynamics of a thin viscous film following closure of an initial hole. The dynamics of the film shape is described by a nonlinear evolution equation, for which we obtain a self-similar solution. The analytical results are verified using time-dependent numerical and experimental results for the profile shapes and the minimum film thickness at the center. The universal behavior we identify can be useful for characterizing the time evolution of the leveling process and estimating material properties from experiments.

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  • Received 23 October 2017

DOI:https://doi.org/10.1103/PhysRevFluids.3.032001

©2018 American Physical Society

Physics Subject Headings (PhySH)

Fluid DynamicsNonlinear Dynamics

Authors & Affiliations

Zhong Zheng1,2,*, Marco A. Fontelos3, Sangwoo Shin1,4, and Howard A. Stone1,†

  • 1Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA
  • 2Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom
  • 3Instituto de Ciencias Matemáticas, C/Nicolás Cabrera, Madrid 28049, Spain
  • 4Department of Mechanical Engineering, University of Hawaii at Manoa, Honolulu, Hawaii 96822, USA

  • *zzheng@alumni.princeton.edu
  • hastone@princeton.edu

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Issue

Vol. 3, Iss. 3 — March 2018

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