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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 (CUP)
Citation: ZHENG, Z. ... et al, 2017. Healing capillary films. Journal of Fluid Mechanics, In Press.
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 paper is closed access until 6 months after publication.
Version: Accepted for publication
URI: https://dspace.lboro.ac.uk/2134/27005
Publisher Link: https://www.cambridge.org/core/journals/journal-of-fluid-mechanics
ISSN: 0022-1120
Appears in Collections:Closed Access (Maths)

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