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Healing capillary films

  • Zhong Zheng (a1) (a2), Marco A. Fontelos (a3), Sangwoo Shin (a1) (a4), Michael C. Dallaston (a5), Dmitri Tseluiko (a6), Serafim Kalliadasis (a5) and Howard A. Stone (a1)...
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, 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.

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Corresponding author
Email addresses for correspondence: zzheng@alumni.princeton.edu, marco.fontelos@icmat.es, hastone@princeton.edu
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Z. Zheng and M. A. Fontelos contributed equally to this work.

§

Present address: School of Computing, Electronics and Mathematics, and Flow Measurement and Fluid Mechanics Research Centre, Coventry University, Coventry CV1 5FB, UK.

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