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Title: Healing capillary films
Authors: Zheng, Zhong
Fontelos, Marco
Shin, S.
Dallaston, Michael C.
Tseluiko, Dmitri
Kalliadasis, Serafim
Stone, Howard
Keywords: Thin film
Surface tension
Similarity solution
Issue Date: 2017
Publisher: © Cambridge University Press
Citation: ZHENG, Z. ... et al, 2017. Healing capillary films. Journal of Fluid Mechanics, 838, pp. 404-434.
Abstract: Consider the dynamics of a healing film driven by surface tension, that is, the inward spreading process of a liquid film to fill a hole. The film is modelled using the lubrication (or thin-film) approximation, which results in a fourth-order nonlinear partial differential equation. We obtain a self-similar solution describing the early-time relaxation of an initial step-function condition and a family of self-similar solutions governing the finite-time healing. The similarity exponent of this family of solutions is not determined purely from scaling arguments; instead, the scaling exponent is a function of the finite thickness of the prewetting film, which we determine numerically. Thus, the solutions that govern the finite-time healing are self-similar solutions of the second kind. Laboratory experiments and time-dependent computations of the partial differential equation are also performed. We compare the self-similar profiles and exponents with both measurements in experiments and time-dependent computations near the healing time, and we observe good agreement in each case.
Description: This article has been published in a revised form in Journal of Fluid Mechanics at https://doi.org/10.1017/jfm.2017.777. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © Cambridge University Press.
Version: Accepted for publication
DOI: 10.1017/jfm.2017.777
URI: https://dspace.lboro.ac.uk/2134/27005
Publisher Link: https://doi.org/10.1017/jfm.2017.777
ISSN: 0022-1120
Appears in Collections:Published Articles (Maths)

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