Healing capillary films

Zhong Zheng, Marco A. Fontelos, Sangwoo Shin, Michael C. Dallaston, Dmitri Tseluiko, Serafim Kalliadasis, Howard A. Stone

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


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, obtained by matching the estimated prewetting film thickness, with both measurements in experiments and time-dependent computations near the healing time, and we observe good agreement in each case.

Original languageEnglish (US)
Pages (from-to)404-434
Number of pages31
JournalJournal of Fluid Mechanics
StatePublished - Mar 10 2018

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


  • Capillary flows
  • contact lines
  • thin films


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