Lubricated wrinkles: imposed constraints affect the dynamics of wrinkle coarsening

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 $\lambda \propto t^{1\mathrm{/}6}$. We show that taking proper account of the compression constraint leads to a logarithmic correction of this result, $\lambda \propto (t\mathrm{/}\log t{)}^{1\mathrm{/}6}$. This correction is significant over experimentally observable time spans, and leads us to reassess previously published experimental data.