JFM-17-S-0002_Revised_Manuscript_dt-sk-zz.pdf (2.57 MB)
Healing capillary films
journal contributionposted on 2017-10-19, 14:55 authored by Zhong Zheng, Marco Fontelos, S. Shin, Michael C. Dallaston, Dmitri TseluikoDmitri Tseluiko, Serafim Kalliadasis, Howard Stone
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.
- Mathematical Sciences
Published inJournal of Fluid Mechanics
CitationZHENG, Z. ... et al, 2017. Healing capillary films. Journal of Fluid Mechanics, 838, pp. 404-434.
Publisher© Cambridge University Press
- AM (Accepted Manuscript)
NotesThis 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.