Lubricated wrinkles

We investigate the problem of an elastic beam above a thin viscous layer. The beam is subject to a fixed end-to-end displacement, which will ultimately cause it to adopt the Euler-buckled state. However, additional liquid must be drawn in to allow this buckling. In the interim, the beam forms a wrinkled state with wrinkles coarsening over time. This problem has been studied experimentally by Vandeparre \textit{et al.~Soft Matter} (2010), who provided a scaling argument suggesting that the wavelength, $\lambda$, of the wrinkles grows according to $\lambda\sim t^{1/6}$. However, a more detailed theoretical analysis shows that, in fact, $\lambda\sim(t/\log t)^{1/6}$. We present numerical results to confirm this and show that this result provides a better account of previous experiments.