Lubricated wrinkles: imposed constraints affect the dynamics of wrinkle coarsening

TL;DR

This paper investigates how imposed constraints influence the coarsening dynamics of wrinkles in an elastic sheet on a viscous liquid, revealing a logarithmic correction to the previously predicted scaling law.

Contribution

The study introduces a refined model accounting for compression constraints, showing a logarithmic correction to the wrinkle wavelength growth law during coarsening.

Findings

Logarithmic correction to the wrinkle wavelength scaling law.

Reassessment of previous experimental data.

Significant impact of constraints on wrinkle dynamics.

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.