TY - JOUR
T1 - Healing capillary films
AU - Zheng, Zhong
AU - Fontelos, Marco A.
AU - Shin, Sangwoo
AU - Dallaston, Michael C.
AU - Tseluiko, Dmitri
AU - Kalliadasis, Serafim
AU - Stone, Howard A.
N1 - Funding Information:
We acknowledge financial support by the Engineering and Physical Sciences Research Council of the UK through grants no. EP/L020564/1, EP/K008595/1 and EP/K041134/1.
Publisher Copyright:
© 2018 Cambridge University Press.
PY - 2018/3/10
Y1 - 2018/3/10
N2 - 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.
AB - 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.
KW - Capillary flows
KW - contact lines
KW - thin films
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U2 - 10.1017/jfm.2017.777
DO - 10.1017/jfm.2017.777
M3 - Article
AN - SCOPUS:85040797421
VL - 838
SP - 404
EP - 434
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
SN - 0022-1120
ER -