Lubricated wrinkles: imposed constraints affect the dynamics of wrinkle coarsening

Abstract

We study the dynamic coarsening of wrinkles in an elastic sheet that is compressed while lying on a thin layer of viscous liquid. When the ends of the sheet are instantaneously brought together by a small distance, viscous resistance initially prevents the sheet from adopting a globally buckled shape. Instead, the sheet accommodates the compression by wrinkling. Previous scaling arguments suggested that a balance between the sheet's bending stiffness and viscous effects lead to a wrinkle wavelength $\lambda$ that increases with time $t$ according to $\lambda \propto t^{1/6}$. We show that taking proper account of the compression constraint leads to a logarithmic correction of this result, $\lambda \propto (t/\log t{)}^{1/6}$. This correction is significant over experimentally observable time spans, and leads us to reassess previously published experimental data.

arXiv comment12 pages. Version accepted in Phys. Rev. Fluids (with small correction to bibliography)

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